Ambiguous Bayesian Games

Bayesian games can handle the incomplete information about players’ types. However, in real life, the information could be not only incomplete but also ambiguous for lack of sufficient evidence, i.e., a player cannot have a precise probability about each type of the other players. To address this issue, this paper firstly extends the Bayesian games to ambiguous Bayesian games. Then, we introduce the concept of a solution to this kind of games and discuss their properties, especially about solution existence, how the ambiguity degree and players’ ambiguity attitude influence the outcomes of an ambiguous Bayesian game, the case of lower boundary probability, and the missing situation. We also illustrate our game model, especially in the public security domain.