Symmetric zero-sum games with only asymmetric equilibria
We know that a) two-player symmetric zero-sum games with non-empty equilibrium sets always admit symmetric equilibria and that b) two-player and multiplayer symmetric non-zero-sum games might have only asymmetric equilibria (Fey, 2012). But what about multiplayer symmetric zero-sum games? This paper shows that these games might also have only asymmetric equilibria. One of the examples employed to illustrate this point is the three-candidate version of the popular Hotelling–Downs model of electoral competition. This demonstrates that symmetric games with only asymmetric equilibria are not technical paradoxes but are integrated in economics and political science literature for quite a while.
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References listed on IDEAS
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- Osborne Martin J., 1993.
"Candidate Positioning and Entry in a Political Competition,"
Games and Economic Behavior,
Elsevier, vol. 5(1), pages 133-151, January.
- Martin J. Osborne, 1992. "Candidate Positioning and Entry in a Political Competition," Department of Economics Working Papers 1992-02, McMaster University.
- Fey, Mark, 2012. "Symmetric games with only asymmetric equilibria," Games and Economic Behavior, Elsevier, vol. 75(1), pages 424-427.
- Shaked, A, 1982. "Existence and Computation of Mixed Strategy Nash Equilibrium for 3-Firms Location Problem," Journal of Industrial Economics, Wiley Blackwell, vol. 31(1-2), pages 93-96, September.
- Osborne, Martin J & Pitchik, Carolyn, 1986. "The Nature of Equilibrium in a Location Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 223-237, February. Full references (including those not matched with items on IDEAS)