Preprint 62/2013

Periodic Strategies and Rationalizability in Perfect Information 2-Player Strategic Form Games

Vasilis Oikonomou and Jürgen Jost

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Submission date: 08. Jul. 2013
Pages: 44
published as: Periodic strategies : a new solution concept and an algorithm for non-trivial strategic form games.
In: Advances in complex systems, 21 (2018) 1, art-no. 1750009 
DOI number (of the published article): 10.1142/S0219525917500096
published as: Periodic strategies and rationalizability in perfect information 2-player strategic form games.
In: Journal of physics / Conference series, 410 (2013), art-no. 012070 
DOI number (of the published article): 10.1088/1742-6596/410/1/012070
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We define and study periodic strategies in two player finite strategic form games. This concept can arise from some epistemic analysis of the rationalizability concept of Bernheim and Pearce. We analyze in detail the pure strategies and mixed strategies cases. In the pure strategies case, we prove that every two player finite action game has at least one periodic strategy, making the periodic strategies an inherent characteristic of these games. Applying the algorithm of periodic strategies in the case where mixed strategies are used, we find some very interesting outcomes with useful quantitative features for some classes of games. Particularly interesting are the implications of the algorithm to collective action games, for which we were able to establish the result that the collective action strategy can be incorporated in a purely non-cooperative context. Moreover, we address the periodicity issue for the case the players have a continuum set of strategies available. We also discuss whether periodic strategies can imply any sort of cooperativity. In addition, we put the periodic strategies in an epistemic framework.

06.02.2019, 02:13