Background: Adam Smith, John Nash, and Hollywood

Concept:  What is Nash Equilibrium, and Why it matters?

A real-world example

Wise of Crowd vs  Crowd Trouble

Questions & Answers

Adam Smith vs John Nash

•  Nash’s eureka movement: “Adam Smith needs revision.”

  AS:  “In competition, individual ambition serves the common good."

   

•  JN: Adam Smith is wrong because:
   “the best result would come from everyone in the group doing what is best for himself and the group."
   

• At this point, Nash rushes out of the bar and spends the next few months writing his treatise on general equilibrium theory. 

• Although we do not know how Nash’s friend acted but the Hollywood simply wrong on Nash equilibrium

What is Nash Equilibrium?

• Some definitions and assumptions:

• We assume that all economic agents (players) have complete information and all actions are taken simultaneously.

• Equilibrium: ... everyone is doing the best s/he can given what everyone else is doing

• Players:  Each decision-maker in a game os called a player

• Strategies:  Each course of action open to a player during the game is called a strategy

• Payoffs: The final return to each player at the conclusion of a game is called a payoff.

What is Nash Equilibrium?

1.  In a Nash equilibrium, every player in a group makes the best decision for /himself/herself, based on what s/he thinks the others will do.
    

2. And no one can do better by changing strategy: every member of the group is doing as well as they possibly can.
    

3. This does not mean the optimal outcome for society.
    

4. Nash showed that every “game” with a finite number of players, each with a finite number of options to choose from, would have at least one such equilibrium.

    

Prisoner's Dilemma

•  Two criminals in separate prison cells face the same offer from the public prosecutor.
   
•  If they both confess to bloody murder, they each face ten years in jail.
   
• If one stays quiet while the other confesses, then the snitch will get to go free, while the other will face a lifetime in jail.
   
• And if both hold their tongue, then they each face a minor charge and only a year in the clink. 

Result?

Prisoner's Dilemma

Nash Equilibrium:
the only stable outcome is for both to confess.

Wise of Crowd vs  Crowd Trouble

• The Nash equilibrium helped us to understand (in a neat mathematical way) how self-improving individuals could lead to self-harming crowds.
   
• This tragic outcome is all too common in the real world.
   
• Left freely to plunder the sea, individuals will fish more than is best for the group, depleting fish stocks.
   
• Employees competing to impress their boss by staying the longest in the office will encourage workforce exhaustion.
   
• Why do countries emit too much carbon into the atmosphere? Everyone would be better off if only we could agree to show some restraint.

Summary and Why Hollywood is Wrong

Nash equilibrium, no one is able to improve their own situation by changing strategy.