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The Duel Discounted Stochastic Game

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  • Athanasios Kehagias

    (Aristotle University of Thessaloniki)

Abstract

A duel involves two stationary players who shoot at each other until at least one of them dies; a truel is similar but involves three players. In the past, the duel has been studied mainly as a component of the truel, which has received considerably more attention. However we believe that the duel is interesting in itself. In this paper we formulate the duel (with either simultaneous or sequential shooting) as a discounted stochastic game. We show that this game has a unique Nash equilibrium in stationary strategies; however, it also possesses cooperation-promoting Nash equilibria in nonstationary strategies. We show that these are also subgame perfect equilibria. Finally, we argue that the nature of the game and its equilibria is similar to that of the repeated Prisoner’s dilemma.

Suggested Citation

  • Athanasios Kehagias, 2024. "The Duel Discounted Stochastic Game," Dynamic Games and Applications, Springer, vol. 14(4), pages 846-864, September.
    • Handle: RePEc:spr:dyngam:v:14:y:2024:i:4:d:10.1007_s13235-023-00540-9
    DOI: 10.1007/s13235-023-00540-9
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    References listed on IDEAS

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    1. Bossert, Walter & Brams, Steven J. & Kilgour, D. Marc, 2002. "Cooperative vs non-cooperative truels: little agreement, but does that matter?," Games and Economic Behavior, Elsevier, vol. 40(2), pages 185-202, August.
    2. Michael Wegener & Evla Mutlu, 2021. "The good, the bad, the well-connected," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(3), pages 759-771, September.
    3. Brams, S. J. & Kilgour, M. D., 2001. "Games That End in a Bang or a Whimper," Working Papers 01-05, C.V. Starr Center for Applied Economics, New York University.
    Full references (including those not matched with items on IDEAS)

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