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On the Nash Equilibria of a Duel with Terminal Payoffs

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  • Athanasios Kehagias

    (Department of Electrical and Computer Engineering, Aristotle University, 54124 Thessaloniki, Greece)

Abstract

We formulate and study a two-player duel game as a terminal payoffs stochastic game. Players P 1 , P 2 are standing in place and, in every turn, each may shoot at the other (in other words, abstention is allowed). If P n shoots P m ( m ≠ n ), either they hit and kill them (with probability p n ) or they miss and P m is unaffected (with probability 1 − p n ). The process continues until at least one player dies; if no player ever dies, the game lasts an infinite number of turns. Each player receives a positive payoff upon killing their opponent and a negative payoff upon being killed. We show that the unique stationary equilibrium is for both players to always shoot at each other. In addition, we show that the game also possesses “ cooperative ” (i.e., non-shooting) non-stationary equilibria . We also discuss a certain similarity that the duel has to the iterated Prisoner’s Dilemma .

Suggested Citation

  • Athanasios Kehagias, 2023. "On the Nash Equilibria of a Duel with Terminal Payoffs," Games, MDPI, vol. 14(5), pages 1-12, September.
    • Handle: RePEc:gam:jgames:v:14:y:2023:i:5:p:62-:d:1244563
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    References listed on IDEAS

    as
    1. 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.
    2. Chakravarty,Satya R. & Mitra,Manipushpak & Sarkar,Palash, 2015. "A Course on Cooperative Game Theory," Cambridge Books, Cambridge University Press, number 9781107058798.
    3. 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.
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