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Nash Demand Game

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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)

S

Games with similar payoffs

should have similar equilibria

x

Nash Demand Game

Uncertainty about the boundary

iso-probability curves

0

S

1

define a new game

Nash Demand Game

0

S

1

or define on a narrower

band of uncertainty

Nash Demand Game

Uncertainty about the boundary

0

0

S

S

1

1

Define a sequence of with

uncertainty bands converging to 0

0

0

S

S

1

1

Nash Demand Game

Uncertainty about the boundary

0

0

S

S

1

1

Nash Demand Game

Nash Demand Game

Equilibria

Solving the game

Nash Demand Game

Solving the game

0

Denote:

S

1

Nash Demand Game

???

Solving the game

Nash Demand Game

???

0

S

1

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)

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

The Nash Bargaining

Solution

Nash Demand Game

Equilibria