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De Figueiredo (2002) - Electoral Competition Political Uncertainty And Policy Insulation (view source)
Revision as of 19:45, 28 May 2010
, 19:45, 28 May 2010no edit summary
A player's strategy at <math>t\,</math> describes what he will do given all possible histories <math>H_t\,</math>, where <math>H_t\,</math> is made up of the choices of nature <math>N_t\,</math> and the action sets of both players <math>A_{At}\,</math> and <math>A_{Bt}\,</math>, where <math>N_t = (n_1, \ldots, n_t)\,</math> and <math>A_{At} = (A_{A1},\ldots, A_{A(t-1)})\,</math>, and likewise for <math>A_{Bt}\,</math>. The game is one of complete information.
:<math>s \;=\; \sum_{k=0}^\infty ar^k = \frac{a}{1-r}\; \mbox{ or }\; \sum_{k=m}^\infty ar^k=\frac{ar^m}{1-r}</math>
provided that <math>r\,</math> is less than 1 (which is needed for convergence).
Then one can solve for <math>\beta_A^*\,</math>, the threshold <math>\beta\,</math> if <math>A\,</math> defects as:
Note that cooperation can not be sustained if <math>\beta < \frac{1}{2}\,</math>.
<math>\beta\,</math> could be high because:
