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Published May 2019 | public
Journal Article

The duality gap for two-team zero-sum games


We consider multiplayer games in which the players fall in two teams of size k, with payoffs equal within, and of opposite sign across, the two teams. In the classical case of k = 1, such zero-sum games possess a unique value, independent of order of play. However, this fails for all k > 1; we can measure this failure by a duality gap, which quantifies the benefit of being the team to commit last to its strategy. We show that the gap equals 2(1−2^(1−k)) for m = 2 and 2(1−m^(−(1−o(1))k)) for m > 2, with m being the size of the action space of each player. Extensions hold also for different-size teams and players with various-size action spaces. We further study the effect of exchanging order of commitment among individual players (not only among the entire teams). The class of two-team zero-sum games is motivated from the weak selection model of evolution, and from considering teams such as firms in which independent players (ideally) have shared utility.

Additional Information

© 2019 Published by Elsevier Inc. Received 8 February 2017, Available online 27 March 2019. LJS was supported in part by NSF grants 1319745/1618795 and BSF grant 2012333; and part of the work was done while he was in residence at the Israel Institute for Advanced Studies, supported by a EURIAS Senior Fellowship co-funded by the Marie Skłodowska-Curie Actions under the 7th Framework Programme. UVV was supported in part by NSF Grant CCF-1410022. An earlier conference version of this work appeared in Proc. ITCS 2017.

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