On Two-Player Interval-Valued Fuzzy Bayesian Games

Game theory is an important basis to simulate several situations where multiple agents interact strategically for decision making and support. In many applications, such as auctions, frequently used for resource management involving two or more agents competing for the resources, the interacting agents only know their own characteristics and must make decisions while having to estimate the characteristics of the others. When probabilities are assigned for the different types of the interacting agents, this kind of strategic interaction constitutes a Bayesian game. In cases in which it is very difficult to characterize the private information of each agent, the payoffs can be given by approximate (not probabilistic) values, but the concept of Bayesian Nash equilibrium cannot be applied in this context. Fuzzy set theory is an excellent basis for studying this type of game, where the payoffs are represented by fuzzy numbers. When it is the case that there is also uncertainty about such fuzzy numbers, the use of interval fuzzy numbers appears as a good modeling alternative. This paper introduces an approach for interval-based fuzzy Bayesian games, based on interval-valued fuzzy probabilities for modeling the types of agents involved in the interaction. We present two different case studies, namely the (Interval) Fuzzy Bayesian Hiring Game and (Interval) Fuzzy Bayesian Prisoner's Dilemma with Moral Standards, comparing the results obtained with the crisp, fuzzy and interval fuzzy approaches, highlighting a particular case in which the interval fuzzy approach presents a solution although the two other do not. (C) 2016 Wiley Periodicals, Inc.