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Nash on a rotary : two theorems with implications for electoral politics

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  • Basu,Kaushik
  • Mitra,Tapan

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.

Suggested Citation

  • Basu,Kaushik & Mitra,Tapan, 2016. "Nash on a rotary : two theorems with implications for electoral politics," Policy Research Working Paper Series 7701, The World Bank.
  • Handle: RePEc:wbk:wbrwps:7701
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    References listed on IDEAS

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    1. Martin J. Osborne, 1995. "Spatial Models of Political Competition under Plurality Rule: A Survey of Some Explanations of the Number of Candidates and the Positions They Take," Canadian Journal of Economics, Canadian Economics Association, vol. 28(2), pages 261-301, May.
    2. Richard Schmalensee, 1978. "Entry Deterrence in the Ready-to-Eat Breakfast Cereal Industry," Bell Journal of Economics, The RAND Corporation, vol. 9(2), pages 305-327, Autumn.
    3. Steven C. Salop, 1979. "Monopolistic Competition with Outside Goods," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 141-156, Spring.
    4. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65, pages 135-135.
    5. Matsushima, Noriaki, 2001. "Cournot competition and spatial agglomeration revisited," Economics Letters, Elsevier, vol. 73(2), pages 175-177, November.
    6. repec:cup:apsrev:v:57:y:1963:i:02:p:368-377_24 is not listed on IDEAS
    7. Pal, Debashis, 1998. "Does Cournot competition yield spatial agglomeration?," Economics Letters, Elsevier, vol. 60(1), pages 49-53, July.
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    Keywords

    Peace&Peacekeeping;

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