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  • 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

  • The BargainBuyer 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(uyers reservation price) s(ellers reservation price) b 050100150200250

    si) b - s > 0 Surplus How to divide?

  • The BargainBuyer 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(uyers reservation price) s(ellers reservation price) b 050100150200250

    si) b - s > 0 Surplus How to divide?

  • The BargainBuyer 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(uyers reservation price) s(ellers reservation price) b 050100150200250

    si) b > s If b and s are known to both players: How should the surplus be divided?

  • The BargainBuyer 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(uyers reservation price) s(ellers reservation price) b 050100150200250

    si) b > s If b and s are known to both players: How should the surplus be divided?Surplus = 50

  • The BargainBuyer 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(uyers reservation price) s(ellers reservation price) b 050100150200250

    sii) b = s

  • The BargainBuyer 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(uyers reservation price) s(ellers reservation price) b 050100150200250

    s(iii) b < sNo zone of agreement

  • The BargainBuyer 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(uyers reservation price) s(ellers reservation price) b 050100150200250

    s(iii) b < sNo zone of agreementWhat happens if information is incomplete?

  • We Play a Game

    PROPOSER RESPONDER

    Player # ____Player # ____

    Offer $ _____ Accept Reject

  • We Play a Game

    PROPOSER RESPONDER

    Player # ____Player # ____

    Offer $ _____ Accept Reject

  • We Play a Game

    PROPOSER RESPONDER

    Player # ____Player # ____

    Offer $ _____ Accept Reject

  • The Ultimatum GameOFFERS543210REJECTED ACCEPTEDN = 20Mean = $1.309 Offers > 0 Rejected1 Offer < 1.00 (20%) Accepted

    (3/6/00)

  • The Ultimatum GameOFFERS543210REJECTEDACCEPTEDN = 33Mean = $1.7510 Offers > 0 Rejected1 Offer < $1 (20%) Accepted

    (2/28/01)

  • The Ultimatum GameOFFERS543210REJECTEDACCEPTEDN = 37Mean = $1.6910 Offers > 0 Rejected*3 Offers < $1 (20%) Accepted

    (2/27/02)* 1 subject offered 0

  • The Ultimatum GameOFFERS543210REJECTED ACCEPTEDN = 12Mean = $2.772 Offers > 0 Rejected0 Offers < 1.00 (20%) Accepted

    (7/10/03)

  • The Ultimatum GameOFFERS543210REJECTED ACCEPTEDN = 17Mean = $2.303 Offers > 0 Rejected0 Offers < 1.00 (20%) Accepted

    (3/10/04)

  • The Ultimatum GameOFFERS543210REJECTED ACCEPTEDN = 119Mean = $2.2834 Offers > 0 Rejected5/25 Offers < 1.00 (20%) Accepted

    Pooled data

  • The Ultimatum GameOFFERS543210REJECTED ACCEPTEDN = 119Mean = $2.2834 Offers > 0 Rejected5/25 Offers < 1.00 (20%) Accepted

    Pooled data

  • The Ultimatum GameP2

    5

    2.28

    0

    0 2.72 5 P12.50

    1.00What is the lowest acceptable offer?8/84/421/232/22/23/318/2613/15N = 119Mean = $2.2834 Offers > 0 Rejected5/25 Offers < 1.00 (20%) Accepted

    Pooled data5/63/17

  • The Ultimatum GameP2

    5

    2.28

    0

    0 2.72 5 P12.50

    1.00What is the lowest acceptable offer?8/84/421/232/22/23/318/2613/15N = 119Mean = $2.2834 Offers > 0 Rejected5/25 Offers < 1.00 (20%) Accepted

    Pooled data5/63/17

  • The Ultimatum GameTheory predicts very low offers will be made and accepted.

    Experiments show:Mean offers are 30-40% of the totalMode = 50%Offers

  • The Ultimatum GameTheory predicts very low offers will be made and accepted.

    Experiments show:Mean offers are 30-40% of the totalMode = 50%Offers

  • The Ultimatum GameTheory predicts very low offers will be made and accepted.

    Experiments show:Mean offers are 30-40% of the totalMode = 50%Offers

  • The Ultimatum GameHow can we explain the divergence between predicted and observed results?

    Stakes are too lowFairnessRelative shares matterEndowments matterCulture, norms, or mannersPeople make mistakesTime/Impatience

  • The Ultimatum GameHow can we explain the divergence between predicted and observed results?

    Stakes are too lowFairnessRelative shares matterEndowments matterCulture, norms, or mannersPeople make mistakesTime/Impatience

  • The Ultimatum GameHow can we explain the divergence between predicted and observed results?

    Stakes are too lowFairnessRelative shares matterEndowments matterCulture, norms, or mannersPeople make mistakesTime/Impatience

  • The Ultimatum GameHow can we explain the divergence between predicted and observed results?

    Stakes are too lowFairnessRelative shares matterEndowments matterCulture, norms, or mannersPeople make mistakesTime/Impatience

  • The Ultimatum GameHow can we explain the divergence between predicted and observed results?

    Stakes are too lowFairnessRelative shares matterEndowments matterCulture, norms, or mannersPeople make mistakesTime/Impatience

  • The Ultimatum GameHow can we explain the divergence between predicted and observed results?

    Stakes are too lowFairnessRelative shares matterEndowments matterCulture, norms, or mannersPeople make mistakesTime/Impatience

  • We Play Some Games

    PROPOSER RESPONDER

    Player # ____Player # ____

    Offer 2 or 5 Accept Reject(Keep 8 5)

  • We Play Some GamesAn offer to give 2 and keep 8 is accepted:

    PROPOSER RESPONDER

    Player # ____Player # ____

    Offer 2 or 5 Accept Reject(Keep 8 5)

  • Fair Play8 0 5 0 8 0 2 02 0 5 0 2 0 8 0

    GAME AGAME B

  • Fair Play8 0 8 0 8 010 02 0 2 0 2 0 0 0

    GAME CGAME D

  • Fair Play8 0 5 0 8 0 2 02 0 5 0 2 0 8 0

    GAME AGAME B

  • Fair Play8 0 8 0 8 010 02 0 2 0 2 0 0 0

    GAME CGAME D

  • Fair PlayAB C D50%

    40

    30

    20

    10

    03/71/42/40/9Rejection Rates, (8,2) Offer(5,5) (2,8) (8,2) (10,0) Alternative Offer4/18/01, in Class.

    24 (8,2) Offers 2 (5,5) Offers N = 26

  • Fair PlayAB C D50%

    40

    30

    20

    10

    05/72/31/22/12Rejection Rates, (8,2) Offer(5,5) (2,8) (8,2) (10,0) Alternative Offer4/15/02, in Class.

    24 (8,2) Offers 6 (5,5) Offers N = 30

  • Fair PlayAB C D50%

    40

    30

    20

    10

    0Source: Falk, Fehr & Fischbacher, 1999Rejection Rates, (8,2) Offer

    (5,5) (2,8) (8,2) (10,0) Alternative Offer

  • Fair PlayWhat determines a fair offer?

    Relative sharesIntentionsEndowmentsReference groupsNorms, manners, or history

  • Fair PlayThese 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)

  • Bargaining GamesBargaining 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.

  • Bargaining GamesBargaining 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 pro