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

Basu, Kaushik ; Mitra, Tapan

World Bank, Washington, DC

关键词: OPEN ACCESS;    COMMON;    CHOICE;    GOODS;    THEORY;   

DOI  :  10.1596/1813-9450-7701
RP-ID  :  WPS7701

学科分类：社会科学、人文和艺术（综合）

来源: World Bank Open Knowledge Repository

【 摘 要 】

The paper provides a completecharacterization of Nash equilibria for games in which ncandidates choose a strategy in the form of a platform, eachfrom a circle of feasible platforms, with the aim ofmaximizing the stretch of the circle from where thecandidate’s platform will receive support from the voters.Using this characterization, it is shown that if the sum ofall players’ payoffs is 1, the Nash equilibrium payoff ofeach player in an arbitrary Nash equilibrium must berestricted to the interval [1/2(n − 1), 2/(n + 1)]. Thisimplies that in an election with four candidates, acandidate who is attracting less than one-sixth of thevoters can do better by changing his or her strategy.