Search results for "Shapley value"
showing 7 items of 17 documents
A value for multichoice games
2000
Abstract A multichoice game is a generalization of a cooperative TU game in which each player has several activity levels. We study the solution for these games proposed by Van Den Nouweland et al. (1995) [Van Den Nouweland, A., Potters, J., Tijs, S., Zarzuelo, J.M., 1995. Cores and related solution concepts for multi-choice games. ZOR-Mathematical Methods of Operations Research 41, 289–311]. We show that this solution applied to the discrete cost sharing model coincides with the Aumann-Shapley method proposed by Moulin (1995) [Moulin, H., 1995. On additive methods to share joint costs. The Japanese Economic Review 46, 303–332]. Also, we show that the Aumann-Shapley value for continuum game…
The Serial Property and Restricted Balanced Contributions in discrete cost sharing problems
2006
We show that the Serial Poperty and Restricted Balanced Contributions characterize the subsidy-free serial cost sharing method (Moulin (1995)) in discrete cost allocation problems.
Weighted weak semivalues
2000
We introduce two new value solutions: weak semivalues and weighted weak semivalues. They are subfamilies of probabilistic values, and they appear by adding the axioms of balanced contributions and weighted balanced contributions respectively. We show that the effect of the introduction of these axioms is the appearance of consistency in the beliefs of players about the game.
The equal collective gains value in cooperative games
2021
AbstractThe property of equal collective gains means that each player should obtain the same benefit from the cooperation of the other players in the game. We show that this property jointly with efficiency characterize a new solution, called the equal collective gains value (ECG-value). We introduce a new class of games, the average productivity games, for which the ECG-value is an imputation. For a better understanding of the new value, we also provide four alternative characterizations of it, and a negotiation model that supports it in subgame perfect equilibrium.
The three wives problem and Shapley value
2015
We examine the Talmudic three wives problem, which is a generalization of the Talmudic contested garment problem solved by Aumann and Maschler (1985) using coalitional procedure. This problem has many practical applications. In an attempt to unify all Talmudic methods, Guiasu (2010, 2011) asserts that it can be explained in terms of “run-to-the-bank”, that is, of Shapley value in a “cumulative game”. It can be challenged because the coalitional procedure yields the same result as the nucleolus, which corresponds to a “dual game”. As Guiasu's solution is paradoxical (it has all the appearances of truth), my contribution consists in explaining the concepts, particularly truncation, that play …
A strategic approach for the discounted Shapley values
2014
The family of discounted Shapley values is analyzed for cooperative games in coalitional form. We consider the bargaining protocol of the alternating random proposer introduced in Hart and Mas-Colell (Econometrica 64:357–380, 1996). We demonstrate that the discounted Shapley values arise as the expected payoffs associated with the bargaining equilibria when a time discount factor is considered. In a second model, we replace the time cost with the probability that the game ends without agreements. This model also implements these values in transferable utility games, moreover, the model implements the \(\alpha \)-consistent values in the nontransferable utility setting.
Solidarity in games with a coalition structure
2010
Abstract A new axiomatic characterization of the two-step Shapley value Kamijo (2009) is presented based on a solidarity principle of the members of any union: when the game changes due to the addition or deletion of players outside the union, all members of the union will share the same gains/losses.