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Deep Thought

Deep Thought. Why can’t the ant and the caterpillar just get along? One eats grass, the other eats Caterpillars … Oh, I see now. ~ Jack Handey . (Translation: Today is another lesson teaching you how to get the best deal for yourself from bargaining.). Readings. Readings.

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Deep Thought

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  1. Deep Thought Why can’t the ant and the caterpillar just get along? One eats grass, the other eats Caterpillars … Oh, I see now. ~ Jack Handey. (Translation: Today is another lesson teaching you how to get the best deal for yourself from bargaining.) BA 445 Lesson B.2 Sequential Bargaining and Impatience

  2. Readings • Readings • Baye “Sequential Bargaining” (see the index) • Dixit Chapters 1, 2, 3 BA 445 Lesson B.2 Sequential Bargaining and Impatience

  3. Overview • Overview BA 445 Lesson B.2 Sequential Bargaining and Impatience

  4. Overview BA 445 Lesson B.2 Sequential Bargaining and Impatience

  5. Best Alternative to No Agreement • Best Alternative to No Agreement BA 445 Lesson B.2 Sequential Bargaining and Impatience

  6. Best Alternative to No Agreement Overview • Best Alternative to No Agreement is added to a bargainer’s share of the fixed positive gain from an agreement. — So, a seller can increase her price from a sale by finding alternative buyers. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  7. Best Alternative to No Agreement • Comment: When solving any Bargaining Game, a bargainer’s share of the fixed positive gain from an agreement is added to their Best Alternative To No Agreement (BATNA). In particular, a bargainer can increase their total payoff from an agreement by increasing their BATNA. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  8. Best Alternative to No Agreement • Question: Suppose Buyer Bob values the bag of fresh beans in front of him at 1 dollar and Seller Sabitha, in an effort to improve her bargaining position, has taken the time to find an alternative buyer would would pay $0.60. That drops the gains from a trade between Bob and Sabitha from $1.00 to $0.40. • As before, suppose there is only enough time before his tour bus leaves for Buyer Bob to make one offer to Seller Sabitha for the bag of beans. Seller Sabitha must either accept or reject that offer, and if Sabitha rejects then she can sell to the alternative buyer for $0.60. Will trade occur between Bob and Sabitha? If so, at what price to Bob? BA 445 Lesson B.2 Sequential Bargaining and Impatience

  9. Best Alternative to No Agreement • Answer: The gain from Bob trading with Sabitha is $0.40. To consider all possible price offers (offers by Bob to buy or counteroffers by Sabitha to sell), consider a bargaining payoff table.The game lasts only one round, and gains are measured as a percentage of the $0.40 gain from Bob trading with Sabitha. • As before, Sabitha should accept anything as being better than nothing. So, Bob can get away with 100 percent of the gains minus a pittance. That leaves Bob with $0.40 gains from trade, and Sabitha with $0.00, meaning Bob pays $1.00-$0.40 = $0.60 to Sabitha, and Sabitha receives $0.60+$0.00 = $0.60 from Bob. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  10. Best Alternative to No Agreement Comment: In any Bargaining Game, a bargainers’ shares of the fixed positive gain from an agreement depends solely on the sequence of who makes offers and on any depreciation of the gains from an agreement over the bargaining rounds. In particular, the bargainers’ shares are independent of the level of the gain from an agreement, and of the BATNAs of the bargainers. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  11. Bilateral Alternatives to No Agreement • Bilateral Alternatives to No Agreement BA 445 Lesson B.2 Sequential Bargaining and Impatience

  12. Mutual Alternatives to No Agreement Overview Mutual Alternatives to No Agreement are added to both bargainers’ shares of the gains from an agreement. — So, a union seeks alternative employers and management alternative employees. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  13. Mutual Alternatives to No Agreement • Question: Consider union-management wage bargaining during Thanksgiving Weekend at Medieval Times Dinner Theatre. The extended weekend lasts Thursday through Sunday. On the Wednesday before the weekend, the employee’s union confronts the management over wages. The union presents its demand. The management either accepts or rejects it and returns the next day with a counteroffer. Offers alternate thereafter. Each day Medieval Times operates with union labor, Medieval Times makes a profit of $10,000 before paying union wages. Each day without an agreement with the union, Medieval Times makes a profit of $3,000 after paying for expensive scab (non-union) labor, and union labor earns $2,000 from outside employment. • What initial wage demand should the union make? Should management accept that demand? BA 445 Lesson B.2 Sequential Bargaining and Impatience

  14. Mutual Alternatives to No Agreement Answer: To consider all possible wage offers (offers by the Union to sell labor or offers by Management to buy labor), consider another bargaining payoff table. The game ends if an offer is accepted or if the weekend ends without an accepted offer. Gains are measured as a percentage of the 4x(10-3-2) = 20 thousand gain from accepting the Union’s offer at the beginning. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  15. Mutual Alternatives to No Agreement • Starting 1 bargaining round • from the end of the game and • rolling back to the beginning • determines optimal offers and • counteroffers. • The Union’s initial wage demand should give it 50% of the $20,000 gains from trade, or $10,000, and management should accept that demand. Since the BATNA for Medieval Times is $3,000x4 = $12,000 profit from scab labor and the BATNA for union labor is $2,000x4 = $8,000 from outside employment, the initial wage demand by the union should be $8,000+$10,000 = $18,000, and management should accept that demand, and so earn $12,000+$10,000 = $22,000 profit. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  16. Manipulating Alternatives to No Agreement • Manipulating Alternatives to No Agreement BA 445 Lesson B.2 Sequential Bargaining and Impatience

  17. Manipulating Alternatives to No Agreement • Overview • Manipulating Alternatives to No Agreement can be profitable even when alternatives decrease, depending on the relative decrease. — So, a union strikes as long as it costs management more. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  18. Manipulating Alternatives to No Agreement • Comment: When a strategic bargainer observes that a better outside opportunity translates into a better share in a bargain, he will look for strategic moves that improve those outside opportunities. And he will notice that what matters is his outside opportunity relative to that of his rival. He will do better in the bargaining even if he makes a commitment or a threat that lowers both parties’ outside opportunities, as long as that of the rival is damaged more severely. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  19. Manipulating Alternatives to No Agreement • Question: Reconsider the outcome of the original union-management wage bargaining for Thanksgiving Weekend at Medieval Times Dinner Theatre, where each day Medieval Times operates with union labor, Medieval Times makes a profit of $10,000 before paying union wages, and each day without an agreement with the union, Medieval Times makes profit $3,000 from scab labor and union labor earns outside income $2,000. • Compute how outcomes change if the union gives up $500 per day of outside income to intensify their picketing and, thereby, reduces Medieval Times profit from scab labor by $1,000 per day. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  20. Manipulating Alternatives to No Agreement Answer: The bargaining payoff table is not affected by changing the BATNA for each bargainer. In particular, the Union and Management reach an agreement on the first round, and each get half of the gains from an agreement. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  21. Manipulating Alternatives to No Agreement • Originally, the Union’s initial wage demand should give it 50% of the $20,000 gains from trade, or $10,000, and management should accept that demand. Since the BATNA for Medieval Times is $3,000x4 = $12,000 profit from scab labor and the BATNA for union labor is $2,000x4 = $8,000 from outside employment, the initial wage demand by the union should be $8,000+$10,000 = $18,000, and management should accept that demand, and so earn $12,000+$10,000 = $22,000 profit. • But with intensified picketing, the BATNA for Medieval Times is $2,000x4 = $8,000 and the BATNA for union labor is $1,500x4 = $6,000 and the gains from trade is $26,000. So, the initial wage demand by the union should be $6,000+$13,000 = $19,000, and management should accept that demand, and so earn $8,000+$13,000 = $21,000 profit. The Union does better. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  22. Bargaining with Impatience Bargaining with Impatience BA 445 Lesson B.2 Sequential Bargaining and Impatience

  23. Bargaining with Impatience • Overview • Bargaining and Impatience interact like bargaining and depreciation. They should lead to an agreement before the gains from the agreement actually depreciate in the perception of the bargainers. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  24. Bargaining with Impatience • Comment: Now consider a different kind of cost of delay in reaching an agreement. Suppose the actual monetary value of the total gains from an agreement does not depreciate, but bargainers have a “time value of money” and therefore prefer early agreement to later agreement. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  25. Bargaining with Impatience • Question: Compute a bargaining payoff table for Bargainers A and B making alternating offers over 5 bargaining rounds, with Bargainer A making the first offer, A discounting 10% between each period, and B also discounting 10% between each period. • That is, both bargainers believe that having only 90 cents right now is as good as having $1 one round later. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  26. Bargaining with Impatience • Answer: A bargaining payoff table for Bargainers A and B making alternating offers over 5 bargaining rounds, with Bargainer A making the first offer: BA 445 Lesson B.2 Sequential Bargaining and Impatience

  27. Bargaining with Impatience • Starting 1 bargaining round from the end, B • should accept anything as being better than • nothing. After deducing that, A’s best acceptable • offer to B is a pittance, leaving A with 100. • Rolling back to 2 rounds from the end, A could • reject any offer and get 100 in the next round, • which after A’s 10% discount is worth 90 in the • current round. After deducing that, B’s best acceptable offer to A is 90 plus a pittance, leaving B with 10. • Rolling back to 3 rounds from the end, B could reject any offer and get 10 in the next round, which after B’s 10% discount is worth 9 in the current round. . After deducing that, A’s best acceptable offer to B is 9 plus a pittance, leaving A with 91. • Rolling back to 4 rounds from the end, A could reject any offer and get 91 in the next round, • which after A’s 10% discount is worth 81.9 in the current round. After deducing that, B’s best acceptable offer to A is 81.9 plus a pittance, leaving B with 18.1. • Rolling back to the beginning, B could reject any offer and get 18.1 in the next round, which after B’s 10% discount is worth 16.29 in the current round. . After deducing that, A’s best acceptable offer to B is 16.29 plus a pittance, leaving A with 83.71. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  28. Bargaining with Impatience • Comment: When both • bargainers discount the same • percent, the division of the gains • from trade is the same as if the • object itself were depreciating • by that percentage. • In the current problem, on the one hand, if there are 5 bargaining rounds and if A and B each discount 10%, then A’s best acceptable offer to B is 83.71% plus a pittance, leaving A with 16.29%. On the other hand, if there are 5 bargaining rounds and the object itself depreciates 10% per round, then A’s best acceptable offer to B is, again, 83.71% plus a pittance, leaving A with 16.29%. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  29. Relative Patience Relative Patience BA 445 Lesson B.2 Sequential Bargaining and Impatience

  30. Relative Patience Overview Relative Patience is profitable because bargaining is affected by the possibility of depreciation in the perceived gain from an agreement. — So, China gains when it is more patient than the US. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  31. Relative Patience • Comment: We now see that more patience (less discounting) translates into a better share in a bargain. So a strategic bargainer will learn patience. • The Chinese symbol for patience can also mean restraint and control. It is formed by 2 different characters with the image of blade on the heart. • The word connotes how difficult it is to practice patience. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  32. Relative Patience • Question: Compare outcomes from 5 rounds of bargaining in three different scenarios: • Both bargainers discount the money payoff from an agreement 10 percent each round. • The first mover (the first to make an offer) discounts the money payoff from an agreement 10 percent each round, but the second mover discounts 20 percent. • The first mover (the first to make an offer) discounts the money payoff from an agreement 20 percent each round, but the second mover discounts 10 percent. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  33. Relative Patience • Answer: A bargaining payoff table for Bargainers A and B, with Bargainer A making the first offer, with 5 bargaining rounds, with A discounting 10% between each period, and with B discounting 20% between each period. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  34. Relative Patience • Starting 1 bargaining round from the end, B • should accept anything as being better than • nothing. After deducing that, A’s best • acceptable offer to B is a pittance, leaving A • with 100. • Rolling back to 2 rounds from the end, A • could reject any offer and get 100 in the • next round, which after A’s 10% discount is • worth 90 in the current round. After deducing that, B’s best acceptable offer to A is 90 plus a pittance, leaving B with 10. • Rolling back to 3 rounds from the end, B could reject any offer and get 10 in the next round, which after B’s 20% discount is worth 8 in the current round. . After deducing that, A’s best acceptable offer to B is 8 plus a pittance, leaving A with 92. • Rolling back to 4 rounds from the end, A could reject any offer and get 92 in the next round, • which after A’s 10% discount is worth 82.8 in the current round. After deducing that, B’s best acceptable offer to A is 82.8 plus a pittance, leaving B with 17.2. • Rolling back to the beginning, B could reject any offer and get 17.2 in the next round, which after B’s 20% discount is worth 13.76 in the current round. . After deducing that, A’s best acceptable offer to B is 13.76 plus a pittance, leaving A with 86.24. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  35. Relative Patience • A bargaining payoff table for Bargainers A and B, with Bargainer A making the first offer, with 5 bargaining • rounds, with A discounting 20% between each period, and with B discounting 10% between each period. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  36. Relative Patience • Starting 1 bargaining round from the end, B • should accept anything as being better than • nothing. After deducing that, A’s best • acceptable offer to B is a pittance, leaving • A with 100. • Rolling back to 2 rounds from the end, A • could reject any offer and get 100 in the • next round, which after A’s 20% discount is • worth 80 in the current round. After deducing that, B’s best acceptable offer to A is 80 plus a pittance, leaving B with 20. • Rolling back to 3 rounds from the end, B could reject any offer and get 20 in the next round, which after B’s 10% discount is worth 18 in the current round. . After deducing that, A’s best acceptable offer to B is 18 plus a pittance, leaving A with 82. • Rolling back to 4 rounds from the end, A could reject any offer and get 82 in the next round, • which after A’s 20% discount is worth 65.6 in the current round. After deducing that, B’s best acceptable offer to A is 65.6 plus a pittance, leaving B with 34.4. • Rolling back to the beginning, B could reject any offer and get 34.4 in the next round, which after B’s 10% discount is worth 30.96 in the current round. . After deducing that, A’s best acceptable offer to B is 30.96 plus a pittance, leaving A with 69.04. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  37. Relative Patience • Summary: Compare outcomes from 5 rounds of bargaining in three different scenarios. • Both bargainers discount the money payoff from an agreement 10 percent each round. Outcome: First mover A’s best acceptable offer to B is 16.29%, leaving A with 83.71%. • The first mover (the first to make an offer) discounts the money payoff from an agreement 10 percent each round, but the second mover discounts 20 percent. Outcome: A’s best acceptable offer to B is 13.76%, leaving A with 86.24%. • The first mover (the first to make an offer) discounts the money payoff from an agreement 20 percent each round, but the second mover discounts 10 percent. Outcome: A’s best acceptable offer to B is 30.96 plus a pittance, leaving A with 69.04. • A does best when his is more patient (discounts less) than B. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  38. Relative Patience • Comment: When a strategic bargainer observes that more patience (less discounting) translates into a better share in a bargain, he will seek partners less patient than himself and avoid those more patient. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  39. Summary • Summary BA 445 Lesson B.2 Sequential Bargaining and Impatience

  40. Summary • A bargainers’ shares of the fixed positive gain from an agreement depends solely on the sequence of who makes offers and on any depreciation of, or discounting of, the gains from an agreement over the bargaining rounds. In particular, the bargainers’ shares are independent of the level of the gain from an agreement. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  41. Summary • A bargaining payoff table for Bargainers A and B, with Bargainer A making the first offer, with 5 bargaining rounds, with A discounting 30% between each period, and with B discounting 40% between each period. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  42. Summary • A bargaining payoff table for Bargainers A and B, with Bargainer A making the first offer, with 5 bargaining rounds, with A discounting 40% between each period, and with B not discounting. (If A did not discount, he would have 100% of the gains from an agreement.) BA 445 Lesson B.2 Sequential Bargaining and Impatience

  43. 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 445 Lesson B.2 Sequential Bargaining and Impatience

  44. Review 1: Relative Impatience • Review 1: Relative Impatience BA 445 Lesson B.2 Sequential Bargaining and Impatience

  45. Review 1: Relative Impatience Comment: TheFasterTimes.Com posts an account of bargaining for a tiny glass bottle covered in a landscape painting at Shanghai’s Yuyuan market. The games began at a whopping 380RMB, or about $56US. Over the course of 20 minutes, the buyer brought the price down by pointing out design flaws and pretending to be distracted by a porcelain doll in a red silk dress. When the shopkeeper refused to go below 80RMB, the buyer walked away, slowly. “Come back,” the saleswoman cried, racing after her. “You can have it for 60.”  Deal, at just under $9US, or about 1/6 of the asking price. Bargaining in China is an art form that requires a lot of patience, and a willingness of the buyer to signal their patience by spending time.  BA 445 Lesson B.2 Sequential Bargaining and Impatience

  46. Review 1: Relative Impatience • Question 1. Consider negotiations over the price of a tiny glass bottle covered in a landscape painting at Shanghai’s Yuyuan market. Buyer Betty values the bottle at $65, and Seller Shen’s cost of supplying the bottle is $5. S makes the first offer, with 4 bargaining rounds of alternating offers, and with S discounting 2% between each period. • Compare bargaining outcomes when B discounts 10% between each period with B discounting only 1% between each period, and with B discounting 100% between each period (which is absolute impatience). BA 445 Lesson B.2 Sequential Bargaining and Impatience

  47. Review 1: Relative Impatience • Answer 1: A bargaining payoff table for Bargainers B and S, with Bargainer S making the first offer, with 4 bargaining rounds, with B discounting 10% between each period, and with S discounting 2% between each period. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  48. Review 1: Relative Impatience • A bargaining payoff table for Bargainers B and S, with Bargainer B making the first offer, with 4 bargaining rounds, with B discounting only 1% between each period, and with S discounting 2% between each period. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  49. Review 1: Relative Impatience • A bargaining payoff table for Bargainers B and S, with Bargainer B making the first offer, with 4 bargaining rounds, with S discounting 100% between each period, and with S discounting 2% between each period. BA 445 Lesson B.2 Sequential Bargaining and Impatience

  50. Review 1: Relative Impatience • Summary: In the first case, when B discounts 10% between each period, B captures 82.08% of the $60 gains from trade, or about $49.25, leaving S with about $10.75. Buyer Betty thus makes an acceptable offer of $65-$49.25 = $15.75, leaving Seller Shen with gain $15.75-$5 = $10.75. • On one extreme, when B discounts only 1% between each period, B captures 98.0298% of the $60 gains from trade, or about $58.82, leaving S with about $1.18. Buyer Betty thus makes an acceptable offer of $65-$58.82 = $6.18, leaving Seller Shen with gain $6.18-$5 = $1.18. • On the other extreme, when B discounts 100% between each period, B captures 0% of the $60 gains from trade, or $0, leaving S with $60. Buyer Betty thus makes an acceptable offer of $65, leaving Seller Shen with gain $65-$5 = $60. It is just as if Seller Shen made a take-it-or-leave-it offer. • Buyer Betty does better when she is more patient. In an extreme, she gets no gains when she has no patience. BA 445 Lesson B.2 Sequential Bargaining and Impatience

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