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

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

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

4 Nash Demand Game S 1 0 define a new game

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

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

7 Nash Demand Game S 1 0 S 1 0

8 Equilibria

9 Nash Demand Game Solving the game

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

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

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

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

14 Nash Demand Game Equilibria The Nash Bargaining Solution