Mar 24, 2011

# Mar 24, 2011 - March 24, 2011 - Lecture 20 *Last assignment...

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Bob ʼ s Proft, y **Last assignment (#5) due on Thursday 31st March (in class)** Nash Bargaining Solution : - max (x - X) (y - Y) ------> Nash Product -As we saw last class, the NP like cannot touch the Threat line and is always downward sloping -The Further out the Utility Possibilities curve goes, the higher the Nash Product; this is determined by where the Threat Lines are: X and Y. IF there is a new threat line For both, we reFer to them as Y ʼ and X ʼ -In this case, the Threat Line For Alice (X) moves twice and the one For Bob (Y) moves once -Plus, when the Threat lines reach a point where they both intersect the AB line at the same spot, they become y* and x* Alice ʼ s Threat Utility -Because Alice is better oFF, Bob is a little worse oFF -Your cooperative actions depend on your non-cooperative, outside, actions -Suppose that the AB line is straight : y = M - x x + y = M ----> y = M - x ( M is given; amount in pot ) March 24, 2011 - Lecture 20 Alice ʼ s Proft, x NP = 50 NP = 100 NP = 200 T W (NBS) y* x* X ʼ X (x - X) (y - Y) = 50 Suppose X ---> X ʼ > X (x - X ʼ ) (y - Y) = 50 NBS (old) NBS (new) Y 0 x A B 5 10 15 20 Bob ʼ s Alice ʼ s Alice ʼ s Bob ʼ s Utility in the NBS Alice ʼ s Threat Utility, X Suppose: Y = 15, Bob ʼ s Threat Utility -This is iF Bob ʼ s Threat Utility is fxed and every time, Alice ʼ s Threat Utility goes up, Bob ʼ s goes down a bit, and when Alice ʼ s Threat Utility goes higher than Bob ʼ s, then his goes lower than his minimum, hurting him

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max point of Nash Product (NP) -Nash Product ---> (x - X) (y - Y) ( represents known variables ) -Sub y = M - x into Nash Product (x - X) ([M - x] - Y) ----> x must be such that the Nash Product reaches it ʼ s maximum -Suppose X = 10, Y = 15, M = 100 x N P Becomes ----> (x - 10) (100 - x - 15) = (x - 10) (85 - x) 10 0 2 0 6 5 0 3 0 1 1 0 0 . . . . . . 8 5 0 Firm ʼ s pro±t (Utility Possibility Frontier) o -Solution to the cooperative endeavors depend on your uncooperative outcome (if the uncooperative outcome is better, the ±rst will become even better, higher) -the higher the T (Threat Utility) the better (higher) your Nash Bargaining Solution Non-cooperative Bargaining : (Assignment question on this!) read ) Summer Resort Example:
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Mar 24, 2011 - March 24, 2011 - Lecture 20 *Last assignment...

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