Subgame-perfection in free transition games

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Abstract

We prove the existence of a subgame-perfect e-equilibrium, for every e > 0, in a class of multi-player games with perfect information, which we call free transition games. The novelty is that a non-trivial class of perfect information games is solved for subgame-perfection, with multiple non-terminating actions, in which the payoff structure is generally not (upper or lower) semi-continuous. Due to the lack of semi-continuity, there is no general rule of comparison between the payoffs that 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 construction relies on an iterative scheme which is independent of e and terminates in polynomial time with the following output: for all possible histories h, a pure action ah1ah1 or in some cases two pure actions ah2ah2 and bh2bh2 for the active player at h. The subgame-perfect e-equilibrium then prescribes for every history h that the active player plays ah1ah1 with probability 1 or respectively plays ah2ah2 with probability 1 - d(e) and bh2bh2 with probability d(e). Here, d(e) is arbitrary as long as it is positive and small compared to e, so the strategies can be made “almost” pure.
Original languageEnglish
Pages (from-to)201-207
JournalEuropean Journal of Operational Research
Volume228
Issue number1
DOIs
Publication statusPublished - 1 Jan 2013

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