Feedback Nash equilibria for non-linear differential games in pollution control

Abstract

Dynamic problems of pollution and resource management with stock externalities often require a di¤erential games framework of analysis. In addition they are represented realistically by non linear transition equations. However, feedback Nash equilibrium (FBNE) 1 solutions, which are the desired ones in this case, are di¢ cult to obtain in problems with non linear-quadratic structure. We develop a method to obtain numerically non linear FBNE for a class of such problems, with a speci…c example for shallow lake pollution control.We compare FBNE solutions, by considering the entire equilibrium trajectories, with optimal management and open loop solutions and we show that the value of the best FBNE is in general worse than the open loop and optimal management solutions.

Potential Disasters can Turn the Tragedy into Success

“…In a CPR system, theory suggests that an endogenously driven regime shift can magnify the externality associated with non-cooperation (Mäler et al 2003;Kossioris et al 2008) or cause other kinds of suboptimal outcomes depending on parameter values and the initial state of the system (Crépin and Lindahl 2009). However, the outcomes of these CPR game theoretic settings depend very much on underlying behavioral assumptions: do users cooperate or not and how do users update their strategies and respond to changes in the resource stock?…”

Shallow lake economics run deep: nonlinear aspects of an economic-ecological interest conflict

“…It is readily apparent that this line of research, even in the case of the shallow lake problem, is far from being completed: for instance, the dynamic open loop [14] and closed loop [6,13] games have still to be analysed in a similar fashion. It can be readily conjectured that the classification of dynamic Nash equilibria for small values of the discount factor should resemble Figure 10.…”

Markov perfect Nash equilibria in models with a single capital stock

“…When investigating Markov equilibrium strategies for a differential game, the phenomenon is encountered that the Hamilton-Jacobi equation, which characterises these strategies, has typically many solutions that are not defined on the whole state space (see for instance Wirl 1996, Kossioris et al 2008). In the context of the original game, these solutions are not admissible, as they do not specify the action of the players if the state leaves the domain of definition of one of the strategies.…”

“…This problem is structurally similar to the exploitation of a single renewable resource stock but with a non-concave production function. Recent papers dealing with the shallow lake problem include Brock and Starrett (2003), Mäler et al (2003), Wagener (2003), Kossioris et al (2008), Kiseleva and Wagener (2010), Kossioris et al (2010).…”