De Finetti's control problem with competition

TL;DR

This paper analyzes a competitive resource extraction game modeled as a stochastic control problem, establishing equilibrium strategies and thresholds, and showing how increased competition affects extraction behavior and outcomes.

Contribution

It introduces a Nash equilibrium framework for De Finetti's control problem with competition, characterizing threshold strategies and their dependence on competition intensity.

Findings

Existence of symmetric Nash equilibrium with threshold strategies

Increased competition lowers extraction thresholds

Asymmetric case thresholds ordered by extraction rates

Abstract

We investigate the effects of competition in a problem of resource extraction from a common source with diffusive dynamics. In the symmetric version with identical extraction rates we prove the existence of a Nash equilibrium where the strategies are of threshold type, and we characterize the equilibrium threshold. Moreover, we show that increased competition leads to lower extraction thresholds and smaller equilibrium values. For the asymmetric version, where each agent has an individual extraction rate, we provide the existence of an equilibrium in threshold strategies, and we show that the corresponding thresholds are ordered in the same way as the extraction rates.