Priority-Based Games with Short Sight: Towards a More Realistic Modeling Chanjuan Liu 1 , Fenrong Liu 2 , and Kaile Su 1,3 1 School of Electronics Engineering and Computer Science, Peking University, Beijing, China 2 Department of Philosophy, Tsinghua University, Beijing, China 3 Institute for Integrated and Intelligent Systems, Griffith University, Brisbane, Australia liuchanjuan0612@163.com, fenrong@tsinghua.edu.cn, sukl@pku.edu.cn Abstract. Motivated by real game scenarios, we propose a generalized prioritized game model in which players’ preference and reasons can be studied altogether. We show that the incomparable relation between two histories in game is natural and calls for a new modeling. We generalize all research results of [2] which are based on linearly ordered priority sequence to the situations which allow for incomparable priorities. We look at two kinds of dynamics changes in games with short sight, changes in priority graph and changes in sight. We show that changes of priority in games with short sight result in changes of preference in its canonical representation, and changes of short sight may also lead to preference dynamics in the corresponding games with awareness. 1 Introduction In classical game theory, there are two assumptions of common knowledge and rationality. Namely, the specification of the game are known to all players. And all players are rational in the sense that they prefer strategies that will maximize their individual expected utilities. These assumptions have been noted to be too strong and unrealistic and several attempts have been made to achieve a closer match with reality. For instance, Rubinstein explores the consequences of giving up the rationality assumption in [7] where agents are assumed to be boundedly rational. The evolutionary interpretation of game theory completely gives up any rationality assumption, see e.g [8]. Halpern et al. study the issue of unawareness [1,6], in which players may have no access to the whole game tree when they make decisions because of their ignorance of other player’s strategies. More recently, Grossi and Turrini put up the idea of games with short sight in [2] where players might neither see a part of the terminal nodes of a game tree nor even see any such nodes. This has advanced Halpern’s stance. However, we still see substantial room for improving the previous proposals. Our work in this paper is motivated by the following examples: