Subgame-Perfection in Free Transition Games
AbstractWe prove the existence of a subgame-perfect epsilon-equilibrium, for every epsilon> 0, in a classof multi-player games with perfect information, which we call free transition games. The noveltyis that a non-trivial class of perfect information games is solved for subgame-perfection, withmultiple non-terminating actions, in which the payoff structure is generally not semi-continuous.Due to the lack of semi-continuity, there is no general rule of comparison between the payoffsthat a player can obtain by deviating a large but finite number of times or, respectively,infinitely many times. We introduce new techniques to overcome this difficulty. Our constructionrelies on an iterative scheme which is independent of epsilon and terminates in polynomial timewith the following output: for all possible histories h, a pure action a(1,h) or in some cases twopure actions a(2,h) and b(2,h) for the active player at h. The subgame-perfect epsilon-equilibriumthen prescribes for every history h that the active player plays a(1,h) with probability 1 orrespectively plays a(2,h) with probability 1-delta and b(2,h) with probability delta. Here, deltais arbitrary as long as it is positive and small compared to epsilon, so the strategies can bemade “almost” pure.
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Bibliographic InfoPaper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 047.
Date of creation: 2011
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Web page: http://www.maastrichtuniversity.nl/web/UMPublications.htm
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-01-03 (All new papers)
- NEP-GTH-2012-01-03 (Game Theory)
- NEP-HPE-2012-01-03 (History & Philosophy of Economics)
- NEP-MIC-2012-01-03 (Microeconomics)
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