Infinite sequential games with perfect but incomplete information

Sequential Games with Incomplete Information

Consider the following strategy profile, in which 1 plays a, and 2 plays L. This is a Nash equilibrium. Because there are no subgames, this is also a subgame-perfect Nash equilibrium. But it is a silly equilibrium, because if 2 ever found herself in a situation where she has to move, she would want to play R no matter what her beliefs regarding where she is “inside” that information set. [There...

Approximately Solving Sequential Games With Incomplete Information

Games of incomplete information are notorious for their difficulty which usually makes finding an exact solution intractable. The problem is even harder when the game has multiple stages and sequential decision-making is required. Some efforts have therefore addressed the issue of finding approximate equilibria for various classes of games, but these have mostly been restricted to 1-stage games...

Rationalizability in infinite, dynamic games with incomplete information

In this paper, we analyze two nested iterative solution procedures for infinite, dynamic games of incomplete information. These procedures do not rely on the specification of a type space à la Harsanyi. Weak rationalizability is characterized by common certainty of rationality at the beginning of the game. Strong rationalizability also incorporates a notion of forward induction. The solutions m...

Games with Perfect Information

Games with Incomplete Information

1. Game theory and classical economics. Game theory is a theory of strategic interaction. That is to say, it is a theory of rational behavior in social situations in which each player has to choose his moves on the basis of what he thinks the other players’ countermoves are likely to be. After preliminary work by a number of other distinguished mathematicians and economists, game theory as a sy...