License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2017.56
URN: urn:nbn:de:0030-drops-81429
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Schulman, Leonard ; Vazirani, Umesh V.

The Duality Gap for Two-Team Zero-Sum Games

LIPIcs-ITCS-2017-56.pdf (0.4 MB)


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, due to the von Neumann minimax theorem. 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. In our main result 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.
At a finer level, the cost to a team of individual players acting independently while the opposition employs joint randomness is 1-2^{1-k} for k=2, and 1-\m^{-(1-o(1))k} for m>2.

This class of multiplayer games, apart from being a natural bridge between two-player zero-sum games and general multiplayer games, is motivated from Biology (the weak selection model of evolution) and Economics (players with shared utility but poor coordination).

BibTeX - Entry

  author =	{Leonard Schulman and Umesh V. Vazirani},
  title =	{{The Duality Gap for Two-Team Zero-Sum Games}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{56:1--56:8},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Christos H. Papadimitriou},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-81429},
  doi =		{10.4230/LIPIcs.ITCS.2017.56},
  annote =	{Keywords: multi-player games, duality gap, zero-sum games, evolution}

Keywords: multi-player games, duality gap, zero-sum games, evolution
Collection: 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)
Issue Date: 2017
Date of publication: 28.11.2017

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