Economic Analysis of Social Issues 1st Edition by Alan Grant

Exercise 14

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 me 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. Add payoffs to the following matrix to tell the story, given Woody and Beth's preferences:

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.