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Baron Ferejohn (1989) - Bargaining In Legislatures (view source)
Revision as of 18:27, 19 May 2010
, 18:27, 19 May 2010no edit summary
##The next member proposes <math>z(y)\,</math> such that for the deviator <math>z_j(y) = 0\,</math> and everyone in <math>M(y)\,</math> is to vote for <math>z(y)\,</math> over <math>y\,</math>
##If the next member doesn't propose <math>z(y)\,</math> repeat the above stage to punish that member.
However, this is unsatisfactory as it requires a complete history at all points (which is unrealistic if <math>\delta\,</math> is a reelection probability and new members can't know the history), and if a member were indifferent between enforcing and not, it is only weakly credible.
To restrict the equilibrium space the paper considers '''Stationary Equilibrium'''.
Two sub-games are '''structurally equivalent''' iff:
#The agenda is identical
#Set members who may be recognized (at the next node) are identical
#The strategy sets of the members are identical
An equilibrium is stationary if the continuation values for each structurally equivalent subgame are the same. This necessarily has that strategies are stationary - members take the same actions in structurally equivalent subgames. Not that stationary strategies are history independent.
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:
*A recognised member proposes to give <math>\frac{\delta}{n}\,</math> to <math>\frac{(n-1)}{2}\,</math> randomly choosen other members, and to keep <math>1-\frac{\delta (n-1)}{2n}\,</math> for himself
*Each member votes for any proposal that gives him at least <math>\frac{\delta}{n}\,</math>
*The first vote recieves a majority, so the legislature completes in one session
===In the Paper===
The role of the majority rule (rather than say unaminity) is covered in the paper, as is the case of the stationary equilibrium for an open-rule.
