Game theory based semantics has provided good insights into the decidability and completeness of several modal logics [24]. On the other hand, we can formalise the language and reasoning used in game theory using appropriate types of modal logic [1, 3, 12–15, 23, 25]. This paper is concerned with the latter issue. The starting point in games is a set of players (agents) having certain strategies (decisions) and preferences on the game’s outcomes. Hence we have to represent both the game structure and the agents’ preference relations. When reasoning about the games, we wish to determine the properties that hold in the equilibrium to which the game naturally evolves.

Temporal Logic with Preferences and Reasoning About Games

We use linear time temporal logic formulas to model strategic and extensive form games. This allows us to use temporal tableau to reason about the game structure. We order the nodes of the tableau according to the players’ preferences. Using this, we can derive a decision procedure for reasoning about the equilibria of these games. The main result developed in this paper is that every finite game can be converted into an equivalent bargaining game on temporal tableau, where the players negotiate the equilbrium outcome. The decision method proposed in this paper has a number of merits compared to others that can be found in the growing literature connecting games to logic – it captures a wide variety of game forms, it is easy to understand and implement, and it can be enhanced to take into account bounded rationality assumptions.

G. Venkatesh

Papers

Reasoning about game equilibria using temporal logic