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The Bargain

The Bargain.

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The Bargain

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  1. The Bargain Whoever offers to another a bargain of any kind, proposes to do this. Give me that which I want, and you shall have this which you want …; and it is this manner that we obtain from one another the far greater part of those good offices we stand in need of. It is not from the benevolence of the butcher, the brewer, or the baker that we expect our dinner, but from their regard to their own interest. -- A. Smith, 1776

  2. The Bargain Buyer and seller try to agree on a price. Buyer is better off at a price less than b, Seller at a price above s. If b > s, we say there is a positive zone of agreement, or Surplus: S(urplus) = b(uyer’s reservation price) – s(eller’s reservation price) b 0 50 100 150 200 250 s i) b - s > 0 Surplus How to divide?

  3. The Bargain Buyer and seller try to agree on a price. Buyer is better off at a price less than b, Seller at a price above s. If b > s, we say there is a positive zone of agreement, or Surplus: S(urplus) = b(uyer’s reservation price) – s(eller’s reservation price) b 0 50 100 150 200 250 s i) b - s > 0 Surplus How to divide?

  4. The Bargain Buyer and seller try to agree on a price. Buyer is better off at a price less than b, Seller at a price above s. If b > s, we say there is a positive zone of agreement, orSurplus: S(urplus) = b(uyer’s reservation price) – s(eller’s reservation price) b 0 50 100 150 200 250 s i) b > s If b and s are known to both players: How should the surplus be divided?

  5. The Bargain Buyer and seller try to agree on a price. Buyer is better off at a price less than b, Seller at a price above s. If b > s, we say there is a positive zone of agreement, orSurplus: S(urplus) = b(uyer’s reservation price) – s(eller’s reservation price) b 0 50 100 150 200 250 s i) b > s If b and s are known to both players: How should the surplus be divided? Surplus = 50

  6. The Bargain Buyer and seller try to agree on a price. Buyer is better off at a price less than b, Seller at a price above s. If b = s, we say the price is fully determined, and there is no room for negotiation. S(urplus) = b(uyer’s reservation price) – s(eller’s reservation price) b 0 50 100 150 200 250 s ii) b = s

  7. The Bargain Buyer and seller try to agree on a price. Buyer is better off at a price less than b, Seller at a price above s. If b < s, there is nothing to gained from the exchange. S(urplus) = b(uyer’s reservation price) – s(eller’s reservation price) b 0 50 100 150 200 250 s (iii) b < s No “zone of agreement”

  8. The Bargain Buyer and seller try to agree on a price. Buyer is better off at a price less than b, Seller at a price above s. If b < s, there is nothing to gained from the exchange. S(urplus) = b(uyer’s reservation price) – s(eller’s reservation price) b 0 50 100 150 200 250 s (iii) b < s No “zone of agreement” What happens if information is incomplete?

  9. We Play a Game PROPOSER RESPONDER Player # ____ Player # ____ Offer $ _____ Accept Reject

  10. We Play a Game PROPOSER RESPONDER Player # ____ Player # ____ Offer $ _____ Accept Reject

  11. We Play a Game PROPOSER RESPONDER Player # ____ Player # ____ Offer $ _____ Accept Reject

  12. The Ultimatum Game OFFERS 5 4 3 2 1 0 REJECTEDACCEPTED N = 20 Mean = $1.30 9 Offers > 0 Rejected 1 Offer < 1.00 (20%) Accepted (3/6/00)

  13. The Ultimatum Game OFFERS 5 4 3 2 1 0 REJECTED ACCEPTED N = 33 Mean = $1.75 10 Offers > 0 Rejected 1 Offer < $1 (20%) Accepted (2/28/01)

  14. The Ultimatum Game OFFERS 5 4 3 2 1 0 REJECTED ACCEPTED N = 37 Mean = $1.69 10 Offers > 0 Rejected* 3 Offers < $1 (20%) Accepted (2/27/02) * 1 subject offered 0

  15. The Ultimatum Game OFFERS 5 4 3 2 1 0 REJECTEDACCEPTED N = 12 Mean = $2.77 2 Offers > 0 Rejected 0 Offers < 1.00 (20%) Accepted (7/10/03)

  16. The Ultimatum Game OFFERS 5 4 3 2 1 0 REJECTEDACCEPTED N = 17 Mean = $2.30 3 Offers > 0 Rejected 0 Offers < 1.00 (20%) Accepted (3/10/04)

  17. The Ultimatum Game OFFERS 5 4 3 2 1 0 REJECTEDACCEPTED N = 119 Mean = $2.28 34 Offers > 0 Rejected 5/25 Offers < 1.00 (20%) Accepted Pooled data

  18. The Ultimatum Game OFFERS 5 4 3 2 1 0 REJECTEDACCEPTED N = 119 Mean = $2.28 34 Offers > 0 Rejected 5/25 Offers < 1.00 (20%) Accepted Pooled data

  19. The Ultimatum Game P2 5 2.28 0 What is the lowest acceptable offer? 8/8 4/4 2/2 2/2 3/3 2.50 1.00 21/23 N = 119 Mean = $2.28 34 Offers > 0 Rejected 5/25 Offers < 1.00 (20%) Accepted Pooled data 13/15 5/6 18/26 3/17 0 2.72 5 P1

  20. The Ultimatum Game P2 5 2.28 0 What is the lowest acceptable offer? 8/8 4/4 2/2 2/2 3/3 2.50 1.00 21/23 N = 119 Mean = $2.28 34 Offers > 0 Rejected 5/25 Offers < 1.00 (20%) Accepted Pooled data 13/15 5/6 18/26 3/17 0 2.72 5 P1

  21. The Ultimatum Game Theory predicts very low offers will be made and accepted. Experiments show: • Mean offers are 30-40% of the total • Mode = 50% • Offers <20% are rare and usually rejected Guth Schmittberger, and Schwarze (1982) Kahnemann, Knetsch, and Thaler (1986) Also, Camerer and Thaler (1995)

  22. The Ultimatum Game Theory predicts very low offers will be made and accepted. Experiments show: • Mean offers are 30-40% of the total • Mode = 50% • Offers <20% are rare and usually rejected Guth Schmittberger, and Schwarze (1982) Kahnemann, Knetsch, and Thaler (1986) Also, Camerer and Thaler (1995) How would you advise Proposer?

  23. The Ultimatum Game Theory predicts very low offers will be made and accepted. Experiments show: • Mean offers are 30-40% of the total • Mode = 50% • Offers <20% are rare and usually rejected Guth Schmittberger, and Schwarze (1982) Kahnemann, Knetsch, and Thaler (1986) Also, Camerer and Thaler (1995) How would you advise Proposer? What do you think would happen if the game were repeated?

  24. The Ultimatum Game How can we explain the divergence between predicted and observed results? • Stakes are too low • Fairness • Relative shares matter • Endowments matter • Culture, norms, or “manners” • People make mistakes • Time/Impatience

  25. The Ultimatum Game How can we explain the divergence between predicted and observed results? • Stakes are too low • Fairness • Relative shares matter • Endowments matter • Culture, norms, or “manners” • People make mistakes • Time/Impatience

  26. The Ultimatum Game How can we explain the divergence between predicted and observed results? • Stakes are too low • Fairness • Relative shares matter • Endowments matter • Culture, norms, or “manners” • People make mistakes • Time/Impatience

  27. The Ultimatum Game How can we explain the divergence between predicted and observed results? • Stakes are too low • Fairness • Relative shares matter • Endowments matter • Culture, norms, or “manners” • People make mistakes • Time/Impatience

  28. The Ultimatum Game How can we explain the divergence between predicted and observed results? • Stakes are too low • Fairness • Relative shares matter • Endowments matter • Culture, norms, or “manners” • People make mistakes • Time/Impatience

  29. The Ultimatum Game How can we explain the divergence between predicted and observed results? • Stakes are too low • Fairness • Relative shares matter • Endowments matter • Culture, norms, or “manners” • People make mistakes • Time/Impatience

  30. We Play Some Games PROPOSER RESPONDER Player # ____ Player # ____ Offer 2 or 5 Accept Reject (Keep 8 5)

  31. We Play Some Games An offer to give 2 and keep 8 is accepted: PROPOSER RESPONDER Player # ____ Player # ____ Offer 2 or 5 Accept Reject (Keep 8 5)

  32. Fair Play 8 0 5 0 8 0 2 0 2 0 5 0 2 0 8 0 GAME A GAME B

  33. Fair Play 8 0 8 0 8 0 10 0 2 0 2 0 2 0 0 0 GAME C GAME D

  34. Fair Play 8 0 5 0 8 0 2 0 2 0 5 0 2 0 8 0 GAME A GAME B

  35. Fair Play 8 0 8 0 8 0 10 0 2 0 2 0 2 0 0 0 GAME C GAME D

  36. Fair Play 2/4 Rejection Rates, (8,2) Offer 50% 40 30 20 10 0 3/7 4/18/01, in Class. 24 (8,2) Offers 2 (5,5) Offers N = 26 1/4 0/9 A B C D (5,5) (2,8) (8,2) (10,0) Alternative Offer

  37. Fair Play 5/7 2/3 1/2 Rejection Rates, (8,2) Offer 50% 40 30 20 10 0 4/15/02, in Class. 24 (8,2) Offers 6 (5,5) Offers N = 30 2/12 A B C D (5,5) (2,8) (8,2) (10,0) Alternative Offer

  38. Fair Play Rejection Rates, (8,2) Offer 50% 40 30 20 10 0 Source: Falk, Fehr & Fischbacher, 1999 A B C D (5,5) (2,8) (8,2) (10,0) Alternative Offer

  39. Fair Play What determines a fair offer? • Relative shares • Intentions • Endowments • Reference groups • Norms, “manners,” or history

  40. Fair Play These results show that identical offers in an ultimatum game generate systematically different rejection rates, depending on the other offer available to Proposer (but not made). This may reflect considerations of fairness: i) not only own payoffs, but also relative payoffs matter; ii) intentions matter. (FFF, 1999, p. 1)

  41. Bargaining Games Bargaining involves (at least) 2 players who face the the opportunity of a profitable joint venture, provided they can agree in advance on a division between them. Bargaining involves a combination of common as well as conflicting interests. The central issue in all bargaining games is credibility: the strategic use of threats, bluffs, and promises.

  42. Bargaining Games Bargaining involves (at least) 2 players who face the the opportunity of a profitable joint venture, provided they can agree in advance on a division between them. Bargaining involves a combination of common as well as conflicting interests. The central issue in all bargaining games is credibility: the strategic use of threats, bluffs, and promises.

  43. Bargaining Games Bargaining involves (at least) 2 players who face the the opportunity of a profitable joint venture, provided they can agree in advance on a division between them. Bargaining involves a combination of common as well as conflicting interests. The central issue in all bargaining games is credibility: the strategic use of threats, bluffs, and promises.

  44. Bargaining Games Divide a Dollar P2 1 0 1 P1 Two players have the opportunity to share $1, if they can agree on a division beforehand. Each writes down a number. If they add to $1, each gets her number; if not; they each get 0. Find the NE of this game. P1= x; P2 = 1-x. Disagreement point

  45. Bargaining Games Divide a Dollar P2 1 0 1 P1 Two players have the opportunity to share $1, if they can agree on a division beforehand. Each writes down a number. If they add to $1, each gets her number; if not; they each get 0. Every division s.t. x + (1-x) = 1 is a NE. P1= x; P2 = 1-x. Disagreement point

  46. Subgame Perfection Subgame: a part (or subset) of an extensive game, starting at a singleton node (not the initial node) and continuing to payoffs. Subgame Perfect Nash Equilibrium (SPNE): a NE achieved by strategies that also constitute NE in each subgame. eliminates NE in which the players threats are not credible. selects the outcome that would be arrived at via backwards induction.

  47. Subgame Perfection Chain Store Game A firm (Player 1) is considering whether to enter the market of a monopolist (Player 2). Player 2 can then choose to fight the entrant, or not. 1 Enter Don’t Enter Fight Don’t Fight 2 (2,2) (0,0) (3,1)

  48. Subgame Perfection Chain Store Game A firm (Player 1) is considering whether to enter the market of a monopolist (Player 2). Player 2 can then choose to fight the entrant, or not. 1 Enter Don’t Enter Fight Don’t Fight 2 (2,2) (0,0) (3,1) Subgame

  49. Subgame Perfection Chain Store Game Fight Don’t Enter Don’t 0, 0 3, 1 2, 2 2, 2 1 Enter Don’t Fight Don’t 2 (2,2) (0,0) (3,1) NE = {(E,D), (D,F)}.

  50. Subgame Perfection Chain Store Game Fight Don’t Enter Don’t 0, 0 3, 1 2, 2 2, 2 1 Enter Don’t Fight Don’t 2 (2,2) (0,0) (3,1) NE = {(E,D), (D,F)}, but Fight for Player 2 is an incredible threat.

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