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Smith F09

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Published on October 13, 2007

Author: Belly

Source: authorstream.com

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Nash’s Nobel:  Nash’s Nobel Presentation by: Andrew Smith andrewdsmith8@bw-deloitte.com John F Nash Jr:  John F Nash Jr 1928 - Seminal work 1950 Nobel prize 1994 Cournot Equilibrium:  Cournot Equilibrium Rock Paper Scissors:  Rock Paper Scissors Zero sum game Symmetric payoffs Scissors cut paper Paper covers rock Rock sharpens scissors Losing strategies exist Randomise to avoid losing Role Play Game:  Role Play Game Invitation to tender to supply 10 units Bids allowed: €1 through €5 per unit in intervals of €1 Contract awarded to cheaper supplier Split 50/50 if a tie Red: production cost €1 per unit Blue: production cost €2 per unit Game Payoffs:  Game Payoffs 0 -10 0 10 0 0 0 20 0 30 0 -5 0 0 0 0 0 0 0 0 0 -10 10 0 5 0 10 0 10 0 0 -10 10 5 0 0 20 0 20 0 0 0 0 10 0 0 15 10 30 0 No bid 1 2 3 4 Red Bid (cost €1) 1 2 3 4 5 Blue bid (cost: €2) 0 -10 0 0 0 10 0 20 20 15 0 0 0 0 10 0 20 0 30 0 40 0 No bid 5 Equilibrium:  Equilibrium 0 -10 0 10 0 0 0 20 0 30 0 -5 0 0 0 0 0 0 0 0 0 -10 10 0 5 0 10 0 10 0 0 -10 10 5 0 0 20 0 20 0 0 0 0 10 0 0 15 10 30 0 No bid 1 2 3 4 Red Bid (cost €1) 1 2 3 4 5 Blue bid (cost: €2) 0 -10 0 0 0 10 0 20 20 15 0 0 0 0 10 0 20 0 30 0 40 0 No bid 5 Bargaining Game:  Bargaining Game Player A wishes to sell an asset Player B wishes to buy Third party dealer sells at €10 and buys at €5 Model negotiation between A and B Many Nash equilibria Unique Selten equilibrium Is the Theory Correct?:  Is the Theory Correct? Mathematically, yes But do real games converge to Nash equilibria? Difficult to specify a game and to calibrate a model My “get out of jail” card is to invoke imperfect calibration when my model fails to predict actual outcomes (Possible) Applications:  (Possible) Applications Auction design (eg Telecom licenses) Military / anti-terrorist Regulation / response Capital allocation Underwriting Social policy Premium cycle Nash’s Nobel:  Nash’s Nobel Presentation by: Andrew Smith andrewdsmith8@bw-deloitte.com

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