Anne van den Nouweland

Social and economic networks in cooperative game theory

Preface. Part I: Social and Economic Networks in Cooperative Situations. 1. Games and Networks. 2. Restricted Cooperation in Games. 3. Inheritance of Properties in Communication Situations. 4. Variants on the Basic Model. Part II: Network Formation. 5. Noncooperative Games. 6. A Network-Formation Model in Extensive Form. 7. A Network-Formation Model in Strategic Form. 8. Network Formation with Costs for Establishing Links. 9. A One-Stage Model of Network Formation and Payoff Division. 10. Network Formation and Potential Games. 11. Network Formation and Reward Functions. References. Notations. Index.

Link formation in cooperative situations

Abstract. In this paper we study the endogenous formation of cooperation structures or communication graphs between players in a superadditive TU game. For each cooperation structure that is formed, the payoffs to the players are determined by an exogenously given solution. We model the process of cooperation structure formation as a game in strategic form. It is shown that several equilibrium refinements predict the formation of the complete cooperation structure or some structure which is payoff-equivalent to the complete structure. These results are obtained for a large class of solutions for cooperative games with cooperation structures.

A one-stage model of link formation and payoff division

In this paper we introduce a strategic form model in which cooperation structures and divisions of the payoffs are determined simultaneously. We analyze the cooperation structures and payoff divisions that result according to several equilibrium concepts. We find that essentially no cycles will result and that a player need not profit from a central position in a cooperation structure.

Values of games with probabilistic graphs

Abstract In this paper we consider games with probabilistic graphs. The model we develop is an extension of the model of games with communication restrictions by Myerson (1977) . In the Myerson model each pair of players is joined by a link in the graph if and only if these two players can communicate directly. The current paper considers a more general setting in which each pair of players has some probability of direct communication. The value is defined and characterized in this context. It is a natural extension of the Myerson value and it turns out to be the Shapley value of a modified game.

An extension of the [tau]-value to games with coalition structures

Abstract We introduce the coalitional τ -value, which is an extension of the τ -value for TU-games to games with a coalition structure. We identify a class of TU-games that satisfy the property that for every game in this class and every coalition structure on its player set it holds that the coalitional τ -value can be defined for the corresponding game with a coalition structure. We study properties of the coalitional τ -value and provide an axiomatic characterization of this allocation rule. We use the coalitional τ -value to study bankruptcy problems and the determination of aircraft landing fees.

A new axiomatization of the core of games with transferable utility

Abstract Using a new definition of reduced games, we provide an axiomatization of the core for games with transferable utility using restricted nonemptiness, individual rationality and consistency.

Potential maximizers and network formation

In this paper we study the formation of cooperation structures in superadditive cooperative TU-games.Cooperation structures are represented by hypergraphs.The formation process is modelled as a game in strategic form, where the payoffs are determined according to a weighted (extended) Myerson value.This class of solution concepts turns out to be the unique class resulting in weighted potential games.The argmax set of the weighted potential predicts the formation of the complete structure and structures payoff-equivalent to the complete structure.As by-products we obtain a representation theorem of weighted potential games in terms of weighted Shapley values and a characterization of the weighted (extended) Myerson values.

An axiomatic characterization of the position value for network situations

Network situations as introduced by Jackson and Wolinsky (1996) incorporate the influence of the architecture of a network rather than just the connectivity it provides and thereby provide a more flexible setting than communication situations, which consist of a game with transferable utility and a network. We characterize the position value for network situations along the lines of the characterization of the Shapley value by Shapley (1953). In contrast to previous attempts to provide such an axiomatization, we require no condition on the underlying network. The reason for this is that we exploit the additional flexibility of network situations.

Expectation Formation Rules and the Core of Partition Function Games

This paper proposes axiomatic foundations of expectation formation rules, by which deviating players anticipate the reaction of external players in a partition function game. The projection rule is the only rule satisfying subset consistency and responsiveness to the original partition of non-deviating players. It is also the only rule satisfying subset consistency, independence of the original partition of deviating players, and coherence of expectations. Exogenous rules are the only rules satisfying subset consistency and independence of the original partition, and the pessimistic rule is the only rule generating superadditive coalitional games.

Values for Strategic Games in Which Players Cooperate

In this paper we propose a method to associate a coalitional interval game with each strategic game. The method is based on the lower and upper values of finite two-person zero-sum games. We axiomatically characterize this new method. As an intermediate step, we provide some axiomatic characterizations of the upper value of finite two-person zero-sum games.