Does Flexibility Facilitate Sustainability of Cooperation Over Time? A Case Study from Environmental Economics

• Published in: Journal of optimization theory and applications Vol. 165; no. 2; pp. 657 - 677
• Main Authors: de Frutos, Javier, Martín-Herrán, Guiomar
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.05.2015; Springer Nature B.V
• Subjects: Agreements; Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Case studies; Cooperation; Credibility; Differential equations; Differential games; Economics; Engineering; Environmental economics; Equilibrium; Flexibility; Game theory; Games; Incentives; Mathematical analysis; Mathematics; Mathematics and Statistics; Nonlinearity; Operations Research/Decision Theory; Optimization; Strategy; Studies; Sustainability; Theory of Computation; 91A12; 91A23; 49N70; Cooperation; Differential games; 49N90; Credibility; Environmental economics; Incentive equilibria
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-014-0573-z

In this paper we present nonlinear incentive strategies that can be applied to a class of differential games that are frequently used in the literature, in particular, in environmental economics literature. We consider a class of nonlinear incentive functions that depend on the control variables of both players and on the current value of the state variable. The strategies are constructed to allow some flexibility in the sense that, unlike the common literature on the subject, the optimal state path evolves close to the cooperative trajectory. As a consequence of this flexibility, the incentive equilibrium is credible in a larger region than the one associated with the usual linear incentive strategies.