Optimality and stability of the ideal free distribution with application to temperature control

We extend the theory of the "ideal free distribution" (IFD) from theoretical ecology by providing methods to analytically find the distribution for a relatively general class of "suitability" functions. We show that the resulting IFD is a Nash equilibrium and an evolutionarily stable strategy (ESS). Moreover, we show that for a certain cost function it is a global optimum point. We introduce the "replicator dynamics" for the IFD and show that they provide an allocation strategy that is guaranteed to achieve the IFD. Finally, we show how this allocation strategy can achieve an IFD for a multizone temperature control problem that corresponds to achieving the maximum uniform temperature on a grid under a multivariable saturation constraint