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  1. 1. Game Theory: RefinementsApril 19, 2013
  2. 2. Announcements• Homework 3 is due before class on Monday• Next week we’ll begin talking aboutexternalities
  3. 3. Last Class• Considered more example of Nash equilibriaand strictly dominant strategies• Played a game: Write down ½ of the averageof others’ guesses. Choose from [0,100].– Nash equilibrium: Everyone writes down zero
  4. 4. How did we solve this problem?• If everyone guessed 100, the best number towrite down (best response!) would be 50.• But if everyone wrote 50, the BR is 25.• If all 25, BR is 12.5, … etc• If all 0, BR is 0. Only Nash Equilibrium• This iterative process for finding equilibrium isa ``refinement’’ of Nash equilibrium.
  5. 5. Refinements• Extensions of the basic version of NashEquilibrium we have seen.• The game we played demonstrates a conceptcalled iterated dominance.• Another refinement has to do with the timingof the game; called sequential rationality.
  6. 6. Games in Which Timing MattersOpening a New RestaurantBillDinner BreakfastAliceDinner$1000 (A)$1000 (B)$1600 (A)$1400 (B)Breakfast$1400 (A)$1600 (B)$800 (A)$800 (B)Alice and Bill are each considering opening a restaurant intheir local neighborhood . . . But what kind?
  7. 7. Decision Tree & Backward InductionBillDecidesAliceDecidesOutcomeDDDBBB$1000 (A)$1000 (B)$1600 (A)$1400 (B)$1400 (A)$1600 (B)$800 (A)$800 (B)
  8. 8. A. To Bed, TantrumB. To Bed, Not TantrumC. Not to Bed, TantrumD. Not to Bed, Not Tantrum
  9. 9. Games in Which Timing MattersOpening a Convenience StoreFreeway1 mile1,200 peopleA BC⅓ mile400 people⅓ mile400 people⅓ mile400 people1 mile1,200 peopleStore A opens first . . . Where should theowner of a second convenience store chooseto locate?Monopolisticcompetition
  10. 10. Tendency for MonopolisticCompetitors to ClusterHotelling’s (1929) insights help explain• Why convenience stores and gas stations are often clusteredon the same corner.• Why political candidates often “moderates”.• Why Coca-Cola and Pepsi are so similar.• Why Kellogg’s and Post both have purple raisin bran boxes.
  11. 11. Commitment Problems• In many of the games we’ve looked at players cannot achievethe desired outcome because of a commitment problem—that is they cannot make credible threats or promises abouttheir future actions.• Sometimes, it’s possible to adopt commitment devices‒ Omerta: anyone who testifiesagainst a fellow mob member iskilled.‒ Legally binding contracts‒ Commissions to salespeople
  12. 12. Commitment Problems• Sometimes we want to commit ourselves . . .– Bring a fixed amount of cash when you go out.– Leave your laptop at work so you don’t work from home.– Brush your teeth to avoid snacking later.– Cut up your credit cards.
  13. 13. Commitment Problems• Sometimes psychological incentives can solve commitmentproblems– Guilt– Sympathy towards others
  14. 14. StrangerAGive $Keepthe $Don’tGive $BuyTacos-20 for you20 for the stranger5 for you10 for stranger0 for you0 for strangerYou’re hungry but too busy to go buy lunch, so yougive a stranger $20 to go buy you two fish tacos(which you value at $25).A. Give, KeepB. Give, BuyC. Don’t give
  15. 15. StrangerAGive $Keepthe $Don’tGive $BuyTacos-20 for you-10 for your friend5 for you10 for your friend0 for you0 for your friendYou’re hungry but too busy to go buy lunch, so yougive your best friend $20 to go buy you two fish tacos(which you value at $25).A. Give, KeepB. Give, BuyC. Don’t Give
  16. 16. Lesson• Having a trustworthy trading partner can make both partiesbetter off.• The hard part is identifying people who you can trust.• Reputation matters.
  17. 17. Splitting a cakeDonnieMarie50/50>.5Big/Small<.50.5 (D)0.5 (M)<0.5 (D)>0.5 (M)>0.5 (D)<0.5 (M)