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The N-Player War of Attrition in the Limit of Infinitely Many Players

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  • Peter Helgesson
  • Bernt Wennberg

Abstract

The War of Attrition is a classical game theoretic model that was first introduced to mathematically describe certain non-violent animal behavior. The original setup considers two participating players in a one-shot game competing for a given prize by waiting. This model has later been extended to several different models allowing more than two players. One of the first of these $$N$$ N -player generalizations was due to Haigh and Cannings (Acta Appl Math 14:59–74, 1989 ) where two possible models are mainly discussed; one in which the game starts afresh with new strategies each time a player leaves the game, and one where the players have to stick with the strategy they chose initially. The first case is well understood whereas, for the second case, much is still left open. There are two main results in this paper. The first concerns the asymptotic behavior of the models as the number of players tend to infinity. In particular, we prove that the time evolution of the models coincide in the limit, thus providing a link between the two in the regime of infinitely many players. Secondly we prove, under certain conditions, existence and uniqueness of an ESS in the second model for any given number of players. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Peter Helgesson & Bernt Wennberg, 2015. "The N-Player War of Attrition in the Limit of Infinitely Many Players," Dynamic Games and Applications, Springer, vol. 5(1), pages 65-93, March.
  • Handle: RePEc:spr:dyngam:v:5:y:2015:i:1:p:65-93
    DOI: 10.1007/s13235-014-0110-6
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    References listed on IDEAS

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    1. Paul Klemperer, 2004. "Auctions: Theory and Practice," Online economics textbooks, SUNY-Oswego, Department of Economics, number auction1.
    2. Paul Klemperer & Jeremy Bulow, 1999. "The Generalized War of Attrition," American Economic Review, American Economic Association, vol. 89(1), pages 175-189, March.
    3. Balder, Erik J, 1995. "A Unifying Approach to Existence of Nash Equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(1), pages 79-94.
    4. Guilherme Carmona, 2004. "Nash equilibria of games with a continuum of players," Nova SBE Working Paper Series wp466, Universidade Nova de Lisboa, Nova School of Business and Economics.
    5. Paul Klemperer, 2004. "Auctions: Theory and Practice," Online economics textbooks, SUNY-Oswego, Department of Economics, number auction1.
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    Cited by:

    1. D. Timothy Bishop & Mark Broom & Richard Southwell, 2020. "Chris Cannings: A Life in Games," Dynamic Games and Applications, Springer, vol. 10(3), pages 591-617, September.
    2. Yi Zheng, 2020. "Non-organized boycott: alliance advantage and free riding incentives in uneven wars of attrition," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 10(1), pages 123-141, March.

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