Bounds on the Cost of Stabilizing a Cooperative Game
Bachrach, YB; Elkind, E; Malizia, E; et al.Meir, R; Pasechnik, D; Rosenschein, JS; Rothe, J; Zuckerman, M
Date: 27 December 2018
Journal
The Journal of Artificial Intelligence Research
Publisher
AI Access Foundation
Publisher DOI
Abstract
A key issue in cooperative game theory is coalitional stability, usually captured by the
notion of the core—the set of outcomes that are resistant to group deviations. However,
some coalitional games have empty cores, and any outcome in such a game is unstable. We
investigate the possibility of stabilizing a coalitional game by using ...
A key issue in cooperative game theory is coalitional stability, usually captured by the
notion of the core—the set of outcomes that are resistant to group deviations. However,
some coalitional games have empty cores, and any outcome in such a game is unstable. We
investigate the possibility of stabilizing a coalitional game by using subsidies. We consider
scenarios where an external party that is interested in having the players work together
offers a supplemental payment to the grand coalition, or, more generally, a particular coalition
structure. This payment is conditional on players not deviating from this coalition
structure, and may be divided among the players in any way they wish. We define the
cost of stability as the minimum external payment that stabilizes the game. We provide
tight bounds on the cost of stability, both for games where the coalitional values are nonnegative
(profit-sharing games) and for games where the coalitional values are nonpositive
(cost-sharing games), under natural assumptions on the characteristic function, such as
superadditivity, anonymity, or both. We also investigate the relationship between the cost
of stability and several variants of the least core. Finally, we study the computational
complexity of problems related to the cost of stability, with a focus on weighted voting
games.
Computer Science
Faculty of Environment, Science and Economy
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