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This paper is devoted to the game theoretic analysis of decision situations, in which the players have veto power over the actions undertaken by certain other players. We give a full characterization of the dividends in these games with a permission structure. We find that the collection of these games forms a subspace of the vector space of all games with side payments on a specified player set.Two applications of these results are provided. The first one deals with the projection of additive games on a permission structure. It is shown that the Shapley value of these projected games can be interpreted as an index that measures the power of the players in the permission structure. The second application applies the derived results on games, where the organization structure can be analysed separately from the production capacities of the participating players.

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The problem of topology control is to assign per-node transmission power such that the resulting topology is energy efficient and satisfies certain global properties such as connectivity. The conventional approach to achieve these objectives is based on the fundamental assumption that nodes are socially responsible. We examine the following question: if nodes behave in a selfish manner, how does it impact the overall connectivity and energy consumption in the resulting topologies? We pose the above problem as a noncooperative game and use game-theoretic analysis to address it. We study Nash equilibrium properties of the topology control game and evaluate the efficiency of the induced topology when nodes employ a greedy best response algorithm. We show that even when the nodes have complete information about the network, the steady-state topologies are suboptimal. We propose a modified algorithm based on a better response dynamic and show that this algorithm is guaranteed to converge to energy-efficient and connected topologies. Moreover, the node transmit power levels are more evenly distributed, and the network performance is comparable to that obtained from centralized algorithms.

We introduce a spatial cost topology in the network formation model analyzed by Jackson and Wolinsky, Journal of Economic Theory (1996), 71: 44-74. This cost topology might represent geographical, social, or individual differences. It describes variable costs of establishing social network connections. Participants form links based on a cost-benefit analysis. We examine the pairwise stable networks within this spatial environment. Incentives vary enough to show a rich pattern of emerging behavior. We also investigate the subgame perfect implementation of pairwise stable and efficient networks. We construct a multistage extensive form game that describes the formation of links in our spatial environment. Finally, we identify the conditions under which the subgame perfect Nash equilibria of these network formation games are stable.JEL classification: A14, C70, D20We are very grateful for the constructive comments of Matt Jackson and an anonymous referee. We also like to thank Vince Crawford, Marco Slikker, Edward Droste, Hans Haller, Dimitrios Diamantaras, and Sudipta Sarangi for comments on previous drafts of this paper. We acknowledge Jay Hogan for his programming support.

A situation in which players can generate certain pay-offs by cooperating can be described by a coopemtive gnme with transferable utililies. In this paper we assume that the players who are participating in such a game, are part of some permission structure. This means that there are players who need permission from one or more other players before they can act or cooperate with other players to generate some pay-ofí. It is clear that such a permission structure limits the possibilities of cooperation. We derive a modified game that takes account of these limited cooperation possibilities. We then give axiomatic characterizations of the Shapley value of this modified game. '[n Gilles and Owen (1991) it is assumed that every player needs permission from nt teast one of his direct superiors. This is referred to as the Disjunctiue approach.

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