1 1 Deep Thought BA 445 Lesson B.2 Sequential Bargaining and Impatience 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.)

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

3 3 BA 445 Lesson B.2 Sequential Bargaining and Impatience OverviewOverview

4 4Overview 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. 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. 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. 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. 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.

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

6 6 BA 445 Lesson B.2 Sequential Bargaining and Impatience 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. Best Alternative to No Agreement

7 7 BA 445 Lesson B.2 Sequential Bargaining and Impatience 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. Best Alternative to No Agreement

8 8 BA 445 Lesson B.2 Sequential Bargaining and Impatience 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? Best Alternative to No Agreement

9 9 BA 445 Lesson B.2 Sequential Bargaining and Impatience 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. Best Alternative to No Agreement

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

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

12 BA 445 Lesson B.2 Sequential Bargaining and Impatience 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. Mutual Alternatives to No Agreement

13 BA 445 Lesson B.2 Sequential Bargaining and Impatience 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? Mutual Alternatives to No Agreement

14 BA 445 Lesson B.2 Sequential Bargaining and Impatience 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. Mutual Alternatives to No Agreement

15 BA 445 Lesson B.2 Sequential Bargaining and Impatience 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. Mutual Alternatives to No Agreement

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

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

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

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

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

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

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

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

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

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

26 BA 445 Lesson B.2 Sequential Bargaining and Impatience 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:

27 BA 445 Lesson B.2 Sequential Bargaining and 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 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 in the current round.. After deducing that, A’s best acceptable offer to B is plus a pittance, leaving A with Bargaining with Impatience

28 BA 445 Lesson B.2 Sequential Bargaining and 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%. Bargaining with Impatience

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

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

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

32 BA 445 Lesson B.2 Sequential Bargaining and Impatience Question: Compare outcomes from 5 rounds of bargaining in three different scenarios: 1)Both bargainers discount the money payoff from an agreement 10 percent each round. 2)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. 3)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. Relative Patience

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

34 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 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 in the current round.. After deducing that, A’s best acceptable offer to B is plus a pittance, leaving A with BA 445 Lesson B.2 Sequential Bargaining and Impatience Relative Patience

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

36 BA 445 Lesson B.2 Sequential Bargaining and 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 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 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 in the current round.. After deducing that, A’s best acceptable offer to B is plus a pittance, leaving A with Relative Patience

37 BA 445 Lesson B.2 Sequential Bargaining and Impatience Summary: Compare outcomes from 5 rounds of bargaining in three different scenarios. 1)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%. 2)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%. 3)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 plus a pittance, leaving A with A does best when his is more patient (discounts less) than B. Relative Patience

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

39 BA 445 Lesson B.2 Sequential Bargaining and Impatience SummarySummary

40 BA 445 Lesson B.2 Sequential Bargaining and Impatience 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.

41 BA 445 Lesson B.2 Sequential Bargaining and Impatience 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. Summary

42 BA 445 Lesson B.2 Sequential Bargaining and Impatience 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.) Summary

43 Review Questions BA 445 Lesson B.2 Sequential Bargaining and Impatience 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.

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

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

46 Review 1: Relative Impatience BA 445 Lesson B.2 Sequential Bargaining and 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).

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

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

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

50 Review 1: Relative Impatience BA 445 Lesson B.2 Sequential Bargaining and 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 $ Buyer Betty thus makes an acceptable offer of $65-$49.25 = $15.75, leaving Seller Shen with gain $15.75-$5 = $ On one extreme, when B discounts only 1% between each period, B captures % 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.

51 End of Lesson B.2 BA 445 Lesson B.2 Sequential Bargaining and Impatience BA 445 Managerial Economics