http://www.edegan.com/mediawiki/index.php?title=BPP_Field_Exam_2006_Answers&feed=atom&action=historyBPP Field Exam 2006 Answers - Revision history2024-03-29T02:02:48ZRevision history for this page on the wikiMediaWiki 1.34.2http://www.edegan.com/mediawiki/index.php?title=BPP_Field_Exam_2006_Answers&diff=30024&oldid=previmported>Ed at 21:17, 8 March 20112011-03-08T21:17:29Z<p></p>
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</td></tr></table>imported>Edhttp://www.edegan.com/mediawiki/index.php?title=BPP_Field_Exam_2006_Answers&diff=28114&oldid=previmported>Ed at 21:17, 8 March 20112011-03-08T21:17:29Z<p></p>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*This page is included under the section [[BPP Field Exam]]</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">*This page is provides answers to the [[BPP Field Exam 2006]]</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Answer A.1: The Theory of Partnerships'''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''Answer A.1: The Theory of Partnerships'''</div></td></tr>
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</table>imported>Edhttp://www.edegan.com/mediawiki/index.php?title=BPP_Field_Exam_2006_Answers&diff=30022&oldid=previmported>Tarek at 02:54, 22 February 20112011-02-22T02:54:26Z<p></p>
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</td></tr></table>imported>Tarekhttp://www.edegan.com/mediawiki/index.php?title=BPP_Field_Exam_2006_Answers&diff=28113&oldid=previmported>Tarek at 02:54, 22 February 20112011-02-22T02:54:26Z<p></p>
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</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l8" >Line 8:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''a.) Outline a model of the above situation. Assuming the game is a single-shot and there are no punishments by the partnership (no reputation effects), discuss the equilibrium for your model. Note: you do not have to solve the model; simply discuss the proposition(s) you expect that could be derived and the intuition(s) behind it (them).'''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''a.) Outline a model of the above situation. Assuming the game is a single-shot and there are no punishments by the partnership (no reputation effects), discuss the equilibrium for your model. Note: you do not have to solve the model; simply discuss the proposition(s) you expect that could be derived and the intuition(s) behind it (them).'''</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Assuming the game is single-shot (a finite number of sessions will be held to consider distribution proposals for the surplus), we make the additional assumption that if no allocation is agreed in the final period, then the surplus is not distributed and all partners end up with 0. If so, we have a simple application of Baron & Ferejohn (1989) - [http://www.edegan.com/wiki/index.php/Baron_Ferejohn_%281989%29_-_Bargaining_In_Legislatures#Closed_Rule_-_Two_Sessions Close Rule, Finite Session (e.g. <del class="diffchange diffchange-inline">n=</del>2)]. Backwards induction thus yields a SPNE in which each member, if recognized, makes the same majoritarian proposal to distribute the benefits to a minimal winning majority (characterized in Proposition 1). For simplicity, normalize the total surplus to 1, and consider <del class="diffchange diffchange-inline">n=</del>2 sessions. In equilibrium, the first partner (randomly selected in the first session), proposes an allocation of <math>\frac{\delta}{n}\,</math> to any <math>(n-1)/2\,</math> other selected partners (this is their continuation value for being selected with probability <math>\frac{1}{n}\,</math> and claiming the entire surplus of 1, discounted by <math>\delta\,</math>, in the next and final period) and proposes to keep the remaining <math> 1 - \frac{\delta(n-1)}{2n}\,</math> for himself. The proposal is approved by a majority (the proposer plus his <math>(n-1)/2\,</math> allies receiving positive shares), and the game ends in the first period. Note that the proposer receives the largest share (ranging between <math>(1-\frac{\delta}{3})</math> and <math>(1-\frac{\delta}{2})\,</math>, so at least one half of the total surplus) due to the agenda power from being recognized first, as well as the institutional setup of the closed rule, which excludes amendments from immediate consideration by the voting body. </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Assuming the game is single-shot (a finite number of sessions will be held to consider distribution proposals for the surplus), we make the additional assumption that if no allocation is agreed in the final period, then the surplus is not distributed and all partners end up with 0. If so, we have a simple application of Baron & Ferejohn (1989) - [http://www.edegan.com/wiki/index.php/Baron_Ferejohn_%281989%29_-_Bargaining_In_Legislatures#Closed_Rule_-_Two_Sessions Close Rule, Finite Session (e.g. 2 <ins class="diffchange diffchange-inline">sessions</ins>)]. Backwards induction thus yields a SPNE in which each member, if recognized, makes the same majoritarian proposal to distribute the benefits to a minimal winning majority (characterized in Proposition 1). For simplicity, normalize the total surplus to 1, and consider 2 <ins class="diffchange diffchange-inline">total </ins>sessions. In equilibrium, the first partner (randomly selected in the first session), proposes an allocation of <math>\frac{\delta}{n}\,</math> to any <math>(n-1)/2\,</math> other selected partners (this is their continuation value for being selected with probability <math>\frac{1}{n}\,</math> and claiming the entire surplus of 1, discounted by <math>\delta\,</math>, in the next and final period) and proposes to keep the remaining <math> 1 - \frac{\delta(n-1)}{2n}\,</math> for himself. The proposal is approved by a majority (the proposer plus his <math>(n-1)/2\,</math> allies receiving positive shares), and the game ends in the first period. Note that the proposer receives the largest share (ranging between <math>(1-\frac{\delta}{3})</math> and <math>(1-\frac{\delta}{2})\,</math>, so at least one half of the total surplus) due to the agenda power from being recognized first, as well as the institutional setup of the closed rule, which excludes amendments from immediate consideration by the voting body. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l36" >Line 36:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''d.) Finally, consider what would happen if both voting rights and recognition probabilities were proportional to the shares held, what would you expect in this case?'''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''d.) Finally, consider what would happen if both voting rights and recognition probabilities were proportional to the shares held, what would you expect in this case?'''</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>This issue is not addressed directly in the paper, but we can note that the results from part (c) above held in part because each partner's vote was equally valuable in achieving a majority. Now that voting rights are no longer uniformly distributed, it is not necessary to collect a voting coalition of (n-1)/2 other voters, only to ensure that the total share of yes votes exceeds 50%. <del class="diffchange diffchange-inline">The cheapest </del>strategy <del class="diffchange diffchange-inline">of achieving this outcome would be </del>for the <del class="diffchange diffchange-inline">proposer </del>to <del class="diffchange diffchange-inline">build </del>a <del class="diffchange diffchange-inline">coalition starting with </del>the <del class="diffchange diffchange-inline">least likely </del>to be <del class="diffchange diffchange-inline">recognized </del>(and thus <del class="diffchange diffchange-inline">cheapest) voter and continuing </del>in <del class="diffchange diffchange-inline">this fashion until </del>the <del class="diffchange diffchange-inline">total vote share exceeded 50%</del>. <del class="diffchange diffchange-inline">It is then possible </del>that the <del class="diffchange diffchange-inline">results in part (c) may hold, in </del>the <del class="diffchange diffchange-inline">sense that low probability voters would achieve over-sized gains from </del>the <del class="diffchange diffchange-inline">game</del>, <del class="diffchange diffchange-inline">but this effect would likely </del>be <del class="diffchange diffchange-inline">counter-balanced by </del>the <del class="diffchange diffchange-inline">fact that high probability voters are more likely to be recognized first and are a more necessary component </del>of <del class="diffchange diffchange-inline">any winning coalition</del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>This issue is not addressed directly in the paper, but we can note that the results from part (c) above held in part because each partner's vote was equally valuable in achieving a majority. Now that voting rights are no longer uniformly distributed, it is not necessary to collect a voting coalition of (n-1)/2 other voters, only to ensure that the total share of yes votes exceeds 50%. <ins class="diffchange diffchange-inline">Also, there is no longer a "cheap" </ins>strategy for <ins class="diffchange diffchange-inline">buying votes, as </ins>the <ins class="diffchange diffchange-inline">marginal cost of each vote is roughly equal (up </ins>to a <ins class="diffchange diffchange-inline">factor of <math>\delta</math>) to its marginal benefit, in </ins>the <ins class="diffchange diffchange-inline">sense that each partner invited </ins>to <ins class="diffchange diffchange-inline">join the marginal winning coalition must </ins>be <ins class="diffchange diffchange-inline">compensated only <math>\delta p_i\,</math>, where <math>p_i</math> is their share of the total votes </ins>(and <ins class="diffchange diffchange-inline">also </ins>thus <ins class="diffchange diffchange-inline">their probability of being called upon </ins>in the <ins class="diffchange diffchange-inline">next period to make a proposal)</ins>. <ins class="diffchange diffchange-inline">In eqm, we thus expect that the first partner called up on will choose a coalition of any k other partners such </ins>that the <ins class="diffchange diffchange-inline">sum of </ins>the <ins class="diffchange diffchange-inline">k partners' shares plus </ins>the <ins class="diffchange diffchange-inline">first partner's shares will just exceed 50%</ins>, <ins class="diffchange diffchange-inline">and each of the k partners will </ins>be <ins class="diffchange diffchange-inline">compensated <math>\delta p_k\,</math>, with </ins>the <ins class="diffchange diffchange-inline">original proposer keeping the remainder </ins>of <ins class="diffchange diffchange-inline">the total surplus</ins>.</div></td></tr>
</table>imported>Tarekhttp://www.edegan.com/mediawiki/index.php?title=BPP_Field_Exam_2006_Answers&diff=30021&oldid=previmported>Tarek at 02:33, 21 February 20112011-02-21T02:33:26Z<p></p>
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</tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div>
</td></tr></table>imported>Tarekhttp://www.edegan.com/mediawiki/index.php?title=BPP_Field_Exam_2006_Answers&diff=28112&oldid=previmported>Tarek at 02:33, 21 February 20112011-02-21T02:33:26Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*The first vote receives a majority, so the legislature completes in one session. </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*The first vote receives a majority, so the legislature completes in one session. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>So in the setup described above, we anticipate that should punishment strategies be fully credible, any allocation can be implemented by the partnership in equilibrium. However, with the refinement to stationary equilibrium, we collapse back to the equilibrium prediction from part (a) above, except that now the allocation decision is repeated each year <del class="diffchange diffchange-inline">and each </del>time a (potentially) different partner will enjoy the agenda power and associated rents that comes from being randomly selected to propose an allocation to the partnership first. </div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>So in the setup described above, we anticipate that should punishment strategies be fully credible, any allocation can be implemented by the partnership in equilibrium. However, with the refinement to stationary equilibrium, we collapse back to the equilibrium prediction from part (a) above, except that now the allocation decision is repeated each year<ins class="diffchange diffchange-inline">. So every </ins>time <ins class="diffchange diffchange-inline">an allocation decision is to be made, </ins>a (potentially) different partner will enjoy the agenda power and associated rents that comes from being randomly selected to propose an allocation to the partnership first. </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''c.) Returning to the one-shot/no-reputation case, consider what would happen if partnership shares are not distributed evenly, and members have probabilities of being recognized which are proportional to their shares. What would be the equilibrium strategies and outcomes you would expect in this case?'''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''c.) Returning to the one-shot/no-reputation case, consider what would happen if partnership shares are not distributed evenly, and members have probabilities of being recognized which are proportional to their shares. What would be the equilibrium strategies and outcomes you would expect in this case?'''</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Here we would predict that partners with the lowest probability of recognition (based on their shares) may have the highest ex ante value of the game, as they are the least costly members of any voting coalitions. In equilibrium, the randomly selected partner will always form a coalition of (n-1)/2 other partners with the lowest continuation values, where the continuation value is now given by <math>\delta p_i\,</math>, where <math>p_i\,</math> is the probability of partner i of being recognized in a given period. We conjecture that whenever shares are distributed across partners with a small variance (as discussed in the example from the paper below), this result will generally hold. But where there is a less equal distribution of shares (e.g. one partner has 50% of the shares, and the remaining partners evenly split the 50% remainder evenly across them), then this result may be less robust. Instead, the high probability of selecting the first partner combined with the large number of potential coalitions than can be built by him may lead to the opposite result. </ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>As noted on the top of page 1189 of the article: "in a two-session legislature, if the members have different probabilities <math>p_i\,</math> of being recognized, each has a continuation value <math>v_i(1, g) = p_i\,</math> for any second session subgame. Then, if any member k is recognized in the first stage, he or she can offer <math>\delta p_i\,</math> to the ith member and that member will vote for the proposal. Member k will thus choose the <math>(n-1)/2\,</math> members with the lowest <math>p_i\,</math>. Note that depending on the probabilities the member with the lowest probability of recognition may have the highest ex ante value of the game, and the member with the highest probability of recognition may have the lowest ex ante value of the game. For example, if <math>n=3, p_1=\frac{1}{3}+\epsilon, p_2=\frac{1}{3}, p_3=\frac{1}{3}-\epsilon \,</math>, the ex-ante values <math>v_i\,</math> of the game have limits <math>v_1=\frac{2}{9},</math> <math>v_2=\frac{1}{3},</math> <math>v_3=\frac{4}{9},</math> as <math>\epsilon \rarr 0\,</math>. The member with the lowest probability of recognition thus can do better than the other members because he or she is a less costly member of any majority."</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>As noted on the top of page 1189 of the article: "in a two-session legislature, if the members have different probabilities <math>p_i\,</math> of being recognized, each has a continuation value <math>v_i(1, g) = p_i\,</math> for any second session subgame. Then, if any member k is recognized in the first stage, he or she can offer <math>\delta p_i\,</math> to the ith member and that member will vote for the proposal. Member k will thus choose the <math>(n-1)/2\,</math> members with the lowest <math>p_i\,</math>. Note that depending on the probabilities the member with the lowest probability of recognition may have the highest ex ante value of the game, and the member with the highest probability of recognition may have the lowest ex ante value of the game. For example, if <math>n=3, p_1=\frac{1}{3}+\epsilon, p_2=\frac{1}{3}, p_3=\frac{1}{3}-\epsilon \,</math>, the ex-ante values <math>v_i\,</math> of the game have limits <math>v_1=\frac{2}{9},</math> <math>v_2=\frac{1}{3},</math> <math>v_3=\frac{4}{9},</math> as <math>\epsilon \rarr 0\,</math>. The member with the lowest probability of recognition thus can do better than the other members because he or she is a less costly member of any majority."</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''d.) Finally, consider what would happen if both voting rights and recognition probabilities were proportional to the shares held, what would you expect in this case?'''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''d.) Finally, consider what would happen if both voting rights and recognition probabilities were proportional to the shares held, what would you expect in this case?'''</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">This issue is not addressed directly in the paper, but we can note that the results from part (c) above held in part because each partner's vote was equally valuable in achieving a majority. Now that voting rights are no longer uniformly distributed, it is not necessary to collect a voting coalition of (n-1)/2 other voters, only to ensure that the total share of yes votes exceeds 50%. The cheapest strategy of achieving this outcome would be for the proposer to build a coalition starting with the least likely to be recognized (and thus cheapest) voter and continuing in this fashion until the total vote share exceeded 50%. It is then possible that the results in part (c) may hold, in the sense that low probability voters would achieve over-sized gains from the game, but this effect would likely be counter-balanced by the fact that high probability voters are more likely to be recognized first and are a more necessary component of any winning coalition.</ins></div></td></tr>
</table>imported>Tarekhttp://www.edegan.com/mediawiki/index.php?title=BPP_Field_Exam_2006_Answers&diff=30020&oldid=previmported>Tarek at 01:49, 21 February 20112011-02-21T01:49:03Z<p></p>
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<td colspan="1" style="background-color: #fff; color: #222; text-align: center;">Revision as of 01:49, 21 February 2011</td>
</tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div>
</td></tr></table>imported>Tarekhttp://www.edegan.com/mediawiki/index.php?title=BPP_Field_Exam_2006_Answers&diff=28111&oldid=previmported>Tarek at 01:49, 21 February 20112011-02-21T01:49:03Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 01:49, 21 February 2011</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l14" >Line 14:</td>
<td colspan="2" class="diff-lineno">Line 14:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>We now have an application of Baron & Ferejohn (1989) - [http://www.edegan.com/wiki/index.php/Baron_Ferejohn_%281989%29_-_Bargaining_In_Legislatures#Closed_Rule_-_Infinite_Sessions Closed Rule, Infinite Session] </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>We now have an application of Baron & Ferejohn (1989) - [http://www.edegan.com/wiki/index.php/Baron_Ferejohn_%281989%29_-_Bargaining_In_Legislatures#Closed_Rule_-_Infinite_Sessions Closed Rule, Infinite Session] </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>From Proposition 2 in the paper, if: <math>1 > \delta > \frac{(n+2)}{2(n-1)} \mbox{ and } n \ge 5\,</math> then: Any distribution of benefits (<math>x\,</math>) may be supported.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>From Proposition 2 in the paper, if: <math>1 > \delta > \frac{(n+2)}{2(n-1)} \mbox{ and } n \ge 5\,</math> then: Any distribution of benefits (<math>x\,</math>) may be supported.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This is accomplished through use of punishment strategies for any voter who attempts to deviate from the allocation (<math>x\,</math>), as discussed at length on pp1189-1191. Such punishment strategies suffer from being at times only weakly credible, in that punishers may be indifferent to carrying out their threats, leading voters to anticipate that enforcement may occur with less than probability 1, and thus unraveling the equilibrium. Baron and Ferejohn propose a refinement called Stationary Equilibrium, where members take the same actions in structurally equivalent subgames. Note that two sub-games are structurally equivalent iff: (i) the agenda is identical, (ii) set members who may be recognized (at the next node) are identical, (iii) the strategy sets of the members are identical.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This is accomplished through use of punishment strategies for any voter who attempts to deviate from the allocation (<math>x\,</math>), as discussed at length on pp1189-1191. Such punishment strategies suffer from being at times only weakly credible, in that punishers may be indifferent to carrying out their threats, leading voters to anticipate that enforcement may occur with less than probability 1, and thus unraveling the equilibrium. Baron and Ferejohn propose a refinement called Stationary Equilibrium, where members take the same actions in structurally equivalent subgames. Note that two sub-games are structurally equivalent iff: (i) the agenda is identical, (ii) set members who may be recognized (at the next node) are identical, (iii) the strategy sets of the members are identical.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In the case of equal probabilities, majority rule and <del class="diffchange diffchange-inline">infitite </del>session, Proposition 3 in the paper states that for all <math>\delta \in [0,1]\,</math> a stationary SPNE in pure strategies exists iff:</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In the case of equal probabilities, majority rule and <ins class="diffchange diffchange-inline">infinite </ins>session, Proposition 3 in the paper states that for all <math>\delta \in [0,1]\,</math> a stationary SPNE in pure strategies exists iff:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*A recognized member proposes to give <math>\frac{\delta}{n}\,</math> to <math>\frac{(n-1)}{2}\,</math> randomly chosen other members, and to keep <math>1-\frac{\delta (n-1)}{2n}\,</math> for himself.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*A recognized member proposes to give <math>\frac{\delta}{n}\,</math> to <math>\frac{(n-1)}{2}\,</math> randomly chosen other members, and to keep <math>1-\frac{\delta (n-1)}{2n}\,</math> for himself.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Each member votes for any proposal that gives him at least <math>\frac{\delta}{n}\,</math>.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*Each member votes for any proposal that gives him at least <math>\frac{\delta}{n}\,</math>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*The first vote receives a majority, so the legislature completes in one session. </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*The first vote receives a majority, so the legislature completes in one session. </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">So in the setup described above, we anticipate that should punishment strategies be fully credible, any allocation can be implemented by the partnership in equilibrium. However, with the refinement to stationary equilibrium, we collapse back to the equilibrium prediction from part (a) above, except that now the allocation decision is repeated each year and each time a (potentially) different partner will enjoy the agenda power and associated rents that comes from being randomly selected to propose an allocation to the partnership first. </ins></div></td></tr>
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</table>imported>Tarekhttp://www.edegan.com/mediawiki/index.php?title=BPP_Field_Exam_2006_Answers&diff=30019&oldid=previmported>Tarek at 01:43, 21 February 20112011-02-21T01:43:37Z<p></p>
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<td colspan="1" style="background-color: #fff; color: #222; text-align: center;">Revision as of 01:43, 21 February 2011</td>
</tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div>
</td></tr></table>imported>Tarekhttp://www.edegan.com/mediawiki/index.php?title=BPP_Field_Exam_2006_Answers&diff=28110&oldid=previmported>Tarek at 01:43, 21 February 20112011-02-21T01:43:37Z<p></p>
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</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l4" >Line 4:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>A partnership group has a surplus it needs to allocate to the partners at the end of the year. The procedure it uses (as enshrined in its Operating Agreement) is as follows. Decisions are made by a committee-of-the whole (i.e. the entire partnership). At the annual meeting for the partnership, one of the partners is chosen randomly (with each having an equal likelihood of being selected) to propose an allocation to each of the members, including herself. If her proposal is accepted by a majority of the partnership, then that proposal is implemented. If it is not passed by a majority, then another partner is chosen randomly to make a proposal and the procedure repeats. All of the partners prefer higher allocations to lower allocations, and faster decisions to slower decisions.'''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>A partnership group has a surplus it needs to allocate to the partners at the end of the year. The procedure it uses (as enshrined in its Operating Agreement) is as follows. Decisions are made by a committee-of-the whole (i.e. the entire partnership). At the annual meeting for the partnership, one of the partners is chosen randomly (with each having an equal likelihood of being selected) to propose an allocation to each of the members, including herself. If her proposal is accepted by a majority of the partnership, then that proposal is implemented. If it is not passed by a majority, then another partner is chosen randomly to make a proposal and the procedure repeats. All of the partners prefer higher allocations to lower allocations, and faster decisions to slower decisions.'''</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''a.) Outline a model of the above situation. Assuming the game is a single-shot and there are no punishments by the partnership (no reputation effects), discuss the equilibrium for your model. Note: you do not have to solve the model; simply discuss the proposition(s) you expect that could be derived and the intuition(s) behind it (them).'''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''a.) Outline a model of the above situation. Assuming the game is a single-shot and there are no punishments by the partnership (no reputation effects), discuss the equilibrium for your model. Note: you do not have to solve the model; simply discuss the proposition(s) you expect that could be derived and the intuition(s) behind it (them).'''</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Assuming the game is single-shot (a finite number of sessions will be held to consider distribution proposals for the surplus), we make the additional assumption that if no allocation is agreed in the final period, then the surplus is not distributed and all partners end up with 0. If so, we have a simple application of Baron & Ferejohn (1989) - [http://www.edegan.com/wiki/index.php/Baron_Ferejohn_%281989%29_-_Bargaining_In_Legislatures#Closed_Rule_-_Two_Sessions Close Rule, Finite Session (e.g. n=2)]. Backwards induction thus yields a SPNE in which each member, if recognized, makes the same majoritarian proposal to distribute the benefits to a minimal winning majority (characterized in Proposition 1). For simplicity, normalize the total surplus to 1, and consider n=2 sessions. In equilibrium, the first partner (randomly selected in the first session), proposes an allocation of <math>\frac{\delta}{n}\,</math> to any <math>(n-1)/2\,</math> other selected partners (this is their continuation value for being selected with probability <math>\frac{1}{n}\,</math> and claiming the entire surplus of 1, discounted by <math>\delta\,</math>, in the next and final period) and proposes to keep the remaining <math> 1 - \frac{\delta(n-1)}{2n}\,</math> for himself. The proposal is approved by a majority (the proposer plus his <math>(n-1)/2\,</math> allies receiving positive shares), and the game ends in the first period. Note that the proposer receives the largest share (ranging between <math>(1-\frac{\delta}{3})</math> and <math>(1-\frac{\delta}{2})\,</math>, so at least one half of the total surplus) due to the agenda power from being recognized first, as well as the institutional setup of the closed rule, which excludes amendments from immediate consideration by the voting body. </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Assuming the game is single-shot (a finite number of sessions will be held to consider distribution proposals for the surplus), we make the additional assumption that if no allocation is agreed in the final period, then the surplus is not distributed and all partners end up with 0. If so, we have a simple application of Baron & Ferejohn (1989) - [http://www.edegan.com/wiki/index.php/Baron_Ferejohn_%281989%29_-_Bargaining_In_Legislatures#Closed_Rule_-_Two_Sessions Close Rule, Finite Session (e.g. n=2)]. Backwards induction thus yields a SPNE in which each member, if recognized, makes the same majoritarian proposal to distribute the benefits to a minimal winning majority (characterized in Proposition 1). For simplicity, normalize the total surplus to 1, and consider n=2 sessions. In equilibrium, the first partner (randomly selected in the first session), proposes an allocation of <math>\frac{\delta}{n}\,</math> to any <math>(n-1)/2\,</math> other selected partners (this is their continuation value for being selected with probability <math>\frac{1}{n}\,</math> and claiming the entire surplus of 1, discounted by <math>\delta\,</math>, in the next and final period) and proposes to keep the remaining <math> 1 - \frac{\delta(n-1)}{2n}\,</math> for himself. The proposal is approved by a majority (the proposer plus his <math>(n-1)/2\,</math> allies receiving positive shares), and the game ends in the first period. Note that the proposer receives the largest share (ranging between <math>(1-\frac{\delta}{3})</math> and <math>(1-\frac{\delta}{2})\,</math>, so at least one half of the total surplus) due to the agenda power from being recognized first, as well as the institutional setup of the closed rule, which excludes amendments from immediate consideration by the voting body. </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''b.) Suppose that the partnership (membership) is stable, infinitely-lived, and makes a surplus allocation decision every year. How would you account for this in your model? Discuss equilibrium behavior and strategies using these assumptions (again you do not need to explicitly solve the model, simply explain your reasoning).'''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''b.) Suppose that the partnership (membership) is stable, infinitely-lived, and makes a surplus allocation decision every year. How would you account for this in your model? Discuss equilibrium behavior and strategies using these assumptions (again you do not need to explicitly solve the model, simply explain your reasoning).'''</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">Application </del>of Baron & Ferejohn (1989) - [http://www.edegan.com/wiki/index.php/Baron_Ferejohn_%281989%29_-_Bargaining_In_Legislatures#Closed_Rule_-_Infinite_Sessions Closed Rule, Infinite Session]</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">We now have an application </ins>of Baron & Ferejohn (1989) - [http://www.edegan.com/wiki/index.php/Baron_Ferejohn_%281989%29_-_Bargaining_In_Legislatures#Closed_Rule_-_Infinite_Sessions Closed Rule, Infinite Session] </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">From Proposition 2 in the paper, if: <math>1 > \delta > \frac{(n+2)}{2(n-1)} \mbox{ and } n \ge 5\,</math> then: Any distribution of benefits (<math>x\,</math>) may be supported.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">This is accomplished through use of punishment strategies for any voter who attempts to deviate from the allocation (<math>x\,</math>), as discussed at length on pp1189-1191. Such punishment strategies suffer from being at times only weakly credible, in that punishers may be indifferent to carrying out their threats, leading voters to anticipate that enforcement may occur with less than probability 1, and thus unraveling the equilibrium. Baron and Ferejohn propose a refinement called Stationary Equilibrium, where members take the same actions in structurally equivalent subgames. Note that two sub-games are structurally equivalent iff: (i) the agenda is identical, (ii) set members who may be recognized (at the next node) are identical, (iii) the strategy sets of the members are identical.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">In the case of equal probabilities, majority rule and infitite session, Proposition 3 in the paper states that for all <math>\delta \in [0,1]\,</math> a stationary SPNE in pure strategies exists iff:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*A recognized member proposes to give <math>\frac{\delta}{n}\,</math> to <math>\frac{(n-1)}{2}\,</math> randomly chosen other members, and to keep <math>1-\frac{\delta (n-1)}{2n}\,</math> for himself.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*Each member votes for any proposal that gives him at least <math>\frac{\delta}{n}\,</math>.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">*The first vote receives a majority, so the legislature completes in one session. </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''c.) Returning to the one-shot/no-reputation case, consider what would happen if partnership shares are not distributed evenly, and members have probabilities of being recognized which are proportional to their shares. What would be the equilibrium strategies and outcomes you would expect in this case?'''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''c.) Returning to the one-shot/no-reputation case, consider what would happen if partnership shares are not distributed evenly, and members have probabilities of being recognized which are proportional to their shares. What would be the equilibrium strategies and outcomes you would expect in this case?'''</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>As noted on the top of page 1189 of the article: "in a two-session legislature, if the members have different probabilities <math>p_i\,</math> of being recognized, each has a continuation value <math>v_i(1, g) = p_i\,</math> for any second session subgame. Then, if any member k is recognized in the first stage, he or she can offer <math>\delta p_i\,</math> to the ith member and that member will vote for the proposal. Member k will thus choose the <math>(n-1)/2\,</math> members with the lowest <math>p_i\,</math>. Note that depending on the probabilities the member with the lowest probability of recognition may have the highest ex ante value of the game, and the member with the highest probability of recognition may have the lowest ex ante value of the game. For example, if <math>n=3, p_1=\frac{1}{3}+\epsilon, p_2=\frac{1}{3}, p_3=\frac{1}{3}-\epsilon \,</math>, the ex-ante values <math>v_i\,</math> of the game have limits <math>v_1=\frac{2}{9},</math> <math>v_2=\frac{1}{3},</math> <math>v_3=\frac{4}{9},</math> as <math>\epsilon \rarr 0\,</math>. The member with the lowest probability of recognition thus can do better than the other members because he or she is a less costly member of any majority."</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>As noted on the top of page 1189 of the article: "in a two-session legislature, if the members have different probabilities <math>p_i\,</math> of being recognized, each has a continuation value <math>v_i(1, g) = p_i\,</math> for any second session subgame. Then, if any member k is recognized in the first stage, he or she can offer <math>\delta p_i\,</math> to the ith member and that member will vote for the proposal. Member k will thus choose the <math>(n-1)/2\,</math> members with the lowest <math>p_i\,</math>. Note that depending on the probabilities the member with the lowest probability of recognition may have the highest ex ante value of the game, and the member with the highest probability of recognition may have the lowest ex ante value of the game. For example, if <math>n=3, p_1=\frac{1}{3}+\epsilon, p_2=\frac{1}{3}, p_3=\frac{1}{3}-\epsilon \,</math>, the ex-ante values <math>v_i\,</math> of the game have limits <math>v_1=\frac{2}{9},</math> <math>v_2=\frac{1}{3},</math> <math>v_3=\frac{4}{9},</math> as <math>\epsilon \rarr 0\,</math>. The member with the lowest probability of recognition thus can do better than the other members because he or she is a less costly member of any majority."</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''d.) Finally, consider what would happen if both voting rights and recognition probabilities were proportional to the shares held, what would you expect in this case?'''</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>'''d.) Finally, consider what would happen if both voting rights and recognition probabilities were proportional to the shares held, what would you expect in this case?'''</div></td></tr>
</table>imported>Tarek