On the Nash Equilibria of a Duel with Terminal Payoffs

Athanasios Kehagias ()
Additional contact information
Athanasios Kehagias: Department of Electrical and Computer Engineering, Aristotle University, 54124 Thessaloniki, Greece

Games, 2023, vol. 14, issue 5, 1-12

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 .

Keywords: duel; Nash equilibrium; stochastic games (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2073-4336/14/5/62/pdf (application/pdf)
https://www.mdpi.com/2073-4336/14/5/62/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jgames:v:14:y:2023:i:5:p:62-:d:1244563

Access Statistics for this article

Games is currently edited by Ms. Susie Huang

More articles in Games from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().