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 roundrobin competition with payoffs
along PD lines.

DC
= 5,0

CC=
3,3

DD=
1,1

CD=0,5
Strategy that won overall was TitforTat

Never
scored higher than

TitforTat:
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 shortrun 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/(1w))
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.