Advanced Search
MyIDEAS: Login

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 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.)

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. 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.
  2. Brian Roberson & Dmitriy Kvasov, 2010. "The Non-Constant-Sum Colonel Blotto Game," Purdue University Economics Working Papers 1252, Purdue University, Department of Economics.
  3. Sergiu Hart, 2006. "Discrete Colonel Blotto and General Lotto Games," Discussion Paper Series dp434, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  4. Kvasov, Dmitriy, 2007. "Contests with limited resources," Journal of Economic Theory, Elsevier, vol. 136(1), pages 738-748, September.
  5. 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.
  6. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer, vol. 29(1), pages 1-24, September.
  7. 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)

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, 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.