WASHINGTON UNIV SEATTLE LAB OF STATISTICAL RESEARCH
The paper deals with an attack-defense game in which there are targets for both attacker and defender. There are two versions of the game, discrete and continuous. After these have been discussed, the relation of past research to the game is described. The discrete game is considered in detail and is divided into two cases, fixed target and mobile target for the attacker. In the first, the attackers target is stationary and in the second, the target is mobile. In both cases, expressions for probabilities of victory by either players and termination at each move are derived inductively. The strategies are then examined for the fixed target case along with some payoff kernels. Some strategies, such as the instance where the attacker is ballistic, are considered for the discrete game. Finally, the extension of the results obtained earlier in the paper to the continuous version of the game is discussed.