1. Army A has a single plane with which it can strike one of three possible targets. Army B has one anti-aircraft gun that can be assigned to one of the targets in defence. Army A wishes to maximize the expected value of the damage and army B wishes to minimize it.

The value of target k for each player is v_k, with v₁>v₂>v₃>0. Note: For simplicity assume v1=1, v2=2 and v3=3 for each player.

Army A can destroy a target only if the target is undefended and A attacks it. In this case the payoffs will be (v_{k, -} v_k) respectively for Players A and B. If B successfully defends a target, the payoffs are 0 for each player.

Formulate the situation as a strategic game and solve for all Nash equilibrium/ia.

Hint: Army A has 3 strategies: Attack 1, Attack 2, and Attack 3. Army B has 3 strategies: Defend 1, Defend 2, and Defend 3.

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2. Consider the games depicted below. Player 2 knows which game is being played but player 1 does not. Player 1 believes that with probability 3/4 Game 1 is being played. Solve for all pure Bayes Nash equilibria.

1\2	L	R		1\2	L	R
U	2,1	2,3		U	6,9	-10,-5
D	-1,2	-2,1		D	7,-10	14,5
Game 1				Game2