Advertisement

Social Choice and Welfare

, Volume 40, Issue 4, pp 937–956 | Cite as

The robustness of ‘enemy-of-my-enemy-is-my-friend’ alliances

  • David Rietzke
  • Brian RobersonEmail author
Original Paper

Abstract

We examine a three-player, three-stage game of alliance formation followed by multi-battle conflict. There are two disjoint sets of battlefields, each of which is associated with a player who competes only within that set. The common enemy competes in both sets of battlefields. An ‘enemy-of-my-enemy-is-my-friend’ alliance forms when the two players facing the common enemy agree on a pre-conflict transfer of resources among themselves. We examine the case in which the players may commit to binding ex post transfers (alliances with full commitment) and the case in which ex post transfers are not feasible (self-enforcing alliances). Models that utilize the lottery contest success function typically yield qualitatively different results from those arising in models with the auction contest success function. However, under both contest success functions, alliances with full commitment result in identical alliance transfers for all parameter configurations, and self-enforcing alliances yield identical transfers over a subset of the parameter space. Our results, thus, provide a partial robustness result for ‘enemy-of-my-enemy-is-my-friend’ alliances.

Keywords

Subgame Perfect Equilibrium Marginal Return Alliance Formation Contest Success Function Incentive Compatibility Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alcalde J, Dahm M (2009) Rent seeking and rent dissipation: a neutrality result. J Public Econ 94: 1–7CrossRefGoogle Scholar
  2. Anesi V (2009) Moral Hazard and free riding in collective action. Soc Choice Welf 32: 197–219CrossRefGoogle Scholar
  3. Anesi V, De Donder P (2011) Secondary issues and party politics: an application to environmental policy. Soc Choice Welf 36: 519–546CrossRefGoogle Scholar
  4. Arce MDG, Sandler T (2001) A cooperative game theory of noncontiguous allies. J Public Econ Theory 3: 391–411CrossRefGoogle Scholar
  5. Baye MR, Kovenock D, de Vries CG (1993) Rigging the lobbying process: an application of the all-pay auction. Am Econ Rev 83: 289–294Google Scholar
  6. Baye MR, Kovenock D, de Vries CG (1994) The solution to the Tullock rent-seeking game when R > 2: mixed strategy equilibria and mean dissipation rates. Public Choice 81: 363–380CrossRefGoogle Scholar
  7. Baye MR, Kovenock D, de Vries CG (1996) The all-pay auction with complete information. Econ Theory 8: 291–305Google Scholar
  8. Bloch F (2010) Endogenous formation of alliances in conflicts. In: Garfinkel M, Skaperdas S (eds) Handbook of the economics of peace and conflict. Oxford University Press, OxfordGoogle Scholar
  9. Borel E (1921) La théorie du jeu les équations intégrales à à noyau symétrique, Comptes Rendus de l’Académie, 173, 1304–1308; (English translation by Savage L (1953) The theory of play and integral equations with skew symmetric kernels. Econometrica 21:97–100)Google Scholar
  10. Bossert W, Brams S, Kilgour M (2002) Cooperative vs. non-cooperative truels: little agreement, but does that matter?. Games Econ Behav 40: 185–202CrossRefGoogle Scholar
  11. Che YK, Gale I (1998) Caps on political lobbying. Am Econ Rev 88: 643–651Google Scholar
  12. Clark D, Konrad K (2007) Asymmetric conflict: weakest link against best shot. J Confl Resol 51: 457–469CrossRefGoogle Scholar
  13. Dimico A, Seidmann D (2010) Patterns of conflict and preventive attacks. Working paperGoogle Scholar
  14. Dziubiński M (2011) Non-symmetric discrete General Lotto games. Working paper, University of WarsawGoogle Scholar
  15. Fang H (2002) Lottery versus all-pay auction models of lobbying. Public Choice 112: 351–371CrossRefGoogle Scholar
  16. Finus M, Rundshagen B (2009) Membership rules and stability of coalition structures in positive externality games. Soc Choice Welf 32: 389–406CrossRefGoogle Scholar
  17. Friedman L (1958) Game-theory models in the allocation of advertising expenditures. Oper Res 6: 699–709CrossRefGoogle Scholar
  18. Golman R, Page SE (2009) General Blotto: games of strategic allocative mismatch. Public Choice 138: 279–299CrossRefGoogle Scholar
  19. Hart S (2008) Discrete Colonel Blotto and general lotto games. Int J Game Theory 36: 441–460CrossRefGoogle Scholar
  20. Hiller T (2011) Alliance formation and coercion in networks. Fondazione Eni Enrico Mattei working paper no. 593Google Scholar
  21. Hillman A, Riley J (1989) Politically contestable rents and transfers. Econ Polit 1: 17–39CrossRefGoogle Scholar
  22. Hortala-Vallve R, Llorente-Saguer A (2011) Pure-strategy Nash equilibria in non-zero sum Colonel Blotto games. Int J Theory. doi: 10.1007/s00182-011-0288-4
  23. Ihori T, McGuire MC (2007) Collective risk control and group security: the unexpected consequences of differential risk aversion. J Public Econ Theory 9: 231–263CrossRefGoogle Scholar
  24. Kilgour D, Brams S (1997) The truel. Math Mag 70: 315–326CrossRefGoogle Scholar
  25. Klumpp T, Polborn M (2006) Primaries and the New Hampshire effect. J Public Econ 90: 1073–1114CrossRefGoogle Scholar
  26. Konrad KA (2009) Strategy and dynamics in contests. Oxford University Press, New YorkGoogle Scholar
  27. Konrad KA, Kovenock D (2009) Multi-battle contests. Games Econ Behav 66: 256–274CrossRefGoogle Scholar
  28. Kovenock D, Mauboussin MJ, Roberson B (2010) Asymmetric conflicts with endogenous dimensionality. Korean Econ Rev 26: 287–305Google Scholar
  29. Kovenock D, Roberson B (2010a) Conflicts with multiple battlefields. In: Garfinkel M, Skaperdas S (eds) Handbook of the economics of peace and conflict. Oxford University Press, OxfordGoogle Scholar
  30. Kovenock D, Roberson B (2010b) The optimal defense of networks of targets. Purdue University working paper no. 1251Google Scholar
  31. Kovenock D, Roberson B (2010c) Coalitional Colonel Blotto games with application to the economics of alliances. J. Public Econ. Theory (forthcoming)Google Scholar
  32. Kvasov D (2007) Contests with limited resources. J Econ Theory 136: 738–748CrossRefGoogle Scholar
  33. Laslier JF (2003) Party objectives in the ‘divide-a-dollar’ electoral competition. In: Austen-Smith D, Duggan J (eds) Social choice and strategic decisions: essays in honor of Jeffrey S. Banks. Springer, BerlinGoogle Scholar
  34. Macdonell ST, Mastronardi N (2011) Waging simple wars: a complete characterization of two battlefield Blotto equilibria. Working paper, University of TexasGoogle Scholar
  35. Murdoch JC, Sandler T (1982) A theoretical and empirical analysis of NATO. J Confl Resol 26: 237–263CrossRefGoogle Scholar
  36. Murdoch JC, Sandler T (1984) Complementarity, free riding, and the military expenditures of NATO allies. J Publ Econ 25: 83–101CrossRefGoogle Scholar
  37. Olson M (1965) The logic of collective action. Harvard University Press, Cambridge, MAGoogle Scholar
  38. Olson M, Zeckhauser R (1966) An economic theory of alliances. Rev Econ Stat 48: 266–279CrossRefGoogle Scholar
  39. Roberson B (2006) The Colonel Blotto game. Econ Theory 29: 1–24CrossRefGoogle Scholar
  40. Roberson B, Kvasov D (2011) The non-constant-sum Colonel Blotto game. Econ Theory. doi: 10.1007/s00199-011-0673-z
  41. Robson ARW (2005) Multi-item contests, Australian National University. Working papers in economics and econometrics no. 446Google Scholar
  42. Sandler T (1977) Impurity of defense: an application to the economics of alliances. Kyklos 30: 443–460CrossRefGoogle Scholar
  43. Sandler T (1999) Alliance formation, alliance expansion, and the core. J Confl Resol 43: 727–747CrossRefGoogle Scholar
  44. Sandler T, Cauley J (1975) On the economic theory of alliances. J Confl Resol 19: 330–348CrossRefGoogle Scholar
  45. Shubik M (1954) Does the fittest necessarily survive? Shubik M (ed) Readings in game theory and political behavior. Doubleday, Garden CityGoogle Scholar
  46. Skaperdas S (1998) On the formation of alliances in conflict and contests. Public Choice 96: 25–42CrossRefGoogle Scholar
  47. Snyder J (1989) Election goals and the allocation of campaign resources. Econometrica 57: 637–660CrossRefGoogle Scholar
  48. Szentes B, Rosenthal RW (2003) Beyond chopsticks: symmetric equilibria in majority auction games. Games Econ Beha 45: 278–295CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of ArizonaTucsonUSA
  2. 2.Department of EconomicsKrannert School of Management, Purdue UniversityWest LafayetteUSA

Personalised recommendations