A multimove infinite game with linear payoff.
An analysis of a multimove infinite game with linear-payoff function. The game is symmetric in every respect except for the initial conditions of the two players, which are different. On each move, each player allocates his resources to tasks of attacking, defending, and scoring. His resources for the next move are diminished by the amount that his opponent's attack exceeds his own defense, while his score cumulates from move to move. The game value and the optimal strategies for the players are derived. It is shown that one player has a pure optimal strategy and that the other player must randomize.