# Evolutionary dynamics of a duopoly game with strategic delegation and isoelastic demand

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## Abstract

We analyze a model of strategic delegation in Cournot competition with isoelastic demand. We first consider the static game and then we address an evolutionary version of it. We show that the result for which under quantity competition strategic delegation entails output expansion and higher consumers’ welfare than at the standard Cournot-Nash equilibrium is not necessarily true, but depends on the price elasticity of demand. Then, we study the main welfare implications of the model in order to understand whether the prevailing long-run industry configuration provides the highest welfare. We show that this may occur when both firms provide a mixed incentive and that, in this case, the model admits feasible trajectories the long-run configuration of which yields the highest welfare. Finally, we address the robustness of our results by means of an evolutionary model with heterogeneous players.

### Keywords

Strategic delegation Evolutionary games Quantity competition Isoelastic demand Cartel stability### JEL Classification

C73 L13 L21 D43## Notes

### Acknowledgments

The authors would like to thank Mario Pezzino and Davide Radi as well as the anonymous referees for helpful comments on the paper. The usual disclaimer applies. Fabio Lamantia gratefully acknowledges financial support from EU COST Action IS1104 The EU in the new economic complex geography: models, tools and policy evaluation. This work is part of the research project Dynamic models for behavioral economics, DESP - University of Urbino, Italy.

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