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Deep Thought

Deep Thought.

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Deep Thought

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  1. Deep Thought Sometimes when I fell like killing someone, I do a little trick to calm myself down. I’ll go over to the person’s house and ring the doorbell. When the person comes to the door, I’m gone, but you know what I’ve left on the porch? A jack-o-lantern with a knife stuck in the side of its head with a note that says “You”. After that I usually feel better, and no harm done. ~ Jack Handey. (Translation: Today’s lesson shows credible threats do not have to be executed.) BA 210 Lesson II.8 Beneficial Grim Punishment

  2. Overview Overview BA 210 Lesson II.8 Beneficial Grim Punishment

  3. Lesson Overview Lesson II.8 Beneficial Grim Punishment Example 1: Grim Punishment with Interest Summary Review Questions BA 210 Lesson II.8 Beneficial Grim Punishment

  4. Example 1: Grim Punishment with Interest Example 1: Grim Punishment with Interest BA 210 Lesson II.8 Beneficial Grim Punishment

  5. Example 1: Grim Punishment with Interest Comment: In any prisoners’ dilemma, there are mutual gains from Cooperating by choosing a particular action, but not everyone can be trusted to cooperate because, for at least one person, the cooperative action is not a best response to the other players selecting their cooperative actions. That is, cooperation is not a Nash Equilibrium. We see that cooperation can become a Nash Equilibrium, and so players can be trusted to cooperate, if the dilemma game is repeated indefinitely, and players punish non-cooperation. The most effective punishment is called the Grim Strategy. The punishment inflicts the maximum pain on non-cooperation, and it lasts forever. BA 210 Lesson II.8 Beneficial Grim Punishment

  6. Example 1: Grim Punishment with Interest Question: R.J. Reynolds Tobacco Corp. and Philip Morris Corp. must decide how much money to spend on advertising each year, either $10,000 or zero. If one advertises and the other does not, the advertiser pays $10,000, then takes $100,000 profit from the other. If each advertises, each pays $10,000 but the advertisements cancel out and neither player takes profit from the other. Suppose the yearly interest rate is 10%. What strategies (ROne,POne) should each player choose if they expect this game to last only one time period? Are there mutual gains from cooperative strategies (RCoop,PCoop)? If they expect this game to repeat indefinitely, would Reynolds cooperate each period and choose RCoopif Philip followed the Grim Strategy of punishing non-cooperation? and would Philip cooperate each period and choose PCoopif Reynolds followed the Grim Strategy? BA 210 Lesson II.8 Beneficial Grim Punishment

  7. Example 1: Grim Punishment with Interest Answer: The essential data of the game are the interest rate between periods, r = 10% or r = 0.10 (as a fraction), and the payoffs each period defined by the normal form. For example, with payoffs in thousands of dollars, if Reynolds advertises and Philip does not, Reynolds pays $10,000, then takes $100,000 profit from Philip. Hence, Reynolds makes $90,000 and Philip looses $100,000. BA 210 Lesson II.8 Beneficial Grim Punishment

  8. Example 1: Grim Punishment with Interest What strategies (SOne,COne) should each player choose if they expect this game to last only one time period? In that one-shot game, each player should choose Advertise (ROne=Ad,POne=Ad) since it is the dominate strategy for each player. Each player thus earns -10. Are there mutual gains from cooperative strategies (SCoop,CCoop)? Yes, if both players choose (RCoop=No Ad,Pcoop=No Ad), then each player earns 0, rather than -10. BA 210 Lesson II.8 Beneficial Grim Punishment

  9. Example 1: Grim Punishment with Interest • If players expect this game to repeat indefinitely, each should consider the Grim Strategy, which has has two components. • The Cooperative choice for each player (RCoop=No Ad,Pcoop=No Ad). • The Punishment choice for each player (RPun=Ad,PPun=Ad) , which gives the other player the worst payoff after that player chooses his best response to his punishment. BA 210 Lesson II.8 Beneficial Grim Punishment

  10. Example 1: Grim Punishment with Interest The Grim Strategy is thus, in each period, Cooperate and choose (RCoop=No Ad,Pcoop=No Ad), as long as the other player has Cooperated and chosen (Rcoop=No Ad,Pcoop=No Ad) in every previous period. But otherwise (if the other player has ever made a choice other than cooperation (RCoop=No Ad,Pcoop=No Ad)), then you punish by choosing (RPun=Ad,PPun=Ad) in the next period and in every period thereafter --- forever. BA 210 Lesson II.8 Beneficial Grim Punishment

  11. Example 1: Grim Punishment with Interest Suppose Philip followed the Grim Strategy. Would Reynolds cooperate each period and choose RCoop=No Ad? On the one hand, if Reynolds cooperated each period and choose RCoop=No Ad, then the Grim Strategy says Philip will also cooperate each period and choose Pcoop=No Ad, and so Reynolds earns 0 each period. BA 210 Lesson II.8 Beneficial Grim Punishment

  12. Example 1: Grim Punishment with Interest On the other hand, if Reynolds cheated in any period, then consider the first period when he cheats. In that first period, the Grim Strategy says Philip will still cooperate and choose CCoop=No Ad. Reynolds’ best response to Pcoop=No Ad is Ad, which earns 90 in that period, rather than earning 0 if he had continued to cooperate. So the one period gain from cheating is 90. BA 210 Lesson II.8 Beneficial Grim Punishment

  13. Example 1: Grim Punishment with Interest But starting in the next period and continuing forever, the Grim Strategy says Philip will punish by choosing PPun=Ad. Reynolds’s best response to PPun=Ad is Ad, which earns -10 in each punishment period, rather than earning 0 if he had continued to cooperate. So the eventual loss from cheating is 10. BA 210 Lesson II.8 Beneficial Grim Punishment

  14. Example 1: Grim Punishment with Interest Summing up, if Philip followed the Grim Strategy, then Reynolds would cooperate and choose RCoopeach period exactly if the one period gain of from cheating of 90 does not compensate for the eventual losses of 10 starting the next period. That answer depends on the interest rate r between periods. BA 210 Lesson II.8 Beneficial Grim Punishment

  15. Example 1: Grim Punishment with Interest Comment: To continue the answer, we need the formula that $1 starting next period and continuing for each subsequent period is worth $(1/r) today. To illustrate, consider earning 10 percent interest each period, so r = 0.10. The formula thus becomes $1 starting next period and continuing for each subsequent period is worth $10 today. To prove that formula, consider investing the $10 today. At the end of the first period, you earn $1 interest. Suppose you withdraw that interest and reinvest the $10. Then at the end of the second period, you earn another $1 interest. If you continue withdrawing interest each period, keeping the $10 invested forever, you thus earn $1 interest each period. BA 210 Lesson II.8 Beneficial Grim Punishment

  16. Example 1: Grim Punishment with Interest Use the formula that $1 starting next month and continuing for each subsequent period is worth $(1/r) today. Since the interest rate r = 10% expressed as a fraction is r = 0.10, the eventual losses of 10 is the same as loosing 10/0.10 = 100 today. Therefore, the one period gain of from cheating of 90 does not compensate for the eventual losses of 10 starting the next period, and so Reynolds would cooperate and choose RCoop = No Adeach period. Since the game is symmetric, Philip would cooperate and choose PCoop= No Adeach period if Reynolds followed the Grim Strategy. BA 210 Lesson II.8 Beneficial Grim Punishment

  17. Review Questions • Review Questions • You should try to answer some of the following questions before the next class. • You will not turn in your answers, but students may request to discuss their answers to begin the next class. • Your upcoming Exam 2 and cumulative Final Exam will contain some similar questions, so you should eventually consider every review question before taking your exams. BA 210 Lesson II.8 Beneficial Grim Punishment

  18. Review Questions Review Question 1 BA 210 Lesson II.8 Beneficial Grim Punishment

  19. Review Questions Question 1. Sam’s Club and Costco both sell emergency food supplies. The unit cost to both retailers is $75. The retailers compete on price: the low-price retailer gets all the market and they split the market if they have equal prices. Suppose, each month, they consider prices $85 and $95, and suppose monthly market demands at those prices are 100 and 80. Suppose the monthly interest rate is 0.3%. What strategies (SOne,COne) should each player choose if they expect this game to last only one time period? Are there mutual gains from cooperative strategies (SCoop,CCoop)? If they expect this game to repeat indefinitely, would Sam’s cooperate each period and choose SCoopif Costco followed the Grim Strategy of punishing non-cooperation? and would Costco cooperate each period and choose CCoopif Sam’s followed the Grim Strategy? BA 210 Lesson II.8 Beneficial Grim Punishment

  20. Review Questions Answer: The essential data of the game are the interest rate between periods, r = 0.3% or r = 0.003 (as a fraction), and the payoffs each period defined by the normal form. For example, at Sam’s Club price $95 and Costco price $85, Costco gets the entire market demand of 100, and so makes $(85-75)x100 = $1,000. BA 210 Lesson II.8 Beneficial Grim Punishment

  21. Review Questions What strategies (SOne,COne) should each player choose if they expect this game to last only one time period? In that one-shot game, each player should choose $85 price (SOne=$85,COne=$85) since it is the dominate strategy for each player. Each player thus earns 500. Are there mutual gains from cooperative strategies (SCoop,CCoop)? Yes, if all players choose (SCoop=$95,CCoop=$95), then each player earns 800, rather than 500. BA 210 Lesson II.8 Beneficial Grim Punishment

  22. Review Questions • If players expect this game to repeat indefinitely, each should consider the Grim Strategy, which has has two components. • The Cooperative choice for each player (SCoop=$95,CCoop=$95). • The Punishment choice for each player (SPun=$85,CPun=$85) , which gives the other player the worst payoff after that player chooses his best response to his punishment. BA 210 Lesson II.8 Beneficial Grim Punishment

  23. Review Questions The Grim Strategy is thus, in each period, Cooperate and choose (SCoop=$95,CCoop=$95), as long as the other player has Cooperated and chosen (SCoop=$95,CCoop=$95) in every previous period. But otherwise (if the other player has ever made a choice other than cooperation (SCoop=$95,CCoop=$95)), then you punish by choosing (SPun=$85,CPun=$85) in the next period and in every period thereafter --- forever. BA 210 Lesson II.8 Beneficial Grim Punishment

  24. Review Questions Suppose Costco followed the Grim Strategy. Would Sam’s cooperate each period and choose SCoop=$95? On the one hand, if Sam’s cooperated each period and choose SCoop=$95, then the Grim Strategy says Costco will also cooperate each period and choose CCoop=$95, and so Sam’s earns 800 each period. BA 210 Lesson II.8 Beneficial Grim Punishment

  25. Review Questions On the other hand, if Sam’s cheated in any period, then consider the first period when he cheats. In that first period, the Grim Strategy says Costco will still cooperate and choose CCoop=$95. Sam’s best response to CCoop=$95 is $85, which earns 1000 in that period, rather than earning 800 if he had continued to cooperate. So the one period gain from cheating is 200. BA 210 Lesson II.8 Beneficial Grim Punishment

  26. Review Questions But starting in the next period and continuing forever, the Grim Strategy says Costco will punish by choosing CPun=$85. Sam’s best response to CPun=$85 is $85, which earns 500 in each punishment period, rather than earning 800 if he had continued to cooperate. So the eventual loss from cheating is 300. BA 210 Lesson II.8 Beneficial Grim Punishment

  27. Review Questions Summing up, if Costco followed the Grim Strategy, then Sam’s would cooperate and choose SCoopeach period exactly if the one period gain of from cheating of 200 does not compensate for the eventual losses of 300 starting the next period. Use the formula that $1 starting next month and continuing for each subsequent period is worth $(1/r) today. Since the interest rate r = 0.3% expressed as a fraction is r = 0.003, the eventual losses of 300 is the same as loosing 300/0.003 = 300,000 today. Therefore, the one period gain of from cheating of 200 does not compensate for the eventual losses of 300 starting the next period, and Sam’s would cooperate and choose SCoopeach period. Since the game is symmetric, Costco would cooperate and choose CCoopeach period if Sam’s followed the Grim Strategy. BA 210 Lesson II.8 Beneficial Grim Punishment

  28. Review Questions Review Question 2 BA 210 Lesson II.8 Beneficial Grim Punishment

  29. Review Questions Question 2. Consider 2 bars (A and B) suffering from a serious drunkenness problem that detracts customers because of the violence and smell. It costs $98 weekly in foregone profit for each bar to enforce moderation by stopping service to customers before they become drunk. For each bar that enforces moderation during the week, both bars will have a $50 increase in profit. Suppose the weekly interest rate is 5%. What strategies (AOne,BOne) should each player choose if they expect this game to last only one time period? Are there mutual gains from cooperative strategies (ACoop,BCoop)? If they expect this game to repeat indefinitely, would Player A cooperate each period and choose ACoopif Player B followed the Grim Strategy of punishing non-cooperation? and would B cooperate each period and choose BCoopif A followed the Grim Strategy? BA 210 Lesson II.8 Beneficial Grim Punishment

  30. Review Questions Answer: The essential data of the game are the interest rate between periods, r = 5% or r = 0.05 (as a fraction), and the payoffs each period defined by the normal form. For example, if Bar A does not enforce moderation during the period but Bar B does enforce moderation, then both bars will have a $50 increase in profit but Bar B pays an extra $98 cost, and so nets profit $50-$98 = -$48. BA 210 Lesson II.8 Beneficial Grim Punishment

  31. Review Questions What strategies (AOne,BOne) should each player choose if they expect this game to last only one time period? In that one-shot game, each player should choose Not Enforce (AOne= Not Enforce,BOne= Not Enforce) since it is the dominate strategy for each player. Each player thus earns 0. Are there mutual gains from cooperative strategies (ACoop,BCoop)? Yes, if both players choose (ACoop=Enforce,BCoop=Enforce), then each player earns 2, rather than 0. BA 210 Lesson II.8 Beneficial Grim Punishment

  32. Review Questions • If players expect this game to repeat indefinitely, each should consider the Grim Strategy, which has two components. • The Cooperative choice for each player (ACoop=Enforce, BCoop=Enforce). • The Punishment choice for each player (APun=Not Enforce, BPun=Not Enforce), which gives the other player the worst payoff after that player chooses his best response to his punishment. BA 210 Lesson II.8 Beneficial Grim Punishment

  33. Review Questions The Grim Strategy is thus, in each period, Cooperate and choose (ACoop=Enforce, BCoop=Enforce), as long as the other player has Cooperated and chosen (ACoop=Enforce, BCoop=Enforce) in every previous period. But otherwise (if the other player has ever made a choice other than cooperation), then you punish by choosing (APun=Not Enforce, BPun=Not Enforce) in the next period and in every period thereafter --- forever. BA 210 Lesson II.8 Beneficial Grim Punishment

  34. Review Questions Suppose Bar B followed the Grim Strategy. Would Bar A cooperate each period and choose ACoop=Enforce? On the one hand, if Bar A cooperated each period and choose ACoop=Enforce, then the Grim Strategy says Bar B will also cooperate each period and choose BCoop=Enforce, and so Bar A earns 2 each period. BA 210 Lesson II.8 Beneficial Grim Punishment

  35. Review Questions On the other hand, if Bar A cheated in any period, then consider the first period when he cheats. In that first period, the Grim Strategy says Bar B will still cooperate and choose BCoop=Enforce. Bar A’s best response to cooperation is Not Enforce, which earns 50 in that period, rather than earning 2if he had continued to cooperate. So the one period gain from cheating is 48. BA 210 Lesson II.8 Beneficial Grim Punishment

  36. Review Questions But starting in the next period and continuing forever, the Grim Strategy says Bar B will punish by choosing BPun=Not Enforce. Bar A’s best response to BPun=Not Enforce is to Not Enforce, which earns 0 in each punishment period, rather than earning 2if he had continued to cooperate. So the eventual loss from cheating is 2. BA 210 Lesson II.8 Beneficial Grim Punishment

  37. Review Questions Summing up, if Player B followed the Grim Strategy, then Player A would cooperate and choose ACoopeach period exactly if the one period gain of from cheating of 48 does not compensate for the eventual losses of 2 starting the next period. Use the formula that $1 starting next month and continuing for each subsequent period is worth $(1/r) today. Since the interest rate r = 5% expressed as a fraction is r = 0.05, the eventual losses of 2 is the same as loosing 2/0.05 = 40 today. Therefore, the one period gain of from cheating of 48 compensates for the eventual losses of 2 starting the next period, so Player A would not cooperate and, instead, choose Not Enforce each period. Since the game is symmetric, Player B would not cooperate if Player A followed the Grim Strategy. BA 210 Lesson II.8 Beneficial Grim Punishment

  38. BA 210 Introduction to Microeconomics End of Lesson II.8 BA 210 Lesson II.8 Beneficial Grim Punishment

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