1 1 Deep Thought BA 210 Lesson II.2 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 210 Lesson II.2 Bargaining and ImpatienceOverviewOverview

3 3Overview Lesson II.1 Strategic Bargaining Lesson II.2 Bargaining and Impatience Example 1: Best Alternative to No Agreement Example 2: Mutual Alternatives to No Agreement Example 3: Manipulating Alternatives to No Agreement Example 4: Bargaining with Impatience Example 5: Relative Impatience Lesson II.3 Sequential Quantity Competition Summary Review Questions

4 4 BA 210 Lesson II.2 Bargaining and Impatience Lesson II.2 formulates and solves the following games: Examples 1, 2, 3, 4, 5: Sequential Bargaining Games. Have unique rollback solutions. The solution favors the first mover, and so favors aggressors; favors those with better outside alternatives to an agreement; and favors those with more patience. Overview

5 5 BA 210 Lesson II.2 Bargaining and Impatience Example 1: Best Alternative to No Agreement

6 6 BA 210 Lesson II.2 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. Example 1: Best Alternative to No Agreement

7 7 BA 210 Lesson II.2 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? Example 1: Best Alternative to No Agreement

8 8 BA 210 Lesson II.2 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. Example 1: Best Alternative to No Agreement

9 9 BA 210 Lesson II.2 Bargaining and Impatience Comment: In any Bargaining Game, a bargainer’s 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. Example 1: Best Alternative to No Agreement

10 BA 210 Lesson II.2 Bargaining and Impatience Example 2: Bilateral Alternatives to No Agreement

11 BA 210 Lesson II.2 Bargaining and Impatience Question 1. Consider union-management negotiations over wages for workers during Easter Weekend at Medieval Times Dinner Theatre. The weekend lasts Saturday and Sunday. Each day Medieval Times operates with union labor, it makes a profit of $10,000. On the Friday night 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. 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? Review Questions

12 BA 210 Lesson II.2 Bargaining and Impatience Review Questions Answer 1: 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 2 x (10-3-2) = 10 thousand gain from accepting the Union’s offer at the beginning.

13 Starting 1 bargaining round from the end of the game, when a contract has 50 percent of its original value, the Union should accept anything as being better than nothing. So, Management can get away with the whole 50 percent minus a pittance, leaving the Union with the pittance. Rolling back to the beginning of the game, 2 bargaining rounds from the end, when a contract has 100 percent of its original value, Management could reject any offer and get 50 percent in the next round. So, the Union’s best acceptable offer leaves Management with 50 percent plus a pittance, and the union with 25 percent minus a pittance. BA 210 Lesson II.2 Bargaining and Impatience Review Questions

14 BA 210 Lesson II.2 Bargaining and Impatience Review Questions The Union’s initial wage demand should be for 50% of the $10,000 profits, or $5,000, and management should accept that demand. Since the BATNA for Medieval Times is $3,000 x 2 = $6,000 profit from scab labor and the BATNA for union labor is $2,000 x 2 = $4,000 from outside employment, the initial wage demand by the union should be $4,000+$5,000 = $9,000, and management should accept that demand, and so earn $20,000- $9,000 = $11,000 profit.

15 BA 210 Lesson II.2 Bargaining and Impatience Example 3: Manipulating Alternatives to No Agreement

16 BA 210 Lesson II.2 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. Example 3: Manipulating Alternatives to No Agreement

17 BA 210 Lesson II.2 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. Example 3: Manipulating Alternatives to No Agreement

18 BA 210 Lesson II.2 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. Example 3: Manipulating Alternatives to No Agreement

19 BA 210 Lesson II.2 Bargaining and Impatience Originally, the Union’s initial wage demand should give it 50% of the $10,000 gains from trade, or $5,000, and management should accept that demand. Since the BATNA for Medieval Times is $3,000 x 2 = $6,000 profit from scab labor and the BATNA for union labor is $2,000 x 2 = $4,000 from outside employment, the initial wage demand by the union should be $4,000+$5,000 = $9,000, and management should accept that demand, and so earn $20,000-$9,000 = $11,000 profit. But with intensified picketing, the BATNA for Medieval Times is $2,000 x 2 = $4,000 and the BATNA for union labor is $1,500 x 2 = $3,000 and the gains from trade is $13,000. So, the initial wage demand by the union should be $3,000+$6,500 = $9,500, and management should accept that demand, and so earn $20,000- $9,500 = $10,500 profit. The Union does better. Example 3: Manipulating Alternatives to No Agreement

20 BA 210 Lesson II.2 Bargaining and Impatience Example 4: Bargaining with Impatience

21 BA 210 Lesson II.2 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. Example 4: Bargaining with Impatience

22 BA 210 Lesson II.2 Bargaining and Impatience Question: Compute a bargaining payoff table for Bargainers A and B making alternating offers over 3 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. Example 4: Bargaining with Impatience

23 BA 210 Lesson II.2 Bargaining and Impatience Example 4: Bargaining with Impatience Answer: A bargaining payoff table for Bargainers A and B making alternating offers over 3 bargaining rounds, with Bargainer A making the first offer:

24 BA 210 Lesson II.2 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 the beginning of the game, 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. Example 4: Bargaining with Impatience

25 BA 210 Lesson II.2 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 3 bargaining rounds and if A and B each discount 10%, then A’s best acceptable offer to B is 9 plus a pittance, leaving A with 91. On the other hand, if there are 3 bargaining rounds and the object itself depreciates 10% per round, then A’s best acceptable offer to B is, again, 9 plus a pittance, leaving A with 91. Example 4: Bargaining with Impatience

26 BA 210 Lesson II.2 Bargaining and Impatience Example 5: Relative Impatience

27 BA 210 Lesson II.2 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. Example 5: Relative Impatience

28 BA 210 Lesson II.2 Bargaining and Impatience Question: Compare outcomes from 3 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. Example 5: Relative Impatience

29 BA 210 Lesson II.2 Bargaining and Impatience Answer: A bargaining payoff table for Bargainers A and B, with Bargainer A making the first offer, with 3 bargaining rounds, with A discounting 10% between each period, and with B discounting 20% between each period. Example 5: Relative Impatience

30 BA 210 Lesson II.2 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 the beginning, 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. Example 5: Relative Impatience

31 BA 210 Lesson II.2 Bargaining and Impatience A bargaining payoff table for Bargainers A and B, with Bargainer A making the first offer, with 3 bargaining rounds, with A discounting 20% between each period, and with B discounting 10% between each period. Example 5: Relative Impatience

32 BA 210 Lesson II.2 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 the beginning, 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. Example 5: Relative Impatience

33 BA 210 Lesson II.2 Bargaining and Impatience Summary: Compare outcomes from 3 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 9%, leaving A with 91%. 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 8%, leaving A with 92%. 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 18 plus a pittance, leaving A with 82. A does best when his is more patient (discounts less) than B. Example 5: Relative Impatience

34 BA 210 Lesson II.2 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. Example 5: Relative Impatience

35 BA 210 Lesson II.2 Bargaining and ImpatienceSummarySummary

36 BA 210 Lesson II.2 Bargaining and ImpatienceSummary A bargainer’s 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.

37 BA 210 Lesson II.2 Bargaining and Impatience A bargaining payoff table for Bargainers A and B, with Bargainer A making the first offer, with 3 bargaining rounds, with A discounting 30% between each period, and with B discounting 40% between each period. Example 5: Relative Impatience

38 BA 210 Lesson II.2 Bargaining and Impatience A bargaining payoff table for Bargainers A and B, with Bargainer A making the first offer, with 3 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.) Example 5: Relative Impatience

39 Review Questions BA 210 Lesson II.2 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 1 and cumulative Final Exam will contain some similar questions, so you should eventually consider every review question before taking your exams.

40 BA 210 Lesson II.2 Bargaining and Impatience Review Questions Review Question 1

41 BA 210 Lesson II.2 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 Questions

42 BA 210 Lesson II.2 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 2 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). Review Questions

43 BA 210 Lesson II.2 Bargaining and Impatience Answer 1: A bargaining payoff table for Bargainers B and S, with Bargainer S making the first offer, with 2 bargaining rounds, with B discounting 10% between each period, and with S discounting 2% between each period. Review Questions

44 BA 210 Lesson II.2 Bargaining and Impatience A bargaining payoff table for Bargainers B and S, with Bargainer S making the first offer, with 2 bargaining rounds, with B discounting only 1% between each period, and with S discounting 2% between each period. Review Questions

45 BA 210 Lesson II.2 Bargaining and Impatience A bargaining payoff table for Bargainers B and S, with Bargainer S making the first offer, with 2 bargaining rounds, with B discounting 100% between each period, and with S discounting 2% between each period. Review Questions

46 BA 210 Lesson II.2 Bargaining and Impatience Summary: In the first case, when B discounts 10% between each period, B captures 90% of the $60 gains from trade, or $54, leaving S with $6. Buyer Betty thus makes an acceptable offer of $65-$54 = $11, leaving Seller Shen with gain $11-$5 = $6. On one extreme, when B discounts only 1% between each period, B captures 99% of the $60 gains from trade, or $59.40, leaving S with $0.60. Buyer Betty thus makes an acceptable offer of $65-$59.40 = $5.60, leaving Seller Shen with gain $5.60-$5 = $0.60. 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. Review Questions

47 End of Lesson II.2 BA 210 Lesson II.2 Bargaining and Impatience BA 210 Introduction to Microeconomics