Presentation on theme: "The Evolutionary Games We Play Psychology 3107. Introduction Animals tend to behave in ways that maximize their inclusive fitness Usually pretty straightforward."— Presentation transcript:
Introduction Animals tend to behave in ways that maximize their inclusive fitness Usually pretty straightforward But, sometimes we must know what others are doing before we adopt a strategy What if your mating call is drowned out by others’ calls, what to do, ahh what to do…
Fitness and Strategies In certain cases payoffs, and hence fitness maximization, depend on what other populations are doing When the payoff to one individual depends on the behaviour of others we cannot use the principle of fitness maximization until we know: What the alternatives are What the alternatives are P(encountering alternatives) P(encountering alternatives) Consequences of encounter Consequences of encounter
Game Theory Think of it like a game Each individual’s behaviour is its strategy, payoffs are in units of fitness Players produce more players (offspring) Changes in fitness are directly proportional to payoffs An evolutionary Stable Strategy is one that, when adopted by enough individuals, maximizes payoff
Pure Strategy One that cannot be replaced Food storing Recover your own seeds (Anderssen and Krebs, 1978) If they recovered communally, a selfish hoarder would replace the communals damned quckly
Mixed Strategies Hawks and Doves Not real hawks or doves, strategies Not real hawks or doves, strategies Always fight, or always give up Look at the payoffs Look at the costs Determine what proportion should be hawks and should be doves
Hawks and Doves Say its all Doves Hawk shows up, wins resource Spreads genes Now more hawks Oh oh, now you are fighting, P(injury) =.5 Now being a dove pays Either strategy good when rare, bad when common
Doves and Hawks V =V alue of resource for winner W = cost of a wound T = cost of display (no fighting) (John Maynard Smith, 1978)
Whoa, I know Kung Fu Set up a payoff Matrix Opponent in the contest HawkDove PayoffHawk½(V-W)V Received ByDove0½V-T
ESS as easy as 123 If W > V then there can be no pure ESS In a population of hawks, a small number of doves do better than hawks In a population of hawks, a small number of doves do better than hawks E(dove,hawk) > E(hawk, hawk) E(dove, hawk) = 0 E(hawk, hawk) = ½(V-W) W > V, therefore ½(V-W) V, therefore ½(V-W) < 0
Pure Doves don’t do it either Payoff to Hawk is V Payoff to doves is less than that (½W – T) (½W – T)Hmmm So, what proportion of hawks and doves balances it out?
What is theoretical population biologist to do? Find the proportion (p) of hawks of hawks such that the following equation balances: p ½(V-W) = (1-p) V = p (0) + (1-p) (½V– T) Simply (?) solve for p p = (V+2T) / (W+ 2T)
Apply it, sort of Say V = 10 W = 20 T = 3 Opponent in the contest HawkDove PayoffHawk-510 Received ByDove02
Now, sub that back into the formula P = 16/26 or 8/13 8/13ths of the population, with these payoff values, must be hawks The values are not that important really, the point is that you can determine the point at which a strategy can coexist with another strategy as an ESS Could be percentage of population, or percentage of time each animal adopts a given strategy
So? It is actually applicable that’s so Toads looking for breeding grounds (Davies and Hallaway, 1979) Payoffs determined
Another so Dungflies Should a male hang around poo as it gets older?
Conclusions This is a very brief intro to game theory This stuff is way powerful You have to sit and think some about the payoffs and costs Dynamic programming models are becoming more popular
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