Arbitration and Stability in Cooperative Games with Overlapping Coalitions / 3251
Yair Zick

In cooperative games with overlapping coalitions (overlapping coalition formation games, or OCF games), agents may devote only some of their resources to a coalition, allowing the formation of overlapping coalition structures. Having formed coalitions and generated profits, agents must agree on some reasonable manner in which to divide the payoffs from the coalitions they are members of. In this thesis, we study stability in OCF games. As shown in Chalkiadakis et al. (2010), stability in OCF games strongly depends on the way non-deviators react to deviation; this is because when a set deviates, it may still interact with non-deviators post deviation. We begin by proposing a formal framework for handling deviation in OCF games, which we term arbitration functions. Given a set deviation, the arbitration function specifies the payoff each coalition involving non-deviators is willing to give the deviating set. Using our framework, we define and analyze several OCF solution concepts. We show that under some assumptions on the underlying structure of the OCF game, one can find core outcomes in OCF games in polynomial time. Finally, we provide sufficient conditions for core stability for the conservative, refined and optimistic arbitration functions,