Cooperation 2 Flashcards
(8 cards)
Prisoners dilemma
Players can adopt one of two strategies
Must be
T>R>P>S
How do we check whether D strategiests can invade a population of mainly C strategists?
Assume fitness of each playing is 0
P is small frequency of individuals playing d
Fitness of D -> (1-p)xE(D,C) + pxE(D,D)
5 - 3xp
Fitness of C -> (1-p) x E(C,C) + pxE(C,D)
3 - 3xp
D invades, C not evolutionary stable
How do we check whether C strategists can invade a population consisting of mainly D strategists?
Fitness of D
pxE(D,C) + (1-p)xE(D,D)
Fitness of C
pxE(C,C) + (1-p)xE(C,D)
Fitness of D > fitness of C
D is evolutionary stable
Iterated prisoners dilemma
In the Iterated Prisoner’s Dilemma (IPD), a single game consists of a number of rounds of the simple Prisoner’s dilemma (PD), which allows individuals to react to an opponent’s past behaviour.
If players interact repeatedly before the final tally is made, low expected payoff in future interactions because of retaliation against current defection could render cooperation beneficial.
tit for tat
Describe the extentions of prisoner’s dilemma
Iterated Prisoner’s dilemma
players interact repeatedly
Spatial Prisoner’s dilemma
players interact with their neighbours
Continuous Prisoner’s dilemma
instead all or nothing strategies cooperation varies continuously
What other games promote cooperation?
Snowdrift game
Describe the snowdrift game
Benefit to clearing snow is b
Cost to removing snow is c, where b > c
When cooperator plays against cooperator,
both gain benefit b and they share the cost of clearing the snow,
each paying c/2.
When defector plays against cooperator,
both gain benefit b but defector doesn’t incur any costs
When defector plays against defector,
there are no benefits and no costs to their strategy
Conflicts between evolutionary theorists
Inclusive fitness vs natural selection theory in context of spatial structure
Population genetics vs adaptive dynamics
