1. 1 1Review BA 445 Lesson B.1 Sequential Bargaining and Depreciation We will spend up to 30 minutes reviewing Exam 1 Know how your answers were graded.Know how your answers were graded. Know how to correct your mistakes. Your final exam is cumulative, and may contain similar questions.Know how to correct your mistakes. Your final exam is cumulative, and may contain similar questions. Review

2. 2 2 Deep Thought BA 445 Lesson B.1 Sequential Bargaining and Depreciation I can picture in my mind a world without war, a world without hate. And I can picture us attacking that world, because they’d never expect it. ~ Jack Handey. (Translation: Today’s lesson teaches how to get your best deal from bargaining.)

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

4. 4 4 BA 445 Lesson B.1 Sequential Bargaining and Depreciation OverviewOverview

5. 5 5 Part B Overview Supply and Demand Analysis from Part A helps managers make profitable decisions when there are impersonal competitive markets of large numbers of firms and customers and workers. Game Theory in Parts B and C now completes supply and demand analysis when personal decisions interact. For example, if Carlos tries to sell shoes or Aleisha tries to buy shoes on eBay, they each compete with many potential shoe sellers or buyers, with price determined by aggregate supply and demand. But if, instead, Aleisha happens to walk by Carlos’s trading stall outside the Tijuana Wax Museum, they become tied to a few potential shoe sellers or buyers in Tijuana, and they negotiate a sales price separate from the worldwide competitive market. BA 445 Lesson B.1 Sequential Bargaining and Depreciation Overview

6. 6 6 Each lesson in Parts B and C is divided into examples. Each example asks a Question and supplies an Answer. The questions are like the questions on your exams: A game is described verbally and you are asked questions about its solution. You must formulate the game (identifying players, strategies, payoffs, …) then answer those questions by solving the game. Many examples also include a Comment about what general lesson you learn from the example. BA 445 Lesson B.1 Sequential Bargaining and Depreciation Overview

7. 7 7Overview Bargaining verses Competition depends on the number of alternative buyers and sellers. Bargaining occurs when one buyer and one seller meet separate from a competitive market. Rollback Solutions find your optimal sequence of bargaining offers and counteroffers, or any sequence of decisions, by making your last decision first. — So, before your first cigarette, think about your last. Take-it-or-Leave-it Offers capture the most gains from any agreement. Make the other party an offer and do not let them make a counter offer; they must take your first offer or leave it. Counter Offers by the other party can eliminate the gains that could be captured by your initial offer. — So, a buyer gains more from making an offer if he waits until his tour bus schedule leaves no time for a counteroffer. Bargaining and Depreciation should lead to an agreement before the gains from the agreement actually depreciate. However, the possibility of depreciation affects the bargaining agreement.

8. 8 8 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Bargaining verses Competition

9. 9 9 Overview Bargaining verses Competition depends on the number of alternative buyers and sellers. Bargaining occurs when one buyer and one seller meet separate from a competitive market. BA 445 Lesson B.1 Sequential Bargaining and Depreciation Bargaining verses Competition

10. 10 Question: Suppose Aleisha is willing to offer up to $59 to buy a pair of shoes.Aleisha is willing to offer up to $59 to buy a pair of shoes. Brad, to pay $44; Claudia, $34.01; Darren, $24; Edwina, $10.Brad, to pay $44; Claudia, $34.01; Darren, $24; Edwina, $10.Suppose Andrew is willing to accept down to $8 to sell a pair of shoes.Andrew is willing to accept down to $8 to sell a pair of shoes. Betty, to sell $20; Carlos, $34; Donna, $48; Engelbert, $62.Betty, to sell $20; Carlos, $34; Donna, $48; Engelbert, $62. Compute the competitive-equilibrium price of shoes if all 10 people trade shoes on eBay? (Ignore shipping costs.) Alternatively, suppose Aleisha and Carlos do not use eBay, but Aleisha walks by Carlos’s trading stall outside the Tijuana Wax Museum. Compute the gains if they trade a pair of shoes. Compute the price of shoes if they divide the gains 50-50. BA 445 Lesson B.1 Sequential Bargaining and Depreciation Bargaining verses Competition

11. 11 Answer: Competitive Markets have Many Independent Buyers... Aleisha is willing to offer up to $59 to buy a pair of shoes.Aleisha is willing to offer up to $59 to buy a pair of shoes. Brad, $44; Claudia, $34.01; Darren, $24; Edwina, $10.Brad, $44; Claudia, $34.01; Darren, $24; Edwina, $10. BA 445 Lesson B.1 Sequential Bargaining and Depreciation Aleisha Brad Claudia Darren Edwina Bargaining verses Competition

12. 12 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Aleisha Brad Claudia Darren Edwina … and Many Independent Sellers Andrew is willing to accept down to $8 to sell a pair of shoes.Andrew is willing to accept down to $8 to sell a pair of shoes. Betty, $20; Carlos, $34; Donna, $48; Engelbert, $62.Betty, $20; Carlos, $34; Donna, $48; Engelbert, $62. Engelbert Donna Carlos Betty Andrew Bargaining verses Competition

13. 13 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Aleisha Brad Claudia Darren Edwina Demand equals Supply determines Competitive Price At some price between $34 and $34.01, Aleisha, Brad and Claudia each buy 1 pair, and Andrew, Betty and Carlos each sell.At some price between $34 and $34.01, Aleisha, Brad and Claudia each buy 1 pair, and Andrew, Betty and Carlos each sell. Engelbert Donna Carlos Betty Andrew Bargaining verses Competition

14. 14 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Bargaining Occurs with One Buyer and One Seller If Aleisha and Carlos meet separate from the competitive market, then the gains if they were to trade a pair of shoes is the difference between willingness to pay and willingness to sell. Aleisha is willing to offer $59 to buy a pair of shoes.Aleisha is willing to offer $59 to buy a pair of shoes. Carlos is willing to accept $34 to sell a pair of shoes.Carlos is willing to accept $34 to sell a pair of shoes. The gain from trade is the difference, $25 = $59-$34.The gain from trade is the difference, $25 = $59-$34. If Aleisha and Carlos divided the gains from trade 50-50, then each gets $12.50 gain, meaning Aleisha pays price $46.50 = $59.00-$12.50, and Carlos receives price $46.50 = $34.00+$12.50 Bargaining verses Competition

15. 15 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Rollback Solutions

16. 16 Overview Rollback Solutions find your optimal sequence of bargaining offers and counteroffers, or any sequence of decisions, by making your last decision first. — So, before your first cigarette, think about your last. BA 445 Lesson B.1 Sequential Bargaining and Depreciation Rollback Solutions

17. 17 Comment: Whether Aleisha and Carlos divide the gains from trade 50-50 or 99-1 or some other division depends on the rules for the sequence of bargaining offers and counteroffers. Consider an instructive game to illustrate the best way to make any sequence of decisions. BA 445 Lesson B.1 Sequential Bargaining and Depreciation Rollback Solutions

18. 18 Question: Consider the Century Mark Game Played by pairs of players taking turns.Played by pairs of players taking turns. At each turn, each player chooses a number between 1 and 10 inclusive.At each turn, each player chooses a number between 1 and 10 inclusive. This choice is added to sum of all previous choices (the initial sum is 0).This choice is added to sum of all previous choices (the initial sum is 0). The first player to take the cumulative sum to 100 or more wins.The first player to take the cumulative sum to 100 or more wins. How should you play the game if you were the first player? BA 445 Lesson B.1 Sequential Bargaining and Depreciation Rollback Solutions

19. 19 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Answer: Start at the end of the game and work backward. This is called backward induction and it defines a rollback solution, or rollback equilibrium. In the Century Mark Game, first ask: What number gets you to 100 next turn? If you bring the cumulative sum to 89, you can take the cumulative sum to 100 on your next turn and win no matter what your opponent does. (Whatever your opponent does, you can make the sum of your two moves equal 11, and 89+11 = 100.) Rollback Solutions

20. 20 Complete Rollback Solution If you bring the cumulative sum to 89 on one turn, you can take the cumulative sum to 100 on your next turn and win no matter what your opponent does. (Whatever your opponent does, you can make the sum of your two moves equal 11.)If you bring the cumulative sum to 89 on one turn, you can take the cumulative sum to 100 on your next turn and win no matter what your opponent does. (Whatever your opponent does, you can make the sum of your two moves equal 11.) Hence, if you bring the cumulative sum to 78 on one turn, you can take the cumulative sum to 89 on your next turn (and so eventually win) no matter what your opponent does.Hence, if you bring the cumulative sum to 78 on one turn, you can take the cumulative sum to 89 on your next turn (and so eventually win) no matter what your opponent does. And so on for sums 67, 56, 45, 34, 23, 12.And so on for sums 67, 56, 45, 34, 23, 12. Hence, if you play 1 on your first turn, you can bring the cumulative sum to 12 on your next turn (and so eventually win) no matter what your opponent does.Hence, if you play 1 on your first turn, you can bring the cumulative sum to 12 on your next turn (and so eventually win) no matter what your opponent does. That solution is a strategy --- a complete plan of actions no matter what your opponent does.That solution is a strategy --- a complete plan of actions no matter what your opponent does. BA 445 Lesson B.1 Sequential Bargaining and Depreciation Rollback Solutions

21. 21 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Take-it-or-leave-it Bargaining

22. 22 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Overview Take-it-or-Leave-it Offers capture the most gains from any agreement. Make the other party an offer and do not let them make a counter offer; they must take your first offer or leave it. Take-it-or-leave-it Bargaining

23. 23 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Comment 1: Bargaining Games have three parts. Players or bargainers are managers, customers, or workers, typically considered two at the time.Players or bargainers are managers, customers, or workers, typically considered two at the time. Strategies are offers to divide a fixed positive gain from an agreement, the rejection of such an offer, or the acceptance of such an offer. The most common agreements is trading a good at a particular price.Strategies are offers to divide a fixed positive gain from an agreement, the rejection of such an offer, or the acceptance of such an offer. The most common agreements is trading a good at a particular price. Manager strategies include a price at which to sell a consumption good or a wage to buy workers’ time.Manager strategies include a price at which to sell a consumption good or a wage to buy workers’ time. Customer strategies include a price at which to buy.Customer strategies include a price at which to buy. Worker strategies include a wage at which to sell.Worker strategies include a wage at which to sell. Payoffs are percentage shares of the gain from an agreement, if there is an agreement, or zero if there were no agreement.Payoffs are percentage shares of the gain from an agreement, if there is an agreement, or zero if there were no agreement. Take-it-or-leave-it Bargaining

24. 24 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Comment 2: Bargaining Games in Part II assume Rationality and Perfect Information are Common Knowledge. Rationality means players are perfect calculators and perfect followers of their best strategies. Players have perfect knowledge of their own interests.Rationality means players are perfect calculators and perfect followers of their best strategies. Players have perfect knowledge of their own interests. Perfect Information means players know the bargaining rules and all offers that have taken place.Perfect Information means players know the bargaining rules and all offers that have taken place. Common Knowledge of rationality and perfect information means all players assume all other players are rational and have perfect information, and all players assume all other players assume all other players are rational and have perfect information, and so on.Common Knowledge of rationality and perfect information means all players assume all other players are rational and have perfect information, and all players assume all other players assume all other players are rational and have perfect information, and so on. In contrast, poker professionals (sharks) do not assume bad players (fish or suckers) are rational. Sharks try to trick fish.In contrast, poker professionals (sharks) do not assume bad players (fish or suckers) are rational. Sharks try to trick fish. Take-it-or-leave-it Bargaining

25. 25 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Question: Suppose Buyer Bob values the bag of fresh beans in front of him at 1 dollar and Seller Sabitha has no alternative buyers and has no other value for the beans. 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. Which of the prices $0.01, $0.50, or $0.98 should Buyer Bob offer? Take-it-or-leave-it Bargaining

26. 26 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Answer: Follow two steps to define any Bargaining Game:  Determine the total gain from an agreement. When the agreement means trading a good at a particular price, the gain is the maximum price the buyer were willing to pay minus the minimum price the seller were willing to receive. Here, total gain is $1.  Strategies are then percentage shares of the gain from trade. Here, prices $0.01, $0.50, or $0.98 means Bob takes 99 percent, 50 percent, or 2 percent of the gain from trade.  Determine the bargaining rules. Here, Bob makes an offer that Sabitha accepts or rejects. Either way, the game is then over. Take-it-or-leave-it Bargaining

27. 27 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Comment: Many Sequential-Move Games have complex rollback solutions requiring a game tree to predict future responses to current actions. Game trees or extensive forms consist of nodes and branches. Nodes are connected to one another by the branches, and come in two types. Some nodes are decision nodes, where a player chooses an action branch to another node. The other nodes are terminal nodes, where players receive the outcomes of the actions taken by themselves and all other players. Take-it-or-leave-it Bargaining

28. 28 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Answer (continued): Here is a Game Tree where payoffs list the gains from trade, with payoffs to the first player to act (Bob, the proposer) listed first. Take-it-or-leave-it Bargaining

29. 29 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Starting at the end of the game, Bob predicts rational responses to alternative proposals. Sabitha should accept anything as being better than nothing. Take-it-or-leave-it Offers

30. 30 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Rolling back to the beginning of the game, determine Bob’s rational proposal, where Bob assumes Sabitha is rational. Bob should offer to take 99%. Take-it-or-leave-it Offers

31. 31 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Counter Offers

32. 32 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Overview Counter Offers by the other party can eliminate the gains that could be captured by your initial offer. — So, a buyer gains more from making an offer if he waits until his tour bus schedule leaves no time for a counteroffer. Counter Offers

33. 33 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Comment: Bargainers can get most of the gains from trade by making take-it-or-leave-it offers. So it is best for Buyer Bob to make an offer on a bag of beans just as his tour bus is about to leave. To try to counter the take-it-or-leave-it strategy and get more of the gains from trade, Seller Sabitha can try to make a (quick) counter offer. Counter Offers

34. 34 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Question: Suppose Buyer Bob values the bag of fresh beans in front of him at 1 dollar and Seller Sabitha has no alternative buyers and has no other value for the beans. But now suppose there is only enough time before his tour bus leaves for Bob to make one offer to Sabitha for the bag of beans and for Sabitha to either to accept or to reject and to make a counteroffer that Bob must either accept or reject. Will trade occur? If so, at what price? Counter Offers

35. 35 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Answer: To consider all possible price offers (offers by Bob to buy or counteroffers by Sabitha to sell), consider a bargaining payoff table: Counter Offers

36. 36 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Starting 1 bargaining round from the end of the game, Sabitha either accepts Bob’s offer or makes a counteroffer that Bob must either accept or reject. Bob should accept anything as being better than nothing. So, Sabitha can get away with the whole gain from trade minus a pittance, leaving Bob with the pittance (essentially, a zero gain to Bob). Counter Offers

37. 37 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Rolling back to the beginning (2 bargaining rounds from the end of the game), Sabitha could reject any offer and get 100 percent in the next round. So, Bob’s best acceptable offer leaves Sabitha with 100 percent, and Bob with 0 percent. That is, trade occurs, and Bob pays $1. Counter Offers

38. 38 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Comment: Listening to a counteroffer thus eliminates all the gains from trade that would otherwise have gone to the player making a take-it-or-leave-it offer. Bob should have refused to listen and, so, forced Sabitha to take or leave a first offer of a pittance to Sabitha. Counter Offers

39. 39 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Bargaining with Depreciation

40. 40 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Overview Bargaining and Depreciation should lead to an agreement before the gains from the agreement actually depreciate. However, the possibility of depreciation affects the bargaining agreement. Bargaining with Depreciation

41. 41 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Comment: Bargaining rules change if the value of the good depreciates like ice cream in the time it takes to make counteroffers to offers, and counter-counteroffers to counteroffers and so on. Bargaining with Depreciation

42. 42 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Question: Suppose Buyer Bob values an ice cream bar at 1 dollar and Seller Sam has no alternative buyers and has no other value for the ice cream. Suppose Bob can make the first offer to Sam, who can accept or make a counter offer to Bob, who in turn can accept or make a counter offer to Sam. Offers alternate thereafter. But each counter offer takes valuable time which melts the ice cream and, so, reduces the initial value of the ice cream by 20 cents. What initial price should Buyer Bob offer? Should Seller Sam accept that first offer? Bargaining with Depreciation

43. 43 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Answer: To consider all possible price offers (offers by Bob to buy or offers by Sam to sell), consider another bargaining payoff table. The game ends if an offer is accepted or the ice cream is completely melted and worthless, and gains are measured as a percentage of the $1.00 gain from trading the ice cream before it starts melting. Bargaining with Depreciation

44. 44 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Starting 1 bargaining round from the end of the game, when the ice cream has 20 percent of its original value, Sam should accept anything as being better than nothing. So, Bob can get away with the whole 20 percent minus a pittance, leaving Sam with the pittance. Bargaining with Depreciation

45. 45 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Rolling back to 2 steps to meltdown, when the ice cream has 40 percent of its original value, Bob could reject any offer and get 20 percent in the next round. So, Sam’s best acceptable offer leaves Bob with 20 percent plus a pittance, and Sam with 20 percent minus a pittance. Bargaining with Depreciation

46. 46 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Rolling back to 3 steps to meltdown, when the ice cream has 60 percent of its original value, Sam could reject any offer and get 20 percent in the next round. So, Bob’s best acceptable offer leaves Sam with 20 percent plus a pittance, and Bob with 40 percent minus a pittance. Bargaining with Depreciation

47. 47 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Rolling back to 4 steps to meltdown, when the ice cream has 80 percent of its original value, Bob could reject any offer and get 40 percent in the next round. So, Sam’s best acceptable offer leaves Bob with 40 percent plus a pittance, and Sam with 40 percent minus a pittance. Bargaining with Depreciation

48. 48 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Rolling back to the beginning of the game, when the ice cream has 100% of its original value of $1.00, Sam could reject any offer and get 40 percent in the next round. So, Bob’s best acceptable offer leaves Sam with 40 percent plus a pittance, and Bob with 60 percent minus a pittance. Bargaining with Depreciation

49. 49 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Buyer Bob should thus initially offer price $0.40 for the ice cream, and Seller Sam should accept that first offer. That gives Bob 60 percent of the gain from trade and Sam 40 percent. Bargaining with Depreciation

50. 50 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Comment: The players in that counter offer game did not actually make any counteroffers, but the possibility of counteroffers affected the initial offer. In more advanced games (covered in Part III), counteroffers can actually occur, and ice cream can start melting, if players lack perfect information about the payoffs of other players. Bob’s value of the ice cream, for example, can be unknown to Sam, so Bob can try to signal a lower value of ice cream by offering a low initial price. Sam might then conclude Bob has almost zero value for the ice cream and, so, might counteroffer the ice cream at a price near zero. Counteroffers with Depreciation

51. 51 BA 445 Lesson B.1 Sequential Bargaining and Depreciation SummarySummary

52. 52 BA 445 Lesson B.1 Sequential Bargaining and Depreciation 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 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.

53. 53 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Summary A bargaining payoff table for Bargainers A and B, with Bargainer A making the only offer: 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 percent.

54. 54 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Summary A bargaining payoff table for Bargainers A and B, with Bargainer A making the first offer, when the potential gains from bargaining fully depreciate after 2 Rounds:

55. 55 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Summary Starting 1 bargaining round from the end, when the gain has 33 1/3 percent of its original value, A should accept anything as being better than nothing. After deducing that, B’s best acceptable offer to A is a pittance, leaving B with 25 percent. Rolling back to the beginning, when the gain has 100 percent of its original value, B could reject any offer and get 50 percent in the next round. After deducing that, A’s best acceptable offer to B is 50 percent plus a pittance, leaving A with 50 percent.

56. 56 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Summary A bargaining payoff table for Bargainers A and B, with Bargainer A making the first offer, when the potential gains from bargaining fully depreciate after 3 Rounds:

57. 57 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Summary Starting 1 bargaining round from the end, when the gain has 33 1/3 percent of its original value, 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 25 percent. Rolling back to 2 rounds from the end, when the gain has 66 2/3 percent of its original value, A could reject any offer and get 33 1/3 percent in the next round. After deducing that, B’s best acceptable offer to A is 33 1/3 percent plus a pittance, leaving B with 33 1/3 percent. Rolling back to the beginning, when the gain has 100 percent of its original value, B could reject any offer and get 33 1/3 percent in the next round. After deducing that, A’s best acceptable offer to B is 33 1/3 percent plus a pittance, leaving A with 66 2/3 percent.

58. 58 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Summary A bargaining payoff table for Bargainers A and B, with Bargainer A making the first offer, when the potential gains from bargaining fully depreciate after 4 Rounds:

59. 59 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Summary Starting 1 bargaining round from the end, when the gain has 25 percent of its original value, A should accept anything as being better than nothing. After deducing that, B’s best acceptable offer to A is a pittance, leaving B with 25 percent. Rolling back to 2 rounds from the end, when the gain has 50 percent of its original value, B could reject any offer and get 25 percent in the next round. After deducing that, A’s best acceptable offer to B is 25 percent plus a pittance, leaving A with 25 percent. Rolling back to 3 rounds from the end, when the gain has 75 percent of its original value, A could reject any offer and get 25 percent in the next round. After deducing that, B’s best acceptable offer to A is 25 percent plus a pittance, leaving B with 50 percent. Rolling back to the beginning, when the gain has 100 percent of its original value, B could reject any offer and get 50 percent in the next round. After deducing that, A’s best acceptable offer to B is 50 percent plus a pittance, leaving A with 50 percent.

60. 60 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Summary A bargaining payoff table for Bargainers A and B, with Bargainer A making the first offer, when the potential gains from bargaining fully depreciate after 5 Rounds:

61. 61 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Summary Starting 1 bargaining round from the end, when the gain has 20 percent of its original value, 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 20 percent. Rolling back to 2 rounds from the end, when the gain has 40 percent of its original value, A could reject any offer and get 20 percent in the next round. After deducing that, B’s best acceptable offer to A is 20 percent plus a pittance, leaving B with 20 percent. Rolling back to 3 rounds from the end, when the gain has 60 percent of its original value, B could reject any offer and get 20 percent in the next round. After deducing that, A’s best acceptable offer to B is 20 percent plus a pittance, leaving A with 40 percent. Rolling back to 4 rounds from the end, when the gain has 80 percent of its original value, A could reject any offer and get 40 percent in the next round. After deducing that, B’s best acceptable offer to A is 40 percent plus a pittance, leaving B with 40 percent. Rolling back to the beginning, when the gain has 100 percent of its original value, B could reject any offer and get 40 percent in the next round. After deducing that, A’s best acceptable offer to B is 40 percent plus a pittance, leaving A with 60 percent.

62. 62 Review Questions BA 445 Lesson B.1 Sequential Bargaining and Depreciation 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.

63. 63 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Review 1: Bargaining with Depreciation

64. 64 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Question 1. Consider union-management negotiations over wages for workers during Thanksgiving Weekend at Medieval Times Dinner Theatre. The extended weekend lasts Thursday through Sunday. Each day Medieval Times operates, it makes a profit of $10,000. On the Wednesday 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. Offers alternate thereafter. Medieval Times can open only on those days after an agreement is reached. What initial wage demand should the union make? Should management accept that demand? Review 1: Bargaining with Depreciation

65. 65 BA 445 Lesson B.1 Sequential Bargaining and Depreciation 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 $40,000 gain from accepting the Union’s initial offer. Review 1: Bargaining with Depreciation

66. 66 Starting 1 bargaining round from the end of the game, when a contract has 25 percent of its original value, the Union should accept anything as being better than nothing. So, Management can get away with the whole 25 percent minus a pittance, leaving the Union with the pittance. Rolling back to 2 bargaining rounds from the end, when a contract has 50 percent of its original value, Management could reject any offer and get 25 percent in the next round. So, the Union’s best acceptable offer leaves Management with 25 percent plus a pittance, and the union with 25 percent minus a pittance. BA 445 Lesson B.1 Sequential Bargaining and Depreciation Review 1: Bargaining with Depreciation

67. 67 Rolling back to 3 bargaining rounds before the end, when a contract has 75 percent of its original value, the Union could reject any offer and get 25 percent in the next round. So, Management’s best acceptable offer leaves the Union with 25 percent plus a pittance, and Management with 50 percent minus a pittance. Rolling back to the beginning, 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 50 percent minus a pittance. BA 445 Lesson B.1 Sequential Bargaining and Depreciation Review 1: Bargaining with Depreciation

68. 68 BA 445 Lesson B.1 Sequential Bargaining and Depreciation The Union’s initial wage demand should be for 50% of the $40,000 profits, or $20,000, and management should accept that demand. Review 1: Bargaining with Depreciation

69. 69 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Review 2: Bargaining with Depreciation

70. 70 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Question 2. Consider negotiations over wages for adjunct Management Science Professors at the Business Administration Division of Seaver College of Pepperdine University. Pepperdine seeks a professor for the next 3 semesters. The only candidate is willing to work for $15,000 per semester and Pepperdine is willing to pay up to $25,000 per semester, so the potential gains from trade are $10,000 per semester. Before the first semester, Pepperdine confronts the candidate over wages. Pepperdine presents its offer. The candidate either accepts it or rejects it and returns the next semester with a counteroffer. Offers alternate thereafter. Employment only occurs in those semesters after an agreement is reached. What percentage of the gains from trade should Pepperdine offer? Should the candidate accept that initial offer? Review 2: Bargaining with Depreciation

71. 71 Review 2: Bargaining with Depreciation BA 445 Lesson B.1 Sequential Bargaining and Depreciation Answer 2: To consider all possible wage offers (offers by Pepperdine to buy labor by the candidate to sell labor), consider another bargaining payoff table. The game ends if an offer is accepted or if the three semesters end without an accepted offer, and gains are measured as a percentage of the $30,000 gain from accepting Pepperdine’s offer before the first semester.

72. 72 Review 2: Bargaining with Depreciation BA 445 Lesson B.1 Sequential Bargaining and Depreciation Starting 1 bargaining round from the end of the game, when a contract has 33 1/3 percent of its original value, the Candidate should accept anything as being better than nothing. So, Pepperdine can get away with the whole 33 1/3 percent minus a pittance, leaving the Candidate with the pittance. Rolling back to 2 bargaining rounds from the end, when a contract has 66 2/3 percent of its original value, Pepperdine could reject any offer and get 33 1/3 percent in the next round. So, the Candidate’s best acceptable offer leaves Pepperdine with 33 1/3 percent plus a pittance, and the Candidate with 33 1/3 percent minus a pittance.

73. 73 Review 2: Bargaining with Depreciation BA 445 Lesson B.1 Sequential Bargaining and Depreciation Rolling back to 3 bargaining rounds before the end, when a contract has 100 percent of its original value, the Candidate could reject any offer and get 33 1/3 percent in the next round. So, Pepperdine’s best acceptable offer leaves the Candidate with 33 1/3 percent plus a pittance, and Pepperdine with 66 2/3 percent minus a pittance. Pepperdine’s initial wage offer should be for Pepperdine to keep 66 2/3 percent of the $30,000 gain from employment for all three semesters, and the Candidate should accept that initial offer and, so, keep 33 1/3 percent of the $30,000 gain. In particular, since the Candidate is willing to work for $45,000 for all three semesters, he should be paid $45,000 + $10,000 = $55,000.

74. 74 BA 445 Lesson B.1 Sequential Bargaining and Depreciation Review 3: Bargaining with Depreciation

75. 75 Review 3: Bargaining with Depreciation BA 445 Lesson B.1 Sequential Bargaining and Depreciation Question 3. Two companies, one in Dallas and one in LA, are using the same Boston-based lawyer, William Alan Shatner (aka, Captain Kirk). Each firm needs Shatner’s services in January, February, and March. As a result of coordinating schedules, Shatner could each month make a triangle route (Boston-Dallas-LA) rather than making two separate trips. The airfares each month are: Triangle $1000, Boston-Dallas roundtrip $400, Boston-LA roundtrip $800 Before the January trip, Dallas (the Dallas company) confronts LA (the LA company) over its share of the triangle airfare. Dallas presents its offer. LA either accepts it for each of the three trips, or rejects it and returns after the January trip with a counteroffer. After the January trip, Dallas either accepts that counteroffer for each of the remaining two trips, or rejects it and returns after the February trip with a counteroffer. After the February trip, LA either accepts that counteroffer for the remaining trip, or rejects it and ends the game. What percentage of the gains from trade should Dallas offer? Should LA accept that initial offer?

76. 76 Review 3: Bargaining with Depreciation BA 445 Lesson B.1 Sequential Bargaining and Depreciation Answer 3: To consider all possible offers to split the gains from an agreement on splitting the cost of the triangle route, consider another bargaining payoff table. The game ends if an offer is accepted or if the three months end without an accepted agreement, and gains are measured as a percentage of the gain from using the triangle route for all three months.

77. 77 Review 3: Bargaining with Depreciation BA 445 Lesson B.1 Sequential Bargaining and Depreciation Starting 1 bargaining round from the end of the game, when an agreement has 33 1/3 percent of its original value, LA should accept anything as being better than nothing. So, Dallas can get away with the whole 33 1/3 percent minus a pittance, leaving the LA with the pittance. Rolling back to 2 bargaining rounds from the end, when an agreement has 66 2/3 percent of its original value, Dallas could reject any offer and get 33 1/3 percent in the next round. So, the LA’s best acceptable offer leaves Dallas with 33 1/3 percent plus a pittance, and LA with 33 1/3 percent minus a pittance.

78. 78 Review 3: Bargaining with Depreciation BA 445 Lesson B.1 Sequential Bargaining and Depreciation Rolling back to 3 bargaining rounds before the end, when an agreement has 100 percent of its original value, LA could reject any offer and get 33 1/3 percent in the next round. So, Dallas’s best acceptable offer leaves LA with 33 1/3 percent plus a pittance, and Dallas with 66 2/3 percent minus a pittance. Recall, the airfares each month are: Triangle $1000, Boston-Dallas roundtrip $400, Boston-LA roundtrip $800. In particular, the gain from three triangle trips is 3x(1200-1000) = 600. Dallas’s initial offer should be for Dallas to keep 66 2/3 percent of the $600 gain, or $400. So Dallas pays 3x400-400 = $800. Likewise, LA gains $200 and pays 3x800-200 = $2200.

79. 79 End of Lesson B.1 BA 445 Lesson B.1 Sequential Bargaining and Depreciation BA 445 Managerial Economics