A solution set for fine games
نویسندگان
چکیده
Bumb and Hoede have shown that a cooperative game can be split into two games, the reward game and the fine game, by considering the sign of quantities c v S in the c-diagram of the game. One can then define a solution x for the original game as x = x r − x f , where x r is a solution for the reward game and x f is a solution for the fine game. Due to the distinction of cooperation rewards and fines, for allocating the fines one may use another solution concept than for the rewards. In this paper, fine vectors are introduced and a solution mapping for fine games is defined. We discuss the structure and properties of this mapping and show how the solution set is related to the Shapley value, the core and the Weber set. We also characterize the mapping as the unique mapping satisfying axioms of Efficiency, Pseudo-symmetry, Dummy Player Property and Additivity.
منابع مشابه
Cooperative Benefit and Cost Games under Fairness Concerns
Solution concepts in cooperative games are based on either cost games or benefit games. Although cost games and benefit games are strategically equivalent, that is not the case in general for solution concepts. Motivated by this important observation, a new property called invariance property with respect to benefit/cost allocation is introduced in this paper. Since such a property can be regar...
متن کاملTenable strategy blocks and settled equilibria∗
When people interact in familiar settings, social conventions usually develop so that people tend to disregard alternatives outside the convention. For rational players to usually restrict attention to a block of conventional strategies, no player should prefer to deviate from the block when others are likely to act conventionally and rationally inside the block. We explore two set-valued conce...
متن کاملA Closed-Form Formula for the Fair Allocation of Gains in Cooperative N-Person Games
Abstract This paper provides a closed-form optimal solution to the multi-objective model of the fair allocation of gains obtained by cooperation among all players. The optimality of the proposed solution is first proved. Then, the properties of the proposed solution are investigated. At the end, a numerical example in inventory control environment is given to demonstrate the application and t...
متن کاملA solution defined by fine vectors
Bumb and Hoede have shown that a cooperative game can be split into two games, the reward game and the fine game, by considering the sign of quantities cS in the c-diagram of the game. One can then define a solution x for the original game as x = xr − xf , where xr is a solution for the reward game and xf is a solution for the fine game. Due to the distinction of cooperation rewards and fines, ...
متن کاملAn interval-valued programming approach to matrix games with payoffs of triangular intuitionistic fuzzy numbers
The purpose of this paper is to develop a methodology for solving a new type of matrix games in which payoffs are expressed with triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, the concept of solutions for matrix games with payoffs of TIFNs is introduced. A pair of auxiliary intuitionistic fuzzy programming models for players are established to determine optimal strategies...
متن کامل