Search

Game theory has become a standard tool for depicting and demonstrating various game‐like phenomena by providing appropriate mathematical models and for analyzing and predicting agents' behaviors and their decisions by formalizing solution concepts. The conventional game model mainly concerns ideal systems that would always guarantee optimal responses, which appears unrealistic for practical game scenarios since decision‐making usually entails resource costs. Therefore, this study considers players' decision‐making in extensive games when the computational cost of searching the strategy space is limited. We start with a new mathematical model of extensive games that features a bound on computational resources during players' decision‐making process such that they can only foresee a part of the available alternatives in the future. This model is more appropriate in predicting players' strategies than the conventional model, under which we investigate the effects of computational costs on players' strategies as well as the computational complexity. Furthermore, a simulation experiment is performed to seek the connection between the amount of resources and the goodness of the outcomes. This study is expected to provide a foundation for players' rational decision‐making with computational costs. [ABSTRACT FROM AUTHOR]

In games especially large scale extensive games, players’ actual views of the game might be different from the real one, because of the limit of their computational power. Moreover, players’ views on the underlying game vary from person to person. Based on some existing work on modelling players’ limited foresight in games, we study several interesting types of players in terms of the characteristics of their actual views. The underlying model is closely connected to the well-known algorithm called α − β pruning, and an algorithmic procedure refining classical backward-induction is designed for strategy choosing in the actual process of playing such games. Further, we study the dynamic evolution of players’ foresight and show the resulting preference change. [ABSTRACT FROM AUTHOR]

We study preference dynamics in extensive games with short sight. To do so, first, we represent the priority structure as a partial-ordered priority graph instead of a linear-ordered sequence. By introducing priority graph to extensive games, we obtain the definition of prioritized games and graph-induced preference. Second, in order to deal with the situation in which a player only has incomplete information about the relevant properties and she has to decide her preference, we introduce beliefs and define belief-based preference. We propose an algorithm for such games and further explore its relationship with heuristic search algorithm in AI. Third, we investigate preference dynamics in games with regard to the changes in three kinds of triggers: priority graph, belief, and sight. We show how these changes lead to changes in preference. [ABSTRACT FROM AUTHOR]

The notion of short sight , introduced by Grossi and Turrini, weakens the unrealistic assumption in traditional extensive games that every player is able to perceive the entire game structure. In this paper, we propose a more general model for extensive games with short sight. For reasoning about extensive games with short sight, we propose a new logic language and then present an axiomatization for this logic. We prove the soundness and completeness of the axiomatization. In addition, we show that the logic can formally characterize the solution concepts and Pearce's lemma in games with short sight. [ABSTRACT FROM AUTHOR]