Nash on a Rotary: Two Theorems with Implications for Electoral Politics

31 Pages Posted: 19 Jul 2016

See all articles by Kaushik Basu

Kaushik Basu

Cornell University - Department of Economics; IZA Institute of Labor Economics; Brookings Institution

Tapan Mitra

Cornell University - Department of Economics

Date Written: June 8, 2016

Abstract

The paper provides a complete characterization of Nash equilibria for games in which n candidates choose a strategy in the form of a platform, each from a circle of feasible platforms, with the aim of maximizing the stretch of the circle from where the candidate?s platform will receive support from the voters. Using this characterization, it is shown that if the sum of all players? payoffs is 1, the Nash equilibrium payoff of each player in an arbitrary Nash equilibrium must be restricted to the interval [1/2(n ? 1), 2/(n + 1)]. This implies that in an election with four candidates, a candidate who is attracting less than one-sixth of the voters can do better by changing his or her strategy.

Keywords: Peace & Peacekeeping

Suggested Citation

Basu, Kaushik and Mitra, Tapan, Nash on a Rotary: Two Theorems with Implications for Electoral Politics (June 8, 2016). World Bank Policy Research Working Paper No. 7701. Available at SSRN: https://ssrn.com/abstract=2811348

Kaushik Basu (Contact Author)

Cornell University - Department of Economics ( email )

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IZA Institute of Labor Economics

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Brookings Institution ( email )

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Tapan Mitra

Cornell University - Department of Economics ( email )

414 Uris Hall
Ithaca, NY 14853-7601
United States
607-255-6283 (Phone)

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