Game Problems Which number is closest to the

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 Quiet Fink Quiet 2, 2 0, 3 Fink 3, 0 1, 1 • What happens with altruists? – Try a=1 – For what values of a is this a Prisoners’ dilemma?

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

Nash equilibrium • Make table

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

Domination Left Center Right Top 0, 0 1, 1 Middle 1, 1 3, 0 Bottom 1, 1 2, 2