Question

4. Suppose two bartenders are developing new cocktails for their bar and are playing a simulta- neous game to come up with fruit combinations.

Bartender 1 can choose berries or limes as the fruit theme and bartender 2 can choose bananas or oranges. They both have to drink the new cocktail they create from mixing their choice of fruit. Based on their preferences, they get the following payoffs for different fruity combinations.

If the cocktail has berries and bananas, bartender 1 gets a payoff of 3 and bartender 2 gets a payoff of 4.

If the cocktail has berries and oranges, bartender 1 gets a payoff of 8 and bartender 2 gets a payoff of 6.

If the cocktail has limes and bananas, bartender 1 gets a payoff of 7 and bartender 2 gets a payoff of 9.

If the cocktail has limes and oranges, bartender 1 gets a payoff of 7 and bartender 2 gets a payoff of 5.

(a) Setup the normal form / simultaneous game. Be sure to label players, actions, and payoffs clearly. (3 points)

(b) Solve for all Nash equilibrium strategies. Be sure to show your work clearly. Explain why the set of actions you identify is a Nash Equilibrium. (5 points)

Answer 1

		Bartender 2
		Bananas	Oranges
Bartender 1	Berries	3,4	8,6
	Limes	7,9	7,5

This is a case of dual Nash Equilibrium as the payoffs (8,6) and (7,9) both maximize the profits for each bartender. This can be thought of as follows- If Bartender 1 chooses berries, it is obvious for bartender 2 to choose oranges (8,6) and when bartender 1 chooses limes, bartender 2 chooses bananas(7,9) . Similarly, when bartender 2 chooses bananas, bartender 1 chooses limes (7,9) and when bartender 2 chooses oranges, bartender 1 chooses berries (8,6). hence both the payoffs are Nash equilibria.