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Cooperative congestion games: existence of a Nash-stable coalition structure
Optimization Letters. 2022. Vol. 16. No. 9. P. 2787–2801.
This paper studies a model for cooperative congestion games. There is an array of cooperative games V and a player’s strategy is to choose a subset of the set V. The player gets a certain payoff from each chosen game. The paper demonstrates that if a payoff is the Shapley or the Banzhaf value, then the corresponding cooperative congestion game has a Nash equilibrium in pure strategies. The case is examined where each game in V has a coalition partition. The stability of the vector of coalition structures is determined, taking into account the transitions of players within a game and their migrations to other games. The potential function is defined for coalition partitions, and is used as a means of proving the existence of a stable vector of coalition structures for a certain class of cooperative game values.
Publication based on the results of:
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Purpose
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Vasily Gusev, Iakov Zhukov, / Series WP BRP 268/EC/2024 " ECONOMICS". 2024.
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In a variety of economic situations discrete agents choose one resource among several available resources and, once admitted to the resource of choice, divide it among fellow agents admitted there. The amount of the resource an agent gets is proportional to her relative ability to acquire this particular resource, what we refer to as an ...
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Gusev V., / Series WP BRP "Basic research program". 2021. No. 245.
This paper studies a model for cooperative congestion games. There is an array of cooperative games V and a player’s strategy is to choose a subset of the set V . The player gets a certain payoff from each chosen game. The paper demonstrates that if a payoff is the Shapley or the Banzhaf value, ...
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Gusev V., European Journal of Operational Research 2021 Vol. 295 No. 3 P. 1180–1188
This work proves the existence of a coalition structure that is both Nash-stable and strongly permutation-stable for classes of coalition partition games. Among them are games where player’s payoff are Aumann-Drze value or the weighted value. These results are obtained by adapting the definition of a potential function for coalition partition games. ...
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V. V. Gusev, Mazalov V. V., Operations Research Letters 2019 Vol. 47 No. 6 P. 478–482
The existence of a Nash-stable coalition structure in cooperative games with the Aumann–Dreze value is investigated. Using the framework of potential functions, it is proved that such a coalition structure exists in any cooperative game. In addition, a similar result is established for some linear values of the game, in particular, the Banzhaf value. For ...
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