Common game theory games - Would Cooperation help? Prisoners’ Dilemma Two co-conspirators who are Prisoner Y Dominant strategy for X? now prisoners are interrogated Confess Keep quiet separately. Remaining silent Prisoner Y? Prisoner Confess -5, -5 0, -15 allows both to serve the least X Nash equilibrium/a? amount of time, but both have Keep quiet -15, 0 -2, -2 an incentive to confess. Battle of the Sexes (antiquated, I know) A couple can’t decide where Jan Dominant strategy for Pat? to go on Friday. Pat wants to Dr. Who Zoo For Jan? go to the Dr. Who fan club Dr. Who 3, 2 0, 0 meeting. Jan wants to go to Pat Nash equilibrium/a? the Zoo. Here’s the payoff Zoo 0, 0 2, 3 matrix: Chicken Two people approach head on. The person who flinches Player Y Dominant strategy for X? is viewed as a coward but Flinch No chicken Flinch 2, 2 1, 3 avoids a crash. If neither Player For Y? flinch, a crash occurs, X No chicken 3, 1 0, 0 decreasing both people’s Nash equilibrium/a? utility. Players don’t cooperate. Stag Hunt Two hunters must decide independently whether to hunt a stag or hunt a hare. A Hunter B Dominant strategy for Hunter stag can only be caught when Stag Hare A? both players choose to hunt a Hunter Stag 2, 2 0, 1 stag. A hare can be caught by For B? one hunter but is not worth A Hare 1, 0 1, 1 as much. Nash equilibrium/a? Bonus: Pirate game! Pirates A, B, C have 100 coins to split. Pirate A is slightly stronger than Pirate B, who is slightly stronger than Pirate C. Only two of the three pirates must agree on the split (majority rule). Pirate A proposes first. If other pirates don’t agree, he walks the plank and dies. Then Pirate B may propose a split and Pirate C may or may not accept the split. What happens to the pirates? How are the coins split? .