Representing and reasoning about Bayesian games with epistemic logic

Multi-agent systems are systems which include more than one autonomous agent with either varying information or varying interests, or both. An agent in a multi-agent system should behave rationally, which informally is defined as choosing actions that improve its chance of success. This definition of rationality is adopted to game theory which is the science of studying interactions between agents in multi-agent systems. However, these descriptions do not consider the reasoning abilities of agents. One way to tackle this issue is to use logical declarative languages, as these languages enable reasoning about the best strategy in games by considering other players' rationality and reasoning abilities. Furthermore, logical languages are used to represent game models explicitly and these languages can formulate certain specific situations, such as game theory solutions. Agents are then able to verify the correctness of these formulae in the model, thus these languages equip agents with decision making capability based on reasoning. In this thesis, we study normal form games, in which a set of agents make their decisions simultaneously, without the knowledge about the decisions of other agents, and Bayesian games that let agents face uncertainty and hold private information. We first provide an epistemic language which can model the knowledge of an agent for reasoning about games without uncertainty for reasoning about normal form games. We then extend it for representing and reasoning about Bayesian games. The extended language is used to describe explicit models that assist agents in decision making. In addition, this language is used as an expressive, general, semantically well-defined query language for model checkers. To show that our language is a succinct and expressive language and our approach is practical for a reasonable class of applications, several representative game scenarios are investigated, such as detection of attackers in wireless networks and recognition of the benefits of using cloud computing.