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Published March 2002 | public
Journal Article

Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections


We prove that the support of mixed strategy equilibria of two-player, symmetric, zero-sum games lies in the uncovered set, a concept originating in the theory of tournaments, and the spatial theory of politics. We allow for uncountably infinite strategy spaces, and as a special case, we obtain a long-standing claim to the same effect, due to R. McKelvey (Amer. J. Polit. Sci.30 (1986), 283–314), in the political science literature. Further, we prove the nonemptiness of the uncovered set under quite general assumptions, and we establish, under various assumptions, the coanalyticity and measurability of this set. In the concluding section, we indicate how the inclusion result may be extended to multiplayer, non-zero-sum games.

Additional Information

© 2001 Elsevier Science (USA). Received October 18, 1998; final version received March 28, 2001; published online November 7, 2001. Jeff Banks passed away on December 21, 2000. The second and third authors express their respect and admiration for Jeff as a colleague and dear friend. His contributions to our profession, great as they were, were cut unduly short. We will miss him. We thank an anonymous referee for constructive comments.

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August 21, 2023
October 18, 2023