Pursuit–Evasion Games with incomplete information in discrete time

Pursuit-Evasion Games with incomplete information in discrete time

Pursuit-Evasion Games (in discrete time) are stochastic games with nonnegative daily payoffs, with the final payoff being the cumulative sum of payoffs during the game. We show that such games admit a value even in the presence of incomplete information and that this value is uniform, i.e. there are ǫ-optimal strategies for both players that are ǫ-optimal in any long enough prefix of the game. ...

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...

Bayesian Games: Games with Incomplete Information

Glossary Bayesian game An interactive decision situation involving several decision makers (players) in which each player has beliefs about (i. e. assigns probability distribution to) the payoff relevant parameters and the beliefs of the other players. State of nature Payoff relevant data of the game such as payoff functions, value of a random variable, etc. It is convenient to think of a state...

Dynamic Games with 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...