Beautifully Misleading Mind


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Beautifully Misleading Mind

  1. 1. Beautifully Misleading Mind Presented by: Jura Liaukonyte Ph.D. Student / Instructor University of Virginia “ If it’s true that we are here to help others, then what exactly are the others here for? ” - George Carlin
  2. 2. What is Game Theory ? <ul><li>Study of the behavior of decision makers whose decisions affect each other. </li></ul><ul><li>Provides the language and framework for the discussion of problems in economics, social sciences, evolutionary biology, etc . </li></ul>
  3. 3. Games We Play <ul><li>Group projects free-riding, reputation </li></ul><ul><li>Flat tire coordination </li></ul><ul><li>Mean professors commitment </li></ul><ul><li>GPA trap prisoner’s dilemma </li></ul><ul><li>Tennis / Baseball mixed strategies </li></ul><ul><li>Poker credibility </li></ul><ul><li>Traffic congestion </li></ul><ul><li>Dating information manipulation </li></ul>
  4. 4. Games Businesses Play <ul><li>Market entry commitment </li></ul><ul><li>Drug testing mixed strategies </li></ul><ul><li>Supply chains auctions </li></ul><ul><li>Corporate takeovers winner’s curse </li></ul><ul><li>Fishing congestion </li></ul><ul><li>Patent races game of chicken </li></ul><ul><li>Stock options compensation schemes </li></ul><ul><li>OPEC output collusion & enforcement </li></ul>
  5. 5. Strategically thinking… <ul><li>COMMANDMENT </li></ul><ul><li>Never assume that your opponents’ behavior is fixed. </li></ul><ul><li>Predict their reaction to your behavior. </li></ul>
  6. 6. Simultaneous Games <ul><li>In many situations, strategic player has to determine his strategy without knowledge of what the rival is doing at the same time </li></ul><ul><ul><li>Product design </li></ul></ul><ul><ul><li>Pricing and marketing some new product </li></ul></ul><ul><ul><li>Mergers and acquisitions competition </li></ul></ul><ul><ul><li>Voting and politics </li></ul></ul>
  7. 7. Tools <ul><li>What does it mean to think strategically? </li></ul><ul><li>What kind of tools can we apply to arrive at the optimal solution? </li></ul>
  8. 8. The Beautiful Mind <ul><li>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. </li></ul><ul><li>Proposed that we look for outcomes in which each player is making an optimal choice , given the choices the other players are making. </li></ul><ul><li>At a Nash equilibrium, it is reasonable for each player to believe that all other players are playing optimally. </li></ul>
  9. 9. Episode <ul><li> </li></ul>
  10. 10. A Beautiful Mind <ul><li>The “equilibrium” in the movie: the blonde sitting all alone at the bar while the men dance happily with the brunettes. </li></ul><ul><li>Recall: Nash equilibrium is a situation where no player can gain by changing his decision, given the decisions of the other players. </li></ul>
  11. 11. Clearing up the Confusion <ul><li>Therefore, the scene in the movie does NOT illustrate a Nash equilibrium, but the exact opposite: </li></ul><ul><li>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. </li></ul>
  12. 12. Adam Smith was right <ul><li>The “equilibrium” outcome in the movie is socially inefficient because none of the men get to enjoy the company of the stunning blonde. </li></ul><ul><li>In contrast, a real Nash equilibrium to the game entails a man dancing with the blonde and the others dancing with brunettes. </li></ul><ul><li>In NE, each man is selfishly maximizing his own satisfaction, given the strategies of the others </li></ul><ul><li>The outcome is also socially efficient because it doesn’t squander a dance with the blonde. </li></ul>
  13. 13. Defining the Game <ul><li>Players – John Jr. and Mark </li></ul><ul><li>Strategies – Blonde Sally, Brunette Jane, Brunette Mary </li></ul><ul><li>Payoffs – </li></ul><ul><ul><li>if one gets blonde “utility” is 10 </li></ul></ul><ul><ul><li>If one gets brunette – 7 </li></ul></ul><ul><ul><li>If both choose the same – half of the original “utility” payoff (5 for blonde and 3.5 for brunette) </li></ul></ul>
  14. 14. The Bar Scene: Nash Equilibrium 4 NE and all involve Blonde Sally! John Jr. Mary Jane Sally 3.5 , 3.5 7 , 7 7 , 10 Mary 7 , 7 3.5 , 3.5 7 , 10 Jane 10 , 7 10 , 7 5 , 5 Sally Mark
  15. 15. “ Ah! I finally get it…NOT” Factor <ul><li>Why is the “equilibrium” in the movie so logically appealing? </li></ul><ul><li>Why does it lead even Economics students to believe mistakenly that it is real classic NE? </li></ul>
  16. 16. “ Ah! I finally get it…NOT” Factor <ul><li>The answer lies in the question: </li></ul><ul><li>Because the movie “equilibrium” IS logically appealing and our answer IS NOT : </li></ul><ul><li>The answer we found doesn’t give us desired unique optimal strategy </li></ul><ul><li>It assumes that players are fully rational in their choices </li></ul><ul><li>It assumes that there is no repetitive interaction and learning among players </li></ul><ul><li>It assumes that all players are equally confident in “scoring” a blonde or brunette </li></ul><ul><li>Etc. </li></ul>
  17. 17. The Bar Scene: John Jr. and Mark Choose Now suppose that 2 guys are less confident about “scoring” the blonde If chosen by both If chosen by one 1.05 .15 2.1 .3 7 Mary 1.05 .15 2.1 .3 7 Jane 1 .1 2 .2 10 Sally Expected Value Probability Of Score Expected Value Probability Of Score Score
  18. 18. Nash Equilibrium and Mixed Strategies Now: 2 NE (Brunette, Brunette) in predefined mixed strategies John Jr. Mary Jane Sally 1.05 , 1.05 2.1 , 2.1 2.1 , 2 Mary 2.1 , 2.1 1.05 , 1.05 2.1 , 2 Jane 2 , 2.1 2 , 2.1 1 , 1 Sally Mark
  19. 19. Problem with Blondes and Brunettes <ul><li>The solutions the presented games were based on one important premise: </li></ul><ul><li>– only preferences of men determined payoffs and winning strategies of the game </li></ul>I will let you ponder if it is a reasonable assumption…
  20. 20. Thank you <ul><li>I hope this short lecture has served in clarifying and deciphering Nash equilibrium or lack thereof. </li></ul>Someone: “So… Are you saying it was socially efficient?” Me: “ Now you are thinking like an economist!”