Question

Consider the following story:
Woody loves bowling, and he also loves Beth.
Woody does not particularly like the beach.
The best outcome for Woody is to be at the bowling alley with Beth.
Given the choice of going bowling alone or being at the beach with Beth, Woody would choose to be with Beth.
The worst outcome for Woody is to be at the beach alone.
Beth loves the beach, and she also loves Woody.
Beth does not particularly like bowling.
The best outcome for Beth is to be at the beach with Woody.
Given the choice of going to the beach alone or bowling with Woody, Beth would choose to be with Woody.
The worst outcome for Beth is to be at the bowling alley alone. Woody and Beth plan to meet after work, but each has forgotten where. Suppose the following payoff matrix tells the story, given Woody and Beth's preferences above.
Complete the matrix by filling in the missing payoffs. (Enter your responses as integers.)
Beth
Bowling Beach
Woody Bowling
Beach
a. Find all Nash equilibria in this game, if any.
b. Is this game an archetype? If yes, identify the archetype and explain your selection.

Answer 1

Answer:

a. Both beth and Woody are comfortable at their own preferences and feel dominant in their own strategy.

The outcome to meet somewhere will be either the bowling alley or the beach, any one of Beth and Woody will dominate, however both's priority is to stay together which is fulfilled in both the scenarios.

Explanation:

a. Both beth and Woody are comfortable at their own preferences and feel dominant in their own strategy.

The outcome to meet somewhere will be either the bowling alley or the beach, any one of Beth and Woody will dominate, however both's priority is to stay together which is fulfilled in both the scenarios.