Monte Carlo Simulation of Hedonic Games

Hedonic games have gained interest, by the academic community, in recent years because of their ability to model the grouping preferences of individuals. Hedonic games are an example of non-transferrable utility game in cooperative game theory. Cooperative game theory, or n-person game theory, is a branch of game theory that focuses on coalition formation within groups of players. Examples of hedonic games include the Marriage problem and Roommate problem. The literature on hedonic games has focused on finding analytical solutions because of the computational complexity of finding solutions for hedonic games. The problem with focusing on analytical results is that it does not give a sense of what the general properties of real solutions to hedonic games. In this study, we propose a Monte Carlo simulation to find the distributions of properties of hedonic game solutions. This simulation will involve the random generation a vast number of hedonic games and their solutions. The solutions are found using the core concepts from cooperative game theory. The form of a solution, to a hedonic game, is a coalition structure, which is a collection of disjoint coalitions that cover all the players. The property that we are interested in is the number of coalition structures in the core set. Finding the solution a hedonic game has been shown to be NP-Complete; to overcome this computational limitation, various efficiency improvements were used in finding the solutions including Individually Rational Coalition Lists (IRCL). This paper presents some initial results from this research.