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Pure Nash equilibria in restricted budget games

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Abstract

In budget games, players compete over resources with finite budgets. For every resource, a player has a specific demand and as a strategy, he chooses a subset of resources. If the total demand on a resource does not exceed its budget, the utility of each player who chose that resource equals his demand. Otherwise, the budget is shared proportionally. In the general case, pure Nash equilibria (NE) do not exist for such games. In this paper, we consider the natural classes of singleton and matroid budget games with additional constraints and show that for each, pure NE can be guaranteed. In addition, we introduce a lexicographical potential function to prove that every matroid budget game has an approximate pure NE which depends on the largest ratio between the different demands of each individual player.

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Correspondence to Maximilian Drees.

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A preliminary version of this paper has been published in the Proceedings of COCOON2017, Lecture Notes in Computer Science, 10392, 175–187, 2017 and is available at Springer via https://doi.org/10.1007/978-3-319-62389-4_15.

This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre “On-The-Fly Computing” (SFB 901).

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Drees, M., Feldotto, M., Riechers, S. et al. Pure Nash equilibria in restricted budget games. J Comb Optim 37, 620–638 (2019). https://doi.org/10.1007/s10878-018-0269-7

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  • DOI: https://doi.org/10.1007/s10878-018-0269-7

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