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All-pay 2 $$\times $$ × 2 Hex: a multibattle contest with complementarities

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  • Dan Kovenock
  • Sudipta Sarangi
  • Matt Wiser

Abstract

We examine a modified 2 $$\times $$ × 2 game of Hex in which the winner of each cell is determined by a Tullock contest. The player establishing a winning path of cells in the game wins a fixed prize. Examining the polar cases of all cells being contested simultaneously versus all four cells being contested sequentially, we show that there is an increase in the total expected payoff for the players in the sequential case. We identify conditions under which players have identical and non-identical expected payoffs when the contest order is pre-specified. We also examine dissipation for random order contests. We thus provide a canonical model of a multibattle contest in which complementarities between battlefields are heterogeneous across both battlefields and players. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Dan Kovenock & Sudipta Sarangi & Matt Wiser, 2015. "All-pay 2 $$\times $$ × 2 Hex: a multibattle contest with complementarities," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(3), pages 571-597, August.
    • Handle: RePEc:spr:jogath:v:44:y:2015:i:3:p:571-597
    DOI: 10.1007/s00182-014-0445-7
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    Cited by:

    1. Nicolas Houy & Jean-Philippe Nicolaï & Marie Claire Villeval, 2020. "Always doing your best? Effort and performance in dynamic settings," Theory and Decision, Springer, vol. 89(3), pages 249-286, October.
    2. Ewerhart, Christian & Valkanova, Kremena, 2020. "Fictitious play in networks," Games and Economic Behavior, Elsevier, vol. 123(C), pages 182-206.
    3. Dan Kovenock & Brian Roberson, 2015. "The Optimal Defense of Network Connectivity," Working Papers 15-24, Chapman University, Economic Science Institute.
    4. Cortes-Corrales, Sebastián & Gorny, Paul M., 2018. "Generalising Conflict Networks," MPRA Paper 90001, University Library of Munich, Germany.

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    More about this item

    Keywords

    Contests; All-pay auctions; Multibattle; Complementarity; Hex; C72; C73; D72; D74;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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