User:Cretog8/Scratchpad

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So, testing this reference thingie

McKelvey, Richard; Palfrey, Thomas (1995), "Quantal Response Equilibria for Normal Form Games", Games and Economic Behavior, 10: 6–38

Goeree, Jacob K.; Holt, Charles A.; Palfrey, Thomas (2005), "Regular Quantal Response Equilibrium", Experimental Economics, 8: 347--367

Aumann, Robert; Brandenburger, Adam (1995), "Epistemic Conditions for Nash Equilibrium", Econometrica, 63: 1161–1180

How's that work?

Critiques

For instance, McKelvey, Palfrey and Weber^[1] conducted AMP experiments with the four different payoff tables shown below. They estimated different lambda values for the different games.

	Heads	Tails
heads	9, 0	0, 1
tails	0, 1	1, 0
AMP A

	Heads	Tails
heads	9, 0	0, 4
tails	0, 4	1, 0
AMP B

	Heads	Tails
heads	36, 0	0, 4
tails	0, 4	4, 0
AMP C

	Heads	Tails
heads	4, 0	0, 1
tails	0, 1	1, 0
AMP D

Regular QRE

Existence and Uniqueness

Examples

Asymmetric Matching Pennies

Compare to Matching Pennies

	Heads	Tails
heads	x, 0	0, 1
tails	0, 1	1, 0
Asymmetric Matching Pennies

Like Matching Pennies, AMP has a unique mixed-strategy Nash equilibrium. In the Nash equilibrium, the row player plays heads with probability 1/2, and the column player plays Heads with probability ${\frac {1}{1+x}}$ .

Since in a Nash equilibrium, the determinant of an equilibrium strategy is that the other player can't do any better (is indifferent), the row player's equilibrium strategy is insensitive to x. This insensitivity to of a player to their own payoffs is counter-intuitive, and...

LQRE path

Centipede game

Traveler's dilemma

[1]
McKelvey, Richard; Palfrey, Thomas; Weber, Roberto A. (2000), "The Effects of Payoff Magnitude and Heterogeneity on Behavior in 2x2 Games with Unique Mixed Strategy Equilibria", Journal of Economic Behavior and Organization, 42 (4): 523--548

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