Abstract
Players that participate in acooperative game with transferable utilities are assumed to be part of apermission structure being a hierarchical organization in which there are players that need permission from other players before they can cooperate. Thus a permission structure limits the possibilities of coalition formation.
Various assumptions can be made about how a permission structure affects the cooperation possibilities. In this paper we consider thedisjunctive approach in which it is assumed that each player needs permission from at least one of his predecessors before he can act. We provide an axiomatic characterization of thedisjunctive permission value being theShapley value of a modified game in which we take account of the limited cooperation possibilities.
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References
Aumann RJ, Drèze JH (1974) Cooperative games with coalition structure. International Journal of Game Theory 3: 217–237
Borm P, Owen G, Tijs S (1992) On the position value for communication situations. SIAM Journal on Discrete Mathematics 5: 305–320
Brink R van den (1994) Relational power in hierarchical organizations. Dissertation Tilburg University Tilburg
Brink R van den, Gilles RP (1996) Axiomatizations of the conjunctive permission value for games with permission structures. Games and Economic Behavior 12: 113–126
Brink R van den, Gilles RP (1994) A social power index for hierarchically structured populations of economic agents. In: Gilles RP, Ruys PHM (eds) Imperfections and Behaviour in Economic Organizations Kluwer Dordrecht
Derks J, Peters H (1993) A shapley value for games with restricted coalitions. International Journal of Game Theory 21: 351–366
Faigle U, Kern W (1993) The shapley value for cooperative games under precedence constraints. International Journal of Game Theory 21: 249–266
Gilles RP, Owen G (1994) Games with permission structures: The disjunctive approach. Mimeo Department of Economics Virginia Polytechnic Institute and State University, Blacksburg Virginia
Gilles RP, Owen G, Brink R van den (1992) Games with permission structures: The conjunctive approach. International Journal of Game Theory 20: 277–293
Harsanyi JC (1959) A bargaining model for cooperativen-person games. In: Tucker AW, Luce RD (eds) Contributions to the Theory of Games IV, Princeton UP Princeton 325–355
Kalai E, Postlewaite A, Roberts J (1978) Barriers to trade and disadvantageous middlemen: Non-monotonicity of the core: Journal of Economic Theory 19: 200–209
Myerson RB (1977) Graphs and cooperation in games. Mathematics of Operations Research 2: 225–229
Nouweland A van den (1993) Games and graphs in economic situations. Dissertation, Tilburg University Tilburg
Owen G (1977) Values of games with a priori unions. In: Henn R, Moeschlin O (eds) Essays in Mathematical Economics and Game Theory. Springer Verlag Berlin 76–88
Owen G (1986) Values of graph-restricted games. SIAM Journal of Algebraic Discrete Methods 7: 210–220
Shapley LS (1953) A value forn-person games. In: Kuhn HW, Tucker AW (eds) Annals of Mathematics Studies 28 (Contributions to the Theory of Games Vol 2) Princeton UP Princeton 307–317
Winter E (1989) A value for cooperative games with levels structure of cooperation. International Journal of Game Theory 18: 227–240
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I would like to thank Peter Borm, Rob Gilles and Anne van den Nouweland for their useful remarks on a previous draft of this paper.
Financial support from the Netherlands Organization for Scientific Research (NWO), grant 450-228-022, is gratefully acknowledged.
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Van Den Brink, R. An axiomatization of the disjunctive permission value for games with a permission structure. Int J Game Theory 26, 27–43 (1997). https://doi.org/10.1007/BF01262510
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DOI: https://doi.org/10.1007/BF01262510