Mitigation, Adaptation and Cooperation in Response to Climate Disaster

In this paper, we suggest a two-player differential game model of transboundary pollution that accounts for time-dependent environmental absorption efficiency, which allows the biosphere to switch from a carbon sink to a source. We investigate the impact of negative externalities resulting from a transboundary pollution non-cooperative game wherein countries are dynamically involved. Based on a linear-quadratic specification for the instantaneous revenue function, we assess differences related to both transient path and steady state between cooperative solution, open-loop and Markov perfect Nash equilibria (MPNE). Regarding the methodological contribution of the paper, we suggest a particular structure of the conjectured value function to solve MPNE problems with multiplicative interaction between state variables in one state equation, so that third-order terms that arise in the Hamilton–Jacobi–Bellman equation are made negligible. Using a collocation procedure, we confirm the validity of the particular structure of the conjectured value function. The results suggest unexpected contrasts in terms of pollution control and environmental absorption efficiency management: (i) in the long run, an open-loop Nash equilibrium (OLNE) allows equivalent emissions to the social optimum but requires greater restoration efforts; (ii) although an MPNE is likely to end up with lower emissions and greater restoration efforts than an OLNE, it has a much greater chance of falling in the emergency area; (iii) the absence of cooperation and or precommitment becomes more costly as the initial absorption efficiency decreases; (iv) more heavily discounted MPNE strategies are less robust than OLNE to prevent irreversible switching of the biosphere from a carbon sink to a source.

We investigate the possibility of using public firms to regulate polluting emissions in a Cournot oligopoly where production takes place at constant returns to scale and entails a negative environmental externality. We model the problem as a differential game and investigate (i) the Cournot-Nash game among profit-seeking firms; (ii) the Markov Perfect Nash equilibrium under social planning, where the industry output is entirely controlled by a benevolent planner aiming at the maximisation of social welfare; and (iii) the Markov Perfect Nash equilibrium in a mixed setup where at least one firm is public, while the others remain profit-seeking agents. Our analysis identifies the conditions whereby having a mixed market as a regulatory instrument suffices to drive the industry to the same output, externality and social welfare as under planning, both along the optimal path and in steady state.

We investigate the possibility of using public firms to regulate polluting emissions in a Cournot oligopoly where production takes place at constant returns to scale and entails a negative environmental externality. We model the problem as a differential game and investigate (i) the Cournot-Nash game among profit-seeking firms; (ii) the Markov Perfect Nash equilibrium under social planning, where the industry output is entirely controlled by a benevolent planner aiming at the maximisation of social welfare; and (iii) the Markov Perfect Nash equilibrium in a mixed setup where at least one firm is public, while the others remain profit-seeking agents. Our analysis identifies the conditions whereby having a mixed market as a regulatory instrument suffices to drive the industry to the same output, externality and social welfare as under planning, both along the optimal path and in steady state.

This study formulates a dynamic mixed oligopoly model, in which a state‐owned public firm competes against a private firm over multiple periods. We adopt a differential game formulated by Fershtman and Kamien [Econometrica 55 (1987), pp. 1151–1164] and investigate how the dynamic competition affects the optimal privatization policy. We characterize the open‐loop Nash equilibrium (OLNE) and Markov‐perfect Nash equilibrium (MPNE). We show that in the MPNE, an increase in the degree of privatization has a nonmonotonic effect on the price, increasing it in a wide range of parameter spaces, which is in sharp contrast to the result in the OLNE or static analyses. We also find that the optimal degree of privatization is higher in the MPNE than that in the OLNE and static equilibrium. These results suggest that intertemporal strategic behavior changes the optimal privatization policy.

We characterise the entire set of symmetric stationary Markov-perfect Nash equilibria (MPE) in a differential game of public good investment, using the canonical problem of climate change as an example. We provide a sufficient and necessary condition for MPE and show how the entire set of MPE is constructed. The equilibrium in continuous strategies, unique in our context, is Pareto-dominated by any other equilibrium. If a Pareto- undominated steady state exists, it is sustained by trigger-like strategies, with deviations above and below the steady state leading to different re- sponses. We extend the theory of differential games to deal with payoffs under discontinuous strategies. Our methods work under general functional forms.

We characterise the entire set of symmetric stationary Markov-perfect Nash equilibria (MPE) in a differential game of public good investment, using the canonical problem of climate change as an example. We provide a sufficient and necessary condition for MPE and show how the entire set of MPE is constructed. The equilibrium in continuous strategies, unique in our context, is Pareto-dominated by any other equilibrium. If a Pareto-undominated steady state exists, it is sustained by trigger-like strategies, with deviations above and below the steady state leading to different responses. We extend the theory of differential games to deal with payoffs under discontinuous strategies. Our methods work under general functional forms.

Strategic pollution control under free trade

We consider a dynamic model of an industry consisting of a few large firms, which can manipulate the market outcome, and a mass of small enterprises, each of which has a negligible impact on the market. The production costs of the respective firms depend on the stock of knowledge capital, which accumulates over time through research and development (R &D) investment made by large firms. The model is a variant of the differential game of voluntary provision of public goods, but in contrast to previous studies, we focus on the interaction between market competition and dynamic game outcomes. We derive both open-loop and Markov-perfect Nash equilibria. There exists a unique open-loop Nash equilibrium. By contrast, depending on the parameters of the model, there can be two linear Markov-perfect Nash equilibria. We also examine the short- and long-run effects of a change in the number of large firms. An increase in the number of large firms unambiguously harms both types of firms in the short run but may benefit them in the long run. In the open-loop Nash equilibrium, the relationship between the number of large firms and the steady-state stock of knowledge capital is inverted-U shaped. Concerning the Markov-perfect Nash equilibria, the effect of increased competition from large firms depends on the specific feedback strategy chosen in equilibrium.

In this note, we present a method that allows us to decide when a Markov-perfect Nash equilibrium is not Pareto optimum, without the explicit knowledge of the respective solutions. For that purpose, we establish a sufficient condition in terms of an algebraic inequality where the gradient of the value functions of the cooperative and noncooperative games as well as the state and control variables are involved.

A note on discontinuous value functions and strategies in affine-quadratic differential games

We consider the problem of dynamic bandwidth allocation among different service classes under uncertainty in cognitive radio networks. In such networks, the secondary users compete for bandwidth resources and the service providers compete for users access (e.g., subscription). To address this problem, a two-level dynamic game framework is developed. The underlying dynamic service selection of secondary users is modeled as an evolutionary game based on replicator dynamics. The randomly irrational churning behavior of secondary users is modeled as a stochastic disturbance to the service selection distribution evolution. At the upper level, a bandwidth allocation stochastic differential game is formulated to model the competition among different service providers. The service selection distribution of the underlying evolutionary game describes the state of the upper stochastic differential game and a Markov perfect Nash equilibrium is considered to be the solution. The decentralized nature of the framework makes the system flexible and simple for implementation.

This paper aims to characterize a class of stochastic differential games which satisfy the certainty equivalence principle. This means that the Markov Perfect Nash Equilibrium is also an equilibrium of the associated deterministic game. By focusing on a model scalar game with linear dynamics in the players’ strategies, we solve an inverse problem to find strictly concave utility functions, not necessarily quadratic or logarithmic, for which certainty equivalence is fulfilled. We show a variety of models that satisfy the certainty equivalence principle in a non cooperative game of a productive asset.

In many cases policy makers employ multiple instruments to address a single environmental problem, but much of the economics literature on instrument choice focuses on comparing properties of single policy instruments. We argue that under a fairly broad set of circumstances the use of multiple policy instruments can be justified as optimal in a second-best world. We examine two broad categories of second-best policy making: cases with multiple market failures only some of which can be corrected at any one time; and cases with exogenous (often political) constraints that cannot be removed. The fact that the use of multiple policy instruments can be justified economically in these two cases does not imply, however, that all multiple instruments employed in actual practice are economically justified.

We study the optimal management of capital flows in a small open economy model with financial frictions and multiple policy instruments. The paper reports two main findings. First, both foreign exchange intervention (FXI) and macroprudential polices are tools complementary to the monetary policy rate that can largely reduce inflation and output volatility in a scenario of capital outflows. Second, the optimal policy mix depends on the underlying shock driving capital flows. FXI takes the leading role in response to foreign interest rate shocks, while macroprudential policy becomes the prominent tool for domestic risk shocks. These results highlight the importance of calibrating the use of multiple instruments according to the underlying shocks that induce shifts in capital flows.

Mundell meets Poole: Managing capital flows with multiple instruments in emerging economies