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Bargaining Situations

Bargaining Situations. Input Lecture by J.Yan and Y. Blumer, 22. Nov 2007. © ETH Zürich | Taskforce Kommunikation. Content. Introduction Theoretical approach Examples Wrap-up and Discussion. Introductionary Example – Car Deal. Buyer. 1100$ (Max. Offer ). 2 Possible Solutions

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Bargaining Situations

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  1. Bargaining Situations Input Lecture by J.Yan and Y. Blumer, 22. Nov 2007 © ETH Zürich | Taskforce Kommunikation

  2. Content • Introduction • Theoretical approach • Examples • Wrap-up and Discussion

  3. Introductionary Example – Car Deal Buyer 1100$ (Max. Offer ) • 2 Possible Solutions • No agreement (inefficient outcome) • Agreement (efficient outcome) • Solution is found by • Mutual proposals • Argumentation Bargaining area (surplus value to be distributed) 1000$ (Min. Acceptance) Seller

  4. Solution depends on many factor • Beliefs • Possibility of third-party interventions • Deadline / time costs • Bidding Rules • Need for Agreement • Repetition • Social norms and relationship of players • …

  5. What is a Bargaining Situation? Definition: • Bargaining games refer to situations where two or more players must reach agreement regarding how to distribute an object or monetary amount. • The joint revenue of a coalition is always higher than if players do not cooperate • Player’s preference can be presented by a von-Neumannn-Morgenstern utility function.

  6. Formal description • Situation 1: There are two individuals and one dollar to be assigned to one of them.They must agree on who gets the dollar. If they do not reach an agreement,no one gets the dollar.

  7. Assume now that the individuals have von Neumann-Morgenstern utilities, given by :

  8. Utility possibility set: all pairs of utilities that can be achieved by some lottery

  9. Situation 2: There are two individuals, A and B, and two goods, apples and oranges. Initial endowment: wA= (1; 0) wB= (0, 1) Allocation:

  10. Four possible allocations: Disagreement:

  11. The individuals’ von Neumann-Morgentern utility functions are given by: Corresponding utilities:

  12. Expected utilities: Set of utility possibilities:

  13. Gloves • 2 Knitters each made 3 single gloves • A pair of gloves sells for 5$ • Unsold gloves have no value U2 15 • Bargaining Set • Nash Equilibrium • Pareto Optimum • Threat Point 10 5 U1 15 10 5

  14. U 100 70 UPoor ($) = 1URich ($) = 0.7 $ 100 Poor Vs. Rich • Distribution 100 $ between a poor and a rich • Payout for non – agreement is (0/0) • Different utility functions

  15. (1/99) (28.6/71.4) (50/50) (58.8/41.2) Poor Vs. Rich – Possible Solutions • Ripp Off • Equivalent Utility (Absolute) • Symmetric • Equivalent Utility (Relative) • Disagreement Payoutrich 100 Payoutpoor 100

  16. 2 Vs. 1 • Distribution 100 $ between a team of 2 and a single player • Payout for non – agreement is (0/0) • Different utility functions U 100 50 USingle Player (1$) = 1UTeam Player (1$) = 0.5 (each) $ 100

  17. (33.3/66.6) (50/50) 2 Vs. 1 – Possible Solutions • Equivalent Team Utility (symmetric) • Equivalent Player Utility • Disagreement PayoutTeam 100 PayoutSingle 100

  18. 100 Strategy – a Glimpse • Distribution 100 $ between 2 players • One-shot Game • One player 1 makes an offer for splitting • Accept • Decline (0/0) Utility obtained by aggressive behaviour Best offer UPlayer2 100 Offer triggers change of utility function $ 100 100

  19. Bargaining in the Context of Past Lectures Strategy Rationalities Coalition Bargaining Games Utility Negotiation Communication Non-discrete payoff vectors

  20. Outlook • Situation with many players • Situations with special rules • Viable strategies in real situations • Experience and identification of other players strategies

  21. Sources • “The Art & Science of Negotiation”, Howard Raiffa, 1982 • “Formal Description of Bargaining Situations” • www.gametheory.net • www.wikipedia.org (of course)

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