Stag hunt contests and alliance formation


We consider a three-party game of conflict with potential alliance formation, introducing the concept of a stag hunt alliance and using the concept as a novel solution to the alliance formation puzzle in contests. In a stag hunt alliance, allied inputs interact as (multiplicative) complements in the contest success function, reflecting the idea that allied efforts are coordinated and targeted against non-allies. Allowing for asymmetry among conflicting parties, we find conditions for stable alliance formation and show that, in some circumstances, the formation of an alliance can improve the expected payoffs of both the allied and unallied parties relative to unallied conflict. At the same time, the expected payoffs of allied parties also can be greater than their payoffs under a three-party exogenous settlement division without conflict. Hence, the ability to form stag hunt alliances may not simply change conflict structures, but may sometimes generate conflict when settlements are possible. Our results depend on how allies divide the contest prize in the event of victory, and we consider both the case of exogenous division according to a pre-specified rule and endogenous division in a second-stage intra-alliance contest. We also show that the threat of the latter can be used to establish an intuitive exogenous rule by simple bargaining. Finally, we specify conditions that determine which parties choose to ally with one another.

This is a preview of subscription content, log in to check access.

Fig. 1


  1. 1.

    The terms “contest” and “conflict” are used interchangeably herein.

  2. 2.

    That feature follows the general notion of strategic substitutes and complements originating from Bulow et al. (1985), since we treat allies as if they engage in a non-cooperative game environment even when in an alliance. In equilibrium, the additive alliance CSF then results in an outcome in which an increase in one ally’s efforts provides a direct incentive for the other to reduce theirs; the multiplicative form on the other hand has supermodular properties, so an increase in one ally’s effort increases the incentive for the other ally to provide effort.

  3. 3.

    Boudreau et al. (2017) show that noise in the CSF can also reduce substitutability in order to solve for \(s_{i}^{*}\) or \(s_{j}^{*}\) uniquely.

  4. 4.

    We thank an anonymous reviewer for their help in streamlining this proof.

  5. 5.

    See the seminal work on collective rent seeking by Nitzan (1991), or see Flammand and Troumpounis (2014) for an excellent survey of sharing rules.


  1. Baik, K. H., Kim, I. G., & Na, S. (2001). Bidding for a group-specific public-good prize. Journal of Public Economics, 82(3), 415–429.

    Article  Google Scholar 

  2. Baik, K. H., & Lee, S. (1998). Group rent seeking with sharing. In M. R. Baye (Ed.), Advances in applied microeconomics: Contests (pp. 75–85). Stamford, CT: JAI Press.

    Google Scholar 

  3. Boudreau, J. W., Rentschler, L., & Sanders, S. (2017). On the evolution of prize perceptions in contests. Working Paper.

  4. Bulow, J., Geanakoplos, J., & Klemperer, P. (1985). Multimarket oligopoly: Strategic substitutes and complements. Journal of Political Economy, 93(3), 488–511.

    Article  Google Scholar 

  5. Esteban, J., & Ray, D. (2001). Social decision rules are not immune to conflict. Economics of Governance, 2(1), 59–67.

    Article  Google Scholar 

  6. Esteban, J., & Sákovics, J. (2003). Olson vs. coase: Coalitional worth in conflict. Theory and Decision, 55(4), 339–357.

    Article  Google Scholar 

  7. Flammand, S., & Troumpounis, O. (2014). Prize-sharing rules in collective rent-seeking. Working paper.

  8. Garfinkel, M. R. (2004). On the stability of group formation: Managing the conflict within. Conflict Management and Peace Science, 21(1), 43–68.

    Article  Google Scholar 

  9. Katz, E., Nitzan, S., & Rosenberg, J. (1990). Rent-seeking for pure public goods. Public Choice, 65(1), 49–60.

    Article  Google Scholar 

  10. Ke, C., Konrad, K., & Morath, F. (2013). Brothers in arms—An experiment on the alliance puzzle. Games and Economic Behavior, 77(1), 61–76.

    Article  Google Scholar 

  11. Konrad, K. (2004). Bidding in hierarchies. European Economic Review, 48(6), 1301–1308.

    Article  Google Scholar 

  12. Konrad, K. (2009). Strategy and dynamics in contests. New York, NY: Oxford University Press.

    Google Scholar 

  13. Konrad, K., & Kovenock, D. (2009). The alliance formation puzzle and capacity constraints. Economics Letters, 103, 84–86.

    Article  Google Scholar 

  14. Kovenock, D., & Roberson, B. (2012). Coalitional colonel blotto games with application to the economics of alliances. Journal of Public Economic Theory, 14(4), 653–676.

    Article  Google Scholar 

  15. Lynch, D. (2014). Islamic state in kobani–u.s. coalition airstrikes more effective after coordination with kurdish forces. International Business Times.

  16. Milgrom, P., & Roberts, J. (1990). Rationalizability, learning, and equilibrium in games with strategic complementarities. Econometrica, 58(6), 1255–1277.

    Article  Google Scholar 

  17. Nitzan, S. (1991). Collective rent dissipation. Economic Journal, 101, 1522–1534.

    Article  Google Scholar 

  18. Skaperdas, S. (1998). On the formation of alliances in conflict and contests. Public Choice, 96(1–2), 25–42.

    Article  Google Scholar 

  19. Tullock, G. (1980). Efficient rent seeking. In J. M. Buchanan, R. D. Tollison, & G. Tullock (Eds.), Toward a theory of rent-seeking society (pp. 97–112). College Station, TX: Texas A&M University Press.

    Google Scholar 

  20. Vives, X. (1990). Nash equilibrium with strategic complementarities. Journal of Mathematical Economics, 19(3), 305–321.

    Article  Google Scholar 

  21. Wärneryd, K. (1998). Distributional conflict and jurisdictional organization. Journal of Public Economics, 69(3), 435–450.

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to James W. Boudreau.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Boudreau, J.W., Rentschler, L. & Sanders, S. Stag hunt contests and alliance formation. Public Choice 179, 267–285 (2019).

Download citation


  • Alliance
  • Coalition
  • Conflict
  • Contest
  • Stag hunt
  • Free-ridership
  • Rent dissipation

JEL Classification

  • C71
  • C72
  • D72
  • D74