Multi-Player Agents in Cooperative TU-Games
AbstractA situation in which a finite set of agents can generate certain payoffs by cooperation can be described by a cooperative game with transferable utility (or simply a TU-game) where each agent is represented by one player in the game. In this paper, we assume that one agent can be represented by more than one player. We introduce two solutions for this multi-player agent game model, both being generalizations of the Shapley value for TU-games. The first is the agent-Shapley value and considers the agents in the most unified way in the sense that when an agent enters a coalition then it enters with all its players. The second is the player-Shapley value which takes all players as units, and the payoff of an agent is the sum of the payoffs over all its players. We provide axiomatic characterizations of these two solutions that differ only in a collusion neutrality axiom. The agent-Shapley value satisfies player collusion neutrality stating that collusion of two players belonging to the same agent does not change the payoff of this agent. On the other hand, the player-Shapley value satisfies agent collusion neutrality stating that after a collusion of two agents, the sum of their payoffs does not change. After axiomatizing the player- and agent-Shapley values we apply them to airport games and voting games.
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Bibliographic InfoPaper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 12-001/1.
Date of creation: 02 Jan 2012
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Cooperative TU-game; Shapley value; multi-player agent; collusion neutrality; airport games;
Find related papers by JEL classification:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-01-25 (All new papers)
- NEP-CDM-2012-01-25 (Collective Decision-Making)
- NEP-GTH-2012-01-25 (Game Theory)
- NEP-UPT-2012-01-25 (Utility Models & Prospect Theory)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ni, Debing & Wang, Yuntong, 2007. "Sharing a polluted river," Games and Economic Behavior, Elsevier, vol. 60(1), pages 176-186, July.
- S.C. Littlechild & G.F. Thompson, 1977. "Aircraft Landing Fees: A Game Theory Approach," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 8(1), pages 186-204, Spring.
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