An attack group commander has a single plane which can strike only one of three possible targets.The defender’s commander has one anti?aircraft missile battery that can be assigned to only one of the targets. The plane will fail in its assignment if it attacks a defended target. If the attacked target is undefended, it is destroyed. The number of enemy troops at the three targets is 5, 4 and 1, respectively.The attacker wishes to maximize the defender’s expected losses, so his payoff is the number of enemy casualties, while the defender wishes to minimize the expected troop losses, so his payoff is minus the number of casualties.
What is the normal form of the game? and how to find all equilibria (pure and mixed)?
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