Presentation Transcript
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