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Nash Demand Game

Nash Demand Game. Nash Program (non cooperative games). Demand Game. Topics 3. S. Nash Equilibria of. Nash Demand Game. Too many equilibria !!. Nash’s Solution: Perturb the game’s payoffs, Introduce noise (uncertainty) and then reduce it to 0 (Perfect- trembling hand- Equilibrium).

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Nash Demand Game

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  1. Nash Demand Game Nash Program (non cooperative games) Demand Game Topics 3 S

  2. Nash Equilibria of Nash Demand Game Too many equilibria !! Nash’s Solution: Perturb the game’s payoffs, Introduce noise (uncertainty) and then reduce it to 0 (Perfect- trembling hand- Equilibrium) S Games with similar payoffs should have similar equilibria x

  3. Nash Demand Game Uncertainty about the boundary iso-probability curves 0 S 1

  4. define a new game Nash Demand Game 0 S 1

  5. or define on a narrower band of uncertainty Nash Demand Game Uncertainty about the boundary 0 0 S S 1 1

  6. Define a sequence of with uncertainty bands converging to 0 0 0 S S 1 1 Nash Demand Game Uncertainty about the boundary

  7. 0 0 S S 1 1 Nash Demand Game

  8. Nash Demand Game Equilibria

  9. Solving the game Nash Demand Game

  10. Solving the game 0 Denote: S 1 Nash Demand Game ???

  11. Solving the game Nash Demand Game ??? 0 S 1

  12. Solving the game A Nash Equilibrium of the perturbed game is a Nash Barganing solution of a bargaining problem defined by the frontier Nash Demand Game 0 S 1 (There may be multiple equilibria)

  13. Solving the game Nash Demand Game As the uncertainty band vanishes the Nash Equilibria of the perturbed game converge to the Nash bargaining the solution of the unperturbed game 0 S 1

  14. The Nash Bargaining Solution Nash Demand Game Equilibria

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