The habitat selection game considers how populations should distribute themselves among several patches in such a way that no individual can improve its fitness (i.e. payoff) by moving. Fretwell and Lucas proved that there is a unique such distribution called the Ideal Free Distribution (IFD) if total population size is fixed and patch payoff is a decreasing function of patch population size. I will discuss this result from the perspective of evolutionary game theory, both in terms of the static game-theoretic solution concept of an Evolutionarily Stable Strategy (ESS) and in terms of evolutionary dynamics that assume adaptive movement between patches. I will also develop and analyze a population game model that includes changing total size, which demonstrates the strong predictive power of the IFD.
Group for Research in Decision Analysis