Theory of linear and integer programming
Theory of linear and integer programming
The Cost of Stability in Coalitional Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Computational Aspects of Cooperative Game Theory (Synthesis Lectures on Artificial Inetlligence and Machine Learning)
Subsidies, stability, and restricted cooperation in coalitional games
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
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Cooperative games are a useful framework for modeling multi-agent behavior in environments where agents must collaborate in order to complete tasks. Having jointly completed a task and generated revenue, agents need to agree on some reasonable method of sharing their profits. One particularly appealing family of payoff divisions is the {\em core}, which consists of all coalitionally rational (or, stable) payoff divisions. Unfortunately, it is often the case that the core of a game is empty, i.e. there is no payoff scheme guaranteeing each group of agents a total payoff higher than what they can get on their own. As stability is a highly attractive property, there have been various methods of achieving it proposed in the literature. One natural way of stabilizing a game is via taxation, i.e. reducing the value of some coalitions in order to decrease their bargaining power. Existing taxation methods include the ε-core, the least-core and several others. However, taxing coalitions is in general undesirable: one would not wish to overly tamper with a given coalitional game, or overly tax the agents. Thus, in this work we study minimal taxation policies, i.e. those minimizing the amount of tax required in order to stabilize a given game. We show that games that minimize the total tax are to some extent a linear approximation of the original games, and explore their properties. We demonstrate connections between the minimal tax and the cost of stability, and characterize the types of games for which it is possible to obtain a tax-minimizing policy using variants of notion of the eps-core, as well as those for which it is possible to do so using reliability extensions.