A strict partial order on payoff configurations and its some properties. (English) Zbl 1229.91044
Summary: This paper proposes a method for comparison of payoff configurations in the framework of characteristic function form games with non-transferable utility. The proposed method in this paper is a relation derived from objections and counter-objections. Some examples which show how the proposed method works are given. This paper presents propositions which show that the proposed method satisfies the properties, called strict partial order and independence from linear transformation and parallel shift. An example verifies that the proposed method does not satisfy the property called monotonicity.
MSC:
| 91A12 | Cooperative games |
| 91B26 | Auctions, bargaining, bidding and selling, and other market models |
| 91A30 | Utility theory for games |
References:
| [1] | Aumann, R. J.; Maschler, M., The bargaining set for cooperative games, Annals of Mathematics Studies, vol. 52 (1964), Princeton University Press: Princeton University Press Princeton, New Jersey · Zbl 0132.14003 |
| [2] | Davis, M.; Maschler, M., The kernel of a cooperative game, Naval Research Logistics Quarterly, 12, 223-259 (1965) · Zbl 0204.20202 |
| [3] | Gillies, D. B., Solutions to general non-zero-sum games, Contributions to the Theory of Games, vol. IV (1959), Princeton University Press · Zbl 0085.13106 |
| [4] | Kojima, K.; Inohara, T., An acyclic relation for comparison of bargaining powers of coalitions and its interrelationship with bargaining set, Applied Mathematics and Computation, 215, 3665-3668 (2010) · Zbl 1182.91082 |
| [5] | Peleg, B.; Sudholter, P., Introduction to the Theory of Cooperative Games (2007), Springer · Zbl 1193.91002 |
| [6] | Schmeidler, D., The nucleolus of a characteristic function game, SIAM Journal of Applied Mathematics, 17, 1163-1170 (1969) · Zbl 0191.49502 |
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