We formulate and study a two-player static duel game as a nonzero-sum
discounted stochastic game. Players P1β,P2β are standing in place and, in
each turn, one or both may shoot at the other player. If Pnβ shoots at
Pmβ (mξ =n), either he hits and kills him (with probability pnβ) or
he misses him and Pmβ is unaffected (with probability 1βpnβ). The
process continues until at least one player dies; if nobody ever dies, the game
lasts an infinite number of turns. Each player receives unit payoff for each
turn in which he remains alive; no payoff is assigned to killing the opponent.
We show that the the always-shooting strategy is a NE but, in addition, the
game also possesses cooperative (i.e., non-shooting) Nash equilibria in both
stationary and nonstationary strategies. A certain similarity to the repeated
Prisoner's Dilemma is also noted and discussed