Correlated games on simple networks

Abstract

In this thesis, the equilibrium response strategies for correlated two- and three-agent Battle of the Sexes as well as Pure Coordination game networks are analyzed. Response strategy is a recently proposed addition to the concept of correlated equilibria, in which the agents can choose whether or not to follow the instructions from the correlation device. A classification is proposed of the different Nash equilibria in the response strategy based on stability under fluctuations and whether or not they are realizable with any correlation device. For the two agent networks, the entire phase space is mapped out. For the three agent networks, choices were made for which equilibria to consider. A unique mapping from any realization of the game-theoretical model to the Ising model from physics is defined and analyzed. However, there are some serious complications in this mapping which may limit the use for the analysis of network structures in game theory.