Beautifully Misleading Mind

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Beautifully Misleading Mind
If its true that we are here to help others,
then what exactly are the others here for?
- George Carlin

• Jura Liaukonyte
• Ph.D. Student / Instructor
• University of Virginia

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What is Game Theory ?

• Study of the behavior of decision makers whose
  decisions affect each other.
  
• Provides the language and framework for the
  discussion of problems in economics, social
  sciences, evolutionary biology, etc.

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Games We Play

• Group projects free-riding, reputation
• Flat tire coordination
• Mean professors commitment
• GPA trap prisoners dilemma
• Tennis / Baseball mixed strategies
• Poker credibility
• Traffic congestion
• Dating information manipulation

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Games Businesses Play

• Market entry commitment
• Drug testing mixed strategies
• Supply chains auctions
• Corporate takeovers winners curse
• Fishing congestion
• Patent races game of chicken
• Stock options compensation schemes
• OPEC output collusion enforcement

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Strategically thinking

• COMMANDMENT
• Never assume that your opponents behavior is
  fixed.
  
• Predict their reaction to your behavior.

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Simultaneous Games

• In many situations, strategic player has to
  determine his strategy without knowledge of what
  the rival is doing at the same time
  
• Product design
• Pricing and marketing some new product
• Mergers and acquisitions competition
• Voting and politics

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Tools

• What does it mean to think strategically?
• What kind of tools can we apply to arrive at the
  optimal solution?

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The Beautiful Mind

• Recognized that in any sort of strategic
  interaction, the best choice for single player
  depends critically on his beliefs about what the
  other players might do.

• Proposed that we look for outcomes in which
  each player is making an optimal choice, given
  the choices the other players are making.
  

• At a Nash equilibrium, it is reasonable for each
  player to believe that all other players are
  playing optimally.

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Episode

• http//econ419.blogspot.com/2007/02/beautifully-mi
  sleading-mind.html
  

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A Beautiful Mind

• The equilibrium in the movie the blonde
  sitting all alone at the bar while the men dance
  happily with the brunettes.
  
• Recall Nash equilibrium is a situation where no
  player can gain by changing his decision, given
  the decisions of the other players.
  

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Clearing up the Confusion

• Therefore, the scene in the movie does NOT
  illustrate a Nash equilibrium, but the exact
  opposite
  
• A situation where any one of the men could
  unilaterally gain by switching to the blonde,
  given that the other men are dancing with
  brunettes.

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Adam Smith was right

• The equilibrium outcome in the movie is
  socially inefficient because none of the men get
  to enjoy the company of the stunning blonde.
  
• In contrast, a real Nash equilibrium to the game
  entails a man dancing with the blonde and the
  others dancing with brunettes.
  
• In NE, each man is selfishly maximizing his own
  satisfaction, given the strategies of the others
  
• The outcome is also socially efficient because it
  doesnt squander a dance with the blonde.

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Defining the Game

• Players John Jr. and Mark
• Strategies Blonde Sally, Brunette Jane,
  Brunette Mary
  
• Payoffs
• if one gets blonde utility is 10
• If one gets brunette 7
• If both choose the same half of the original
  utility payoff (5 for blonde and 3.5 for
  brunette)

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The Bar Scene Nash Equilibrium
4 NE and all involve Blonde Sally!
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Ah! I finally get itNOT Factor

• Why is the equilibrium in the movie so
  logically appealing?
  
• Why does it lead even Economics students to
  believe mistakenly that it is real classic NE?

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Ah! I finally get itNOT Factor

• The answer lies in the question
• Because the movie equilibrium IS logically
  appealing and our answer IS NOT
  
• The answer we found doesnt give us desired
  unique optimal strategy
  
• It assumes that players are fully rational in
  their choices
  
• It assumes that there is no repetitive
  interaction and learning among players
  
• It assumes that all players are equally confident
  in scoring a blonde or brunette
  
• Etc.

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The Bar Scene John Jr. and Mark Choose
Now suppose that 2 guys are less confident about
scoring the blonde

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Nash Equilibrium and Mixed Strategies
Now 2 NE (Brunette, Brunette) in predefined mi
xed strategies
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Problem with Blondes and Brunettes

• The solutions the presented games were based on
  one important premise
  
• only preferences of men determined payoffs
  and winning strategies of the game
  

I will let you ponder if it is a reasonable
assumption

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Thank you

• I hope this short lecture has served in
  clarifying and deciphering Nash equilibrium or
  lack thereof.
  

Someone So Are you saying it was socially
efficient? Me Now you are thinking like an eco
nomist!