Game Theory for Computer Scientists - Cooperative Games

This tutorial introduces a cooperative game theory which is one of main parts in game theory. A cooperative game theory consists of two major research topics. The first topic involves how to divide the value of the coalition among agents. We explain the desirable ways of dividing the rewards among cooperative agents, called solution concepts. The traditional cooperative game theory provides a number of solution concepts, such as the core, the Shapley value, and the nucleolus. We introduce some algorithms for dividing the obtained rewards among agents and show their computational complexities. The second topic involves partitioning a set of agents into coalitions so that the sum of the rewards of all coalitions is maximized. This is called Coalition Structure Generation problem (CSG). We explain efficient constraint optimization algorithms for solving the CSG problem. Furthermore, we introduce concise representation schemes for a characteristic function, since it is likely that we can solve solution concepts/CSG problem more efficiently by utilizing concise representation methods for a game.