Advanced Search
MyIDEAS: Login to save this paper or follow this series

Competition For A Majority

Contents:

Author Info

  • PAULO BARELLI
  • SRIHARI GOVINDAN
  • ROBERT WILSON

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.

(This abstract was borrowed from another version of this item.)

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.dklevine.com/archive/refs4786969000000000445.pdf
Download Restriction: no

Bibliographic Info

Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 786969000000000445.

as in new window
Length:
Date of creation: 16 Jun 2012
Date of revision:
Handle: RePEc:cla:levarc:786969000000000445

Contact details of provider:
Web page: http://www.dklevine.com/

Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
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.:
as in new window
  1. Brian Roberson & Dmitriy Kvasov, 2012. "The non-constant-sum Colonel Blotto game," Economic Theory, Springer, Springer, vol. 51(2), pages 397-433, October.
  2. Roger B. Myerson & Daniel Diermeier, 1999. "Bicameralism and Its Consequences for the Internal Organization of Legislatures," American Economic Review, American Economic Association, American Economic Association, vol. 89(5), pages 1182-1196, December.
  3. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, Econometric Society, vol. 67(5), pages 1029-1056, September.
  4. Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp434, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  5. Duggan, John, 2007. "Equilibrium existence for zero-sum games and spatial models of elections," Games and Economic Behavior, Elsevier, Elsevier, vol. 60(1), pages 52-74, July.
  6. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, Elsevier, vol. 136(1), pages 738-748, September.
  7. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, Springer, vol. 29(1), pages 1-24, September.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Capraro, Valerio & Scarsini, Marco, 2013. "Existence of equilibria in countable games: An algebraic approach," Games and Economic Behavior, Elsevier, Elsevier, vol. 79(C), pages 163-180.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:cla:levarc:786969000000000445. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (David K. Levine).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.