Taxation and stability in cooperative games

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 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 ε-core, as well as those for which it is possible to do so using reliability extensions. Copyright © 2013, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved

Taxation and Stability in Cooperative Games

ABSTRACT Cooperative games are a useful framework for modeling multiagent 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 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 ε-core, as well as those for which it is possible to do so using reliability extensions

Core Allocations for Cooperation Problems in Vaccination

Vaccination is a very effective measure to fight an outbreak of an infectious disease, but it often suffers from delayed deliveries and limited stockpiles. To use these limited doses of vaccine effectively, health agencies can decide to cooperate and share their doses. In this study, we analyze this type of cooperation. Typically cooperation leads to an increased total return, but cooperation is only plausible when this total return can be distributed in a stable way. This makes cooperation a delicate matter. Using cooperative game theory, we derive theoretical sufficient conditions under which cooperation is plausible (i.e., the core is non-empty) and we show that the doses of vaccine can be traded for a market price in those cases. We perform numerical analyses to generalize these findings and we derive analytical expressions for market prices that can be used in general for distributing the total return. Our results demonstrate that cooperation is most likely to be plausible in case of severe shortages and in case of sufficient supply, with possible mismatches between supply and demand. In those cases, trading doses of vaccine for a market price often results in a core allocation of the total return. We confirm these findings with a case study on the redistribution of influenza vaccines