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When Is an Arms Rivalry a Prisoner's Dilemma?

Author

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  • Mark Irving Lichbach

    (University of Illinois at Chicago)

Abstract

This article uses the utility functions from Richardson arms rivalry (R-AR) models to help determine the equilibrium outcomes of 2 × 2 game-theory arms rivalry (GT-AR) models. Three different formulations of a R-AR, one general and two specific, are employed. Four different formulations of a GT-AR, a PD arms rivalry (PD-AR), a Chicken arms rivalry (Chicken-AR), a Deadlock arms rivalry (Deadlock-AR), and a Stag Hunt arms rivalry (Stag Hunt-AR), are also used. I first establish the most general possible restrictions on Richardson-type utility functions that determine the four common 2 × 2 arms rivalry games. I then establish two counterintuitive results: One of the specific formulations of a R-AR may help imply the equilibrium outcomes of a PD- or Deadlock-AR but is inconsistent with the equilibrium outcomes of a Chicken- or Stag Hunt-AR; it is impossible for either specific formulation of a R-AR to ever yield the equilibrium outcome of a Stag Hunt-AR.

Suggested Citation

  • Mark Irving Lichbach, 1990. "When Is an Arms Rivalry a Prisoner's Dilemma?," Journal of Conflict Resolution, Peace Science Society (International), vol. 34(1), pages 29-56, March.
    • Handle: RePEc:sae:jocore:v:34:y:1990:i:1:p:29-56
    DOI: 10.1177/0022002790034001002
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    References listed on IDEAS

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    Cited by:

    1. Sebagh Thierry, 1995. "Recherche De Rente : Jeu de Guerre et Guerre D'enjeux - II," Journal des Economistes et des Etudes Humaines, De Gruyter, vol. 6(2-3), pages 301-320, June.
    2. Juan M. C. Larrosa, 2016. "Arms build-up and arms race in optimal economic growth," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(2), pages 167-182, June.
    3. Sam Perlo-Freeman, 2006. "The Topology of Conflict and Co-operation," Working Papers 0609, Department of Accounting, Economics and Finance, Bristol Business School, University of the West of England, Bristol.

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