ON A THREE-PERSON SILENT MARKSMANSHIP CONTEST

Abstract

In this paper, we consider a three-person silent marksmanship contest. Each of three players 1 , 2 and 3 has a gun with exactly one bullet which may be fired at any time on [0, 1] aiming at his own target. The accuracy function A_i(x) for player i is strictly increasing and differentiable with A_i(0) = 0 and A_i(1) = 1 . The first player hitting his target gets payoff +1 and other two players get payoff zero. For the game, we get a Nash equilibrium point and equilibrium payoff for each player. The form of the Nash equilibrium point differs whether A _1(x)/A_2(x)A_3(x), A_2(x)/A_1(x)A_3 (x) and A_3(x)/A _1(x)A_2(x) decrease or one of these increases. Some examples are given to illustrate the results.