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.