A Dynamic-Logical Characterization of Solutions to Sight-limited Extensive Games

Abstract

An unrealistic assumption in classical extensive game theory is that the complete game tree is fully perceivable by all players. To weaken this assumption, a class of games (called games with short sight) was proposed in literature, modelling the game scenarios where players have only limited foresight of the game tree due to bounded resources and limited computational ability. As a consequence, the notions of equilibria in classical game theory were refined to fit games with short sight. A crucial issue that thus arises is to determine whether a strategy profile is a solution for a game. To study this issue and address the underlying idea and theory on players’ decisions in such games, we adopt a logical way. Specifically, we develop a logic through which features of these games are demonstrated. More importantly, it enables us to characterize the solutions of these games via formulas of this logic. This work not only provides an insight into a more realistic model in game theory, but also enriches the possible applications of logic.