Strong coexistence for a model with endogenous evolution of heterogeneous agents

We propose two exchange economy evolutionary models with heterogeneous agents, in which the share updating mechanisms depend on the goods' consumption, described in terms of the calorie intakes. In the first setting we assume that the share updating rule is monotone in the calorie intake, while in the second framework we suppose that it is non-monotone. In both scenarios we investigate whether there may be multistability phenomena involving nontrivial market stationary equilibria at which the calorie intakes for the two groups of agents differ. The answer is negative in the first setting, while it is affirmative in the second framework.