Game Theory Terms

Dominant strategy: the best strategy regardless of what move the other player makes

Nash equilibrium: an outcome in which neither player has an incentive to unilaterally alter his strategy.

Pareto optimal outcome: an outcome in which there is no other outcome that would make any player better off without making the other player worse off.

R. Axelrod’s Evolution of Cooperation (1984)

R. Axelrod’s PD Tournament

- programs would be entered into round-robin competition with payoffs along PD lines.

- DC = 5,0

- CC= 3,3

- DD= 1,1

- CD=0,5

Strategy that won overall was Tit-for-Tat

- Never scored higher than

- Tit-for-Tat: cooperate on first interaction, then reciprocate other actors play on prior rounds

- Nice: cooperates on first move (v. nasty)

- Provocable: retaliates when defected against

- Forgiving: resumes cooperation after the other cooperates again

- Clear: it pattern of play can be well understood

In repeated (iterated) Prisoner Dilemma interactions, concern for future gains make cooperation preferable over cheating, but…

if short-run gains are valued highly (shadow of future is slight), then cheating and mutual defection prevail over mutual cooperation.

Discount Parameter w

- measure of how much a future payoff compares to current payoffs

- discount parameter = w

- payoff = v

- future payoffs = v*(1/(1-w))

In computer simulations with moderate shadow of the future, TfT wins over nasty strategies (those that defect)

- under above payoffs, TfT is collectively stable so long as w ≥ 2/3

- collectively stable means that a set of TfT strategies would always score as good as or better playing each other than any other strategy would playing them.

- only by playing TfT could any player hope to score as well as those playing TfT

- if w < ½, then ‘all defect’ is best strategy.