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 

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 

How's that work?

Contents 1 Critiques 2 Regular QRE 3 Existence and Uniqueness 4 Examples 4.1 Asymmetric Matching Pennies 4.2 Centipede game 4.3 Traveler's dilemma

[edit] Critiques

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

[edit] Regular QRE

[edit] Existence and Uniqueness

[edit] Examples

[edit] 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 .

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...

[edit] Centipede game

[edit] Traveler's dilemma