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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).

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Presentation Transcript
slide1

Nash Demand Game

Nash Program (non cooperative games)

Demand Game

Topics

3

S

slide2

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

slide3

Nash Demand Game

Uncertainty about the boundary

iso-probability curves

0

S

1

slide4

define a new game

Nash Demand Game

0

S

1

slide5

or define on a narrower

band of uncertainty

Nash Demand Game

Uncertainty about the boundary

0

0

S

S

1

1

slide6

Define a sequence of with

uncertainty bands converging to 0

0

0

S

S

1

1

Nash Demand Game

Uncertainty about the boundary

slide7

0

0

S

S

1

1

Nash Demand Game

slide9

Solving the game

Nash Demand Game

slide10

Solving the game

0

Denote:

S

1

Nash Demand Game

???

slide11

Solving the game

Nash Demand Game

???

0

S

1

slide12

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)

slide13

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

slide14

The Nash Bargaining

Solution

Nash Demand Game

Equilibria

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