Strategic Interaction by Boundedly Rational Players: Structure, Selection, and Computation of Exponential Satisficing Equilibria

We study strategic interaction by boundedly rational players and introduce an algorithm to compute exponential satisficing equilibria that is effective for an open set of normal-form games of full Lebesgue measure. To do so, we analyze the structure of the cognitive tracing procedure, which is used to select an exponential satisficing equilibrium for each value of the preference resolution parameter. As a by-product, we find that there is generically an odd number of such equilibria. To develop a differentiable homotopy algorithm, we design new tools of variable transformations to deal with the non-differentiabilities inherent in the rank-dependency of exponential satisficing. We apply the algorithm to a model of heterogeneous Bertrand competition as well as to a connections model of network formation.