Game Problems

Which number is closest to the circumference of the earth? A) 15,000 miles B) 25,000 miles C) 35,000 miles D) 45,000 miles E) 55,000 miles

Hermaphroditic Fish: Ex 18.1 Two players: Fish 1 and Fish 2 Two strategies: – Demand preferred role – Accept either role Payoffs – H if one gets to play preferred role – L if one plays less preferred role – S if no match

Payoff matrix See Blackboard

When is this game a prisoners’ dilemma? For what values of H, L, and S is it a dominant strategy to demand preferred role? Further question: Suppose S is the value of playing the same game with someone else at a later date. If everybody demands to play preferred role, how does S compare with L?

Extension What if tastes differ so that half of the population prefers role 1 and half prefers role 2? Construct payoff matrix. When is there a dominant strategy?

Altruists Prisoners’ Dilemma: Ex 27.1 Original game What happens with altruists? – Try a=1 – For what values of a is this a Prisoners’ dilemma? 2, 2 0, 3 3, 0 1, 1 QuietFink Quiet Fink

Road Warriors X B Y 6.9,12,15 A 6,9,12,15 20,21,22,23

Nash equilibrium Make table

Road Warriors II A New Road X B Y 6.9,12,15 A 6,9,12,15 20,21,22,23 7,8,9,10

Domination 0,01,01,1 3,0 1,12,12,2 LeftCenterRight Top Middle Bottom