Competition For A Majority
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 such games, we establish sufficient conditions for existence of a value of the game, maximin and minimax strategies for the players, and a Nash equilibrium. If all discontinuities favor one player, then a value exists and that player has a maximin strategy. A property called payoff approachability implies existence of an equilibrium, and that the resulting value is invariant: games with the same payoffs at points of continuity have the same value and ɛ‐equilibria. For voting games in which two candidates propose policies and a candidate wins election if a weighted majority of voters prefer his proposed policy, we provide tie‐breaking rules and assumptions about voters' preferences sufficient to imply payoff approachability. These assumptions are satisfied by generic preferences if the dimension of the space of policies exceeds the number of voters; or with no dimensional restriction, if the electorate is sufficiently large. Each Colonel Blotto game is a special case in which each candidate allocates a resource among several constituencies and a candidate gets votes from those allocated more than his opponent offers; in this case, for simple‐majority rule we prove existence of an equilibrium with zero probability of ties.
(This abstract was borrowed from another version of this item.)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Duggan, John, 2007. "Equilibrium existence for zero-sum games and spatial models of elections," Games and Economic Behavior, Elsevier, vol. 60(1), pages 52-74, July.
- Brian Roberson & Dmitriy Kvasov, 2012.
"The non-constant-sum Colonel Blotto game,"
Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 397-433, October.
- Brian Roberson & Dmitriy Kvasov, 2008. "The Non-Constant-Sum Colonel Blotto Game," CESifo Working Paper Series 2378, CESifo Group Munich.
- Brian Roberson & Dmitriy Kvasov, 2010. "The Non-Constant-Sum Colonel Blotto Game," School of Economics Working Papers 2010-31, University of Adelaide, School of Economics.
- Brian Roberson & Dmitriy Kvasov, 2010. "The Non-Constant-Sum Colonel Blotto Game," Purdue University Economics Working Papers 1252, Purdue University, Department of Economics.
- Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 1-24, September.
- Roger B. Myerson & Daniel Diermeier, 1999. "Bicameralism and Its Consequences for the Internal Organization of Legislatures," American Economic Review, American Economic Association, vol. 89(5), pages 1182-1196, December.
- Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
- Sergiu Hart, 2008. "Discrete Colonel Blotto and General Lotto games," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 441-460, March.
- Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Levine's Bibliography 321307000000000532, UCLA Department of Economics.
- Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Discussion Paper Series dp434, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
- Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September. Full references (including those not matched with items on IDEAS)