Epistemic Game Theory: Putting Algorithms to Work

Abstract

The aim of this study is to construct an epistemic model in which each rational choice under common belief in rationality is supplemented by a type which expresses such a belief. In practice, the finding of type depends on manual solution approach with some mathematical operations in scope of the theory. This approach becomes less convenient with the growth of the size of the game. To solve this difficulty, a linear programming model is constructed for two-player, static and non-cooperative games to find the type that is supporting that player's rational choice is optimal under common belief in rationality and maximizing the utility of the game. Since the optimal choice would only be made from rational choices, it is first necessary to eliminate all strictly dominated choices. In real life, the games are usually large sized. Therefore, the elimination process should be performed in a computer environment. Since software related to game theory was mostly prepared with a result-oriented approach for some types of games, it was necessary to develop software to execute the iterated elimination method. With this regard, a program has been developed that determines the choices that are strictly dominated by pure and randomized choices in two-player games. Two functions named esdc and type are created by using R statistical programming language for the operations performed in both parts, and these functions are added to the content of an R package after its creation with the name EpistemicGameTheory.