Strategic Complexity in Repeated Extensive Games

This paper studies a two-player machine (finite automaton) game in which an extensive game with perfect information is infinitely repeated. We introduce a new measure of strategic complexity named "multiple complexity", which considers the responsiveness of a strategy to information as well as the number of states of machines. In contrast to Piccione and Rubinstein (1993), we prove that a machine game may include non-trivial Nash equilibria. In the sequential-move prisoners' dilemma, cooperation can be sustained in an equilibrium of the machine game.

Evolutionary Game Theory

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Complexity and Efficiency in Repeated Games with Negotiation

This paper considers the "negotiation game" (Busch and Wen, 1995) which combines the features of two-person alternating offers bargaining and repeated games. Despite the forces of bargaining, the negotiation game in general admits a large number of equilibria some of which involve delay in agreement and inefficiency. In order to isolate equilibria in this game, we explicitly consider the complexity of implementing a strategy, introduced in the literature on repeated games played by automata. It turns out that when the players have a preference for less complex strategies (even at the margin) only efficient equilibria survive. Thus, complexity and bargaining in tandem may offer an explanation for co-operation in repeated gamesNegotiation Game, Repeated Game, Bargaining, Complexity, Bounded Rationality, Automaton

Computer Science and Game Theory: A Brief Survey

There has been a remarkable increase in work at the interface of computer science and game theory in the past decade. In this article I survey some of the main themes of work in the area, with a focus on the work in computer science. Given the length constraints, I make no attempt at being comprehensive, especially since other surveys are also available, and a comprehensive survey book will appear shortly.Comment: To appear; Palgrave Dictionary of Economic