Country x is planning to attack country y, and country y is anticipating the attack. Country x can either attack by land or by sea. Country y can either prepare for a land defense or a sea defense. Both countries must choose either an all land or all sea strategy, they may not divide their forces. The following are the probabilities of a successful invasion according to both strategies used.
If x launches an attack by sea and y prepares a defense by sea
the probability of a successful invasion is 80%.
If x launches an attack by sea and y prepares a defense by land
the probability of a successful invasion is 100%.
If x launches an attack by land and y prepares a defense by land
the probability of a successful invasion is 60%.
If x launches an attack by land and y prepares a defense by sea
the probability of a successful invasion is 100%.
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What should the strategy of country x be, assuming the goal is to maximize the probability of a successful invasion? Assume the goal of country y to be to minimize the probability of a successful invasion. What is the final probability of a successful invasion assuming both utilize an optimal strategy?
