Game theory and behaviour evolution

Question 1

Game theory

Answer 1

*An approach to modelling that accounts for the fact that behaving individuals make decisions about how to behave (i.e., they have ’strategies’) that are contingent on the behaviour of others

*These models ask: “can a particular strategy invade a population?

*Considers best behaviour given unknown behaviour of others

Game theory was first applied to evolutionary biology in the 1970s by John Maynard Smith
Built on developments in economics
*notably by John Nash–PhD, 1950–28 page thesis, Nobel Prize winning!

Question 2

Game theory can be applied to:

Answer 2

–market economics
–computing
–artificial intelligence
–accounting
–politics
–military theory

Question 3

Game theory and biology

Answer 3

*The group selection problem:
–group-selected traits are unlikely to be evolutionarily stable.
–But, how to explain altruism & why animals seem to ‘selflessly’ obey social conventions?
-see Maynard Smith 1972, 1974, 1982; Also Dugatkin & Reeve 1998

Question 4

Game theory basics

Answer 4

Strategies = courses of action that provide different potential solutions to a problem.
e.g: different ways of obtaining food

Economics: strategies guided by foresight and design.

Biology: no intelligent foresight is involved:
- so, strategies = the various options available to natural selection during the evolutionary history of the organism.

• ‘strategy’ = behavioural phenotype specifying how an individual will behave in a given situation.
• Over generations more of the feasible genetic alternatives will have arisen & been played against each other.
• Eventually, one or more (equally effective) strategies will emerge triumphant & be resistant to invasion by alternatives. = evolutionarily stable strategies or ESSs (Maynard Smith 1972).

Question 5

evolutionarily stable strategies

Answer 5

ESS = a strategy that, if most members of a population adopt it, cannot be bettered by any feasible alternative strategy.

An ESS strategy must have a fitness (pay-off) that is greater than any possible alternative strategy.

Question 6

Game theory basic assumptions

Answer 6

1) infinite population size,
2) asexual reproduction,
3) Pairwise contests between 2 opponents
4) contests are symmetrical (no physical difference between contestants),
5) finite set of alternative strategies.

• limiting resource & access to resource has fitness consequences,
• fitness gained or lost through interaction with others in population, e.g. contests & aggression.

Question 7

Game theory models: Hawks and Doves

Answer 7

*Wynne-Edwards & Group selection:
–How can contests be so restrained & formalised, amongst individuals competing for limited resources?

*Maynard Smith:
–Model of how displays rather than all-out fighting can be selected for at the level of the individual…………….
»i.e. conflict reduction

Question 8

Definition of hawks and doves

Answer 8

A simple evolutionary scenario of just 2 competing strategies:

Hawk (H):
-escalate fights & continue till injured or opponent retreats (fights to win)

Dove (D):
-restrained competitors: display but don’t fight,
–retreat if opponent escalates (if opponent = H, don’t even bother displaying).

Additional assumptions:
–individuals always behave in same way.
–don’t meet same opponent more than once.
–choice of strategy is heritable.

Question 9

Hawks and doves explanation

Answer 9

–Advantage for H in population of D, as any individual it meets will retreat as soon as H becomes aggressive.

–So, genes for H will spread rapidly through population.

–BUT….as H spreads, it now begins to encounter other Hawks & experience serious aggression in return.

i.e. success (pay-off) is frequency dependent

*Neither ‘Pure’ H nor ‘Pure’ D are ESSs.
*Frequency ­dependent advantage to each strategy when rare.
*Evolutionarily stable solution must be the combination of the two strategies where both do equally well = mixed ESS

(see notes for equation examples + workings)

When cost of injury is high mixed strategy is favoured
When low hawk favoured
When high risk dove favoured

Question 10

Mixed ESS

Answer 10

2 ways that these proportions can be expressed in population:

Polymorphic:
a stable proportion of individuals (p) always do H, & the rest (1 - p) always do D.
= ‘alternative’ strategies.
Individuals have fixed behaviour?

Monomorphic:
- all individuals could play both strategies (individuals can change their behaviour)
- do H with probability p and D with probability 1 - p
- single mixed strategy with alternative tactics

(Gross 1996; Brockmann 2001).

Question 11

In summary: game theory: hawks and doves

Answer 11

–restrained contest behaviour can be accounted for without recourse to group selection (i.e. non-combative, display behaviour can be adaptive).

–Some adopt H (dominant),
–some adopt D (subordinate) strategy
-> conflict reduction.

–Dominance relationships (see next lecture)

Question 12

Game theory models summary

Answer 12

1) Density dependent fitness gained, or lost through interaction of others in population, e.g. contests & aggression. Implies a limiting resource.

2) An ESS is an evolutionary strategy that can’t be invaded by a more successful strategy. Basic model assumes infinite population size, asexual reproduction, pairwise symmetrical contests between 2 opponents & finite set of alternative strategies.

3) In a mixed ESS the strategy is to do H with probability p and D with probability 1- p, or a stable polymorphism could exist where some individuals always do H, and some always do D.

4) Games with repeated encounters with same individuals provide the conditions for learning. If games can be repeated & you’re likely to encounter the same opponent again, then reciprocal altruism can be an ESS