Competition for a Majority

Paulo Barelli, Srihari Govindan and Robert Wilson ()

Research Papers from Stanford University, Graduate School of Business

Abstract: We define the class of two-player zero-sum games with payoffs having mild discontinuities, which in applications typically stem from how ties are resolved. For games in this class we establish sufficient conditions for existence of a value of the game and minimax or Nash equilibrium strategies for the players. We prove first that if all discontinuities favor one player then a value exists and that player has a minimax strategy. Then we establish that a general property called payoff approachability implies that the value results from equilibrium. We prove further that this property implies that every modification of the discontinuities yields the same value; in particular, for every modification, epsilon-equilibria exist. We apply these results to models of elections in which two candidates propose policies and a candidate wins election if a weighted majority of voters prefer his policy. We provide tie-breaking rules and assumptions on voters' preferences sufficient to imply payoff approachability, hence existence of equilibria, and each other tie-breaking rule yields the same value and has epsilon-equilibria. These conclusions are also derived for the special case of Colonel Blotto games in which each candidate allocates his available resources among several constituencies and the assumption on voters' preferences is that a candidate gets votes from those constituencies allocated more resources than his opponent offers. Moreover, for the case of simple-majority rule we prove existence of an equilibrium that has zero probability of ties.

JEL-codes: C62 C72 D72 (search for similar items in EconPapers)
Date: 2012-06
New Economics Papers: this item is included in nep-cdm, nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (10)

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Related works:
Journal Article: Competition for a Majority (2014)
Working Paper: COMPETITION FOR A MAJORITY (2012)
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