Note on non cooperative convex games

The authors learned about the network interdiction games when Dr. Our research is a significant extension of these applied games and includes for instance a two-stage stochastic game with finite scenarios. The authors are grateful to two referees for their constructive comments that have helped improved the presentation of the paper.

The Daniel J. You can also search for this author in PubMed Google Scholar. Correspondence to Jong-Shi Pang. The work was based on research partially supported by the U. Reprints and Permissions. Hao, T. Piecewise affine parameterized value-function based bilevel non-cooperative games. Download citation. Received : 17 July Accepted : 23 October Published : 10 November Issue Date : March Anyone you share the following link with will be able to read this content:.

Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative. Skip to main content. Search SpringerLink Search. Lucas, W. Management Science 13 , , — Luce, R. Raiffa : Games and Decisions. Wiley and Sons, New York, Meyer, P. Blaisdell, Waltham, Massachusetts, , esp.

Maschler, M. Peleg and L. Peleg , B. Schmeidler, D. Shapley, L. Theory of n -Person Games report of an informal conference , Department of Mathematics, Princeton University, ; Annals of Mathematics Study 28 , , — Von Neumann , J.

Morgenstern : Theory of Games and Economic Behavior. Princeton University Press, Whitney, H. Download references. You can also search for this author in PubMed Google Scholar. Reprints and Permissions. Cores of convex games. Int J Game Theory 1, 11—26 Download citation. Shapley y roth. Related Books Free with a 30 day trial from Scribd. Related Audiobooks Free with a 30 day trial from Scribd. Cooperative Game Theory 1.

Operations Research Games. Game Theory has many interactions with economics and with other areas such as Operations Research and social sciences. Game theory is divided into two parts: non-cooperative and cooperative.

Natural questions for individuals or businesses when dealing with cooperation are: Which coalitions should form? How to distribute the collective gains rewards or costs among the members of the formed coalition? Players 1 and 2 possess a left-hand glove and the player 3 possesses a right-hand glove. A single glove is worth nothing and a right-left pair of glove is worth 10 euros. The interpretation of the unanimity game uT is that a gain or cost savings of 1 can be obtained if and only if all players in coalition T are involved in cooperation.

The core is a convex set and the core is a polytope see Rockafellar The core of the LLR game consists of one point 0, 0, CG N —The family of all convex games with player set N. A convex game is balanced and the core of the convex games is nonempty. The Shapley value is a core element if the game is convex.

The class of totally balanced games includes the class of games with a population monotonic allocation scheme pmas Sprumont Interpretation: in larger coalitions, higher rewards or in larger coalitions lower costs. Further, in a convex game all core elements generate pmas. Then a pmas is the total Shapley value.

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