Sam and Billy are two young men both interested in dating the fair Courtney who
ID: 1208860 • Letter: S
Question
Sam and Billy are two young men both interested in dating the fair Courtney who lives in her own apartment. They are the last two people at a party she has hosted, and they each want a chance to be alone with her to tell her how much she means to them. If they are both there, neither one of them says anything, and as long as they are waiting they just are wasting their time. On the other hand, if they both leave, they gain or lose nothing.
a) In the game payoffs below Billy and Sam don’t care if the other person gets to share their feelings with Courtney. Find any Nash equilibria in this game. Does your solution make sense? That is, would two guys behave this way?
BILLY
SAM
Stay
Leave
Stay
-5, -5
100, 0
Leave
0, 75
0, 0
b) Below is another set of payoffs. What do these payoffs say about the attitudes of Sam and Billy? What is the equilibrium now?
BILLY
SAM
Stay
Leave
Stay
-5, -5
100, -75
Leave
-100, 75
0, 0
BILLY
SAM
Stay
Leave
Stay
-5, -5
100, 0
Leave
0, 75
0, 0
Explanation / Answer
a) Neither Sam nor Billiy has no dominant strategy so there will be no Nash equilibrium in this case. They both are not able to decide there own move and are just waiting for other person to take decision about leaving or staying.
b) Now both Sam and Billy have dominant strategy i.e. to stay so the Nash equilibrium here wull be that they both will stay. This tells us that they both are just determined to be with her and not letting other person decide what they should do.
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