4. Sam and Billy are two young men both interested in dating the fair Courtney w
ID: 1209045 • Letter: 4
Question
4. 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
BILLY
SAM
Stay
Leave
Stay
-5, -5
100, 0
Leave
0, 75
0, 0
Explanation / Answer
Nash equilibrium is a strategy profile such that for each players given strategy, it is best response. Alternatively, nash equilibrium is a set of strategies such that each player is doing their best given the strategy of the other player.
If Sam choose to Stay then, best response of Billy will be to leave.
If Billy choose to leave then, best response of Sam will be to Stay.
So, (Stay, Leave) i.e. (100,0) will be nash equilibria.
On the other hand, If Sam choose to Leave then, Best response of Billy will be to Stay.
If Billy choose to Stay then, Best response of Sam will be to Leave.
So, (Leave, Stay) i.e. (0, 75) will be nash equilibria.
No, these would not make any sense as both will not gain from these equilibrium outcome.
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