Optimal Switching from Competition to Cooperation: A Preliminary Exploration

Abstract

In this paper, we tackle a generic optimal regime switching problem where the decision making process is not the same from a regime to another. Precisely, we consider a simple model of optimal switching from competition to cooperation. To this end, we solve a twostage optimal control problem. In the first stage, two players engage in a dynamic game with a common state variable and one control for each player. We solve for open-loop strategies with a linear state equation and linear-quadratic payoffs. More importantly, the players may also consider the possibility to switch at finite time to a cooperative regime with the associated joint optimization of the sum of the individual payoffs. Using theoretical analysis and numerical exercises, we study the optimal switching strategy from competition to cooperation. We also discuss the reverse switching.

On regional integration, fiscal income, and GDP per capita

“…Boucekkine et al (2011) study environmental quality and economic performance in a dynamic game context. Also in a dynamic game model, Boucekkine et al (2020) study a generic optimal regime-switching problem. In the context of our model, it may also be interesting to characterize how integration affects the large jurisdiction's net revenue and GDP per capita.…”

The irreversible pollution game

“…As always, the tricky part of the optimization work lies at the junction of the two regimes, that is, at the switching point (if any). Most of the existing literature on regime switching focuses on optimal individual (for example, central planner) problems, and thus, it has naturally relied on versions of the Pontryagin optimality conditions, including some specific continuity (or transversality) conditions on the maximized Hamiltonians and, in some cases, also on the co-state variables at the switching points (see, for example, Tomiyama (1985), Boucekkine et al (2013aBoucekkine et al ( ,b, 2020). The same technique has been used to characterize open-loop equilibria in dynamic game models with regime switching (see Boucekkine et al (2011), for a two-country game without pollution irreversibility, in addition to Wagener and de Zeeuw (2021), which does deal with irreversibility).…”