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In this paper, we present a stylized dynamic interdependent multi-country energy transition model. The goal of this paper is to provide a starting point for examining the impact of uncertainty in such models. To do this, we define a simple model based on the standard Solow macroeconomic growth model. We consider this model in a two-country setting using a non-cooperative dynamic game perspective. Total carbon dioxide (CO2) emission is added in this growth model as a factor that has a negative impact on economic growth, whereas production can be realized using either green or fossil energy. Additionally, a factor is incorporated that captures the difficulties of using green energy, such as accessibility per country. We calibrate this model for a two-player setting, in which one player represents all countries affiliated with the Organization for Economic Cooperation and Development (OECD) and the other player represents countries not affiliated with the OECD. It is shown that, in general, the model is capable to describe energy transitions towards quite different equilibrium constellations. It turns out that this is mainly caused by the choice of policy parameters chosen in the objective function. We also analyze the optimal response strategies of both countries if the model in equilibrium would be hit by a CO2 shock. Also, here we observe a quite natural response. As the model is quite stylized, a serious study is performed to the impact several model uncertainties have on the results. It turns out that, within the OECD/non-OECD framework, most of the considered uncertainties do not impact results much. However, the way we calibrate policy parameters does carry much uncertainty and, as such, influences equilibrium outcomes a lot.
Valentijn Stienen; Jacob Engwerda. Measuring Impact of Uncertainty in a Stylized Macroeconomic Climate Model within a Dynamic Game Perspective †. Energies 2020, 13, 482 .
AMA StyleValentijn Stienen, Jacob Engwerda. Measuring Impact of Uncertainty in a Stylized Macroeconomic Climate Model within a Dynamic Game Perspective †. Energies. 2020; 13 (2):482.
Chicago/Turabian StyleValentijn Stienen; Jacob Engwerda. 2020. "Measuring Impact of Uncertainty in a Stylized Macroeconomic Climate Model within a Dynamic Game Perspective †." Energies 13, no. 2: 482.
This paper analyzes how the introduction of Eurobonds affects debt dynamics in a two-country monetary union model. Monetary and fiscal authorities are engaged in dynamic government debt stabilization games in which interest rates on government debt adjust endogenously. Three different equilibria are considered: the non-cooperative Nash open-loop equilibrium, the fiscal coordination equilibrium and the fully cooperative equilibrium. It is shown how the effects of Eurobonds depend on the game-theoretic equilibrium/institutional framework in place, the initial debt levels, policy makers’ concerns with debt stabilization and the strength of financial market discipline.
Jacob Engwerda; Bas van Aarle; Tzanis Anevlavis. Debt stabilization games in a monetary union: What are the effects of introducing eurobonds? Journal of Macroeconomics 2018, 59, 78 -102.
AMA StyleJacob Engwerda, Bas van Aarle, Tzanis Anevlavis. Debt stabilization games in a monetary union: What are the effects of introducing eurobonds? Journal of Macroeconomics. 2018; 59 ():78-102.
Chicago/Turabian StyleJacob Engwerda; Bas van Aarle; Tzanis Anevlavis. 2018. "Debt stabilization games in a monetary union: What are the effects of introducing eurobonds?" Journal of Macroeconomics 59, no. : 78-102.
This paper focuses on the possibility that financial markets require risk premia on holding sovereign debt of countries that appear vulnerable from a fiscal sustainability perspective. Both the level of debt as well as the rate of change of debt are assumed to impact on the risk premium. We analyze the impact of such an endogenous risk premium in a simple debt game between a monetary and a fiscal player, as introduced by [Tabellini (1986) Journal of Economic Dynamics and Control 10, 427–442]. The risk premium term adds a nonlinearity to the linear model in case risk premia are absent. We analyze outcomes in case of noncooperative open-loop Nash strategies and in case of cooperative strategies and consider the workings of the risk premium as a market-based disciplining device (in case of high debt) and adjustment rewarding device (in case of a declining debt trajectory).
Tzanis Anevlavis; George Papavassilopoulos; Jacob Engwerda; Bas van Aarle. DEBT STABILIZATION IN THE PRESENCE OF ENDOGENOUS RISK PREMIA: A DYNAMIC GAME APPROACH. Macroeconomic Dynamics 2018, 23, 2616 -2648.
AMA StyleTzanis Anevlavis, George Papavassilopoulos, Jacob Engwerda, Bas van Aarle. DEBT STABILIZATION IN THE PRESENCE OF ENDOGENOUS RISK PREMIA: A DYNAMIC GAME APPROACH. Macroeconomic Dynamics. 2018; 23 (07):2616-2648.
Chicago/Turabian StyleTzanis Anevlavis; George Papavassilopoulos; Jacob Engwerda; Bas van Aarle. 2018. "DEBT STABILIZATION IN THE PRESENCE OF ENDOGENOUS RISK PREMIA: A DYNAMIC GAME APPROACH." Macroeconomic Dynamics 23, no. 07: 2616-2648.
In this article we analyze an optimal management problem that arises in ecological economics using hybrid systems modeling. First, we introduce a discounted autonomous infinite horizon hybrid optimal control problem and develop few tools to analyze the necessary conditions for optimality. Next, using these tools we study the classical shallow lake problem where the nonlinear lake dynamics is described by hybrid dynamics. We show that our results agree with earlier studies on the problem, that is, variation of system parameters induce bifurcations in the optimal solution.
P. V. Reddy; J. M. Schumacher; J. C. Engwerda. Optimal Management with Hybrid Dynamics—The Shallow Lake Problem. Sensing and Control for Autonomous Vehicles 2015, 111 -136.
AMA StyleP. V. Reddy, J. M. Schumacher, J. C. Engwerda. Optimal Management with Hybrid Dynamics—The Shallow Lake Problem. Sensing and Control for Autonomous Vehicles. 2015; ():111-136.
Chicago/Turabian StyleP. V. Reddy; J. M. Schumacher; J. C. Engwerda. 2015. "Optimal Management with Hybrid Dynamics—The Shallow Lake Problem." Sensing and Control for Autonomous Vehicles , no. : 111-136.
In this paper we consider the effectiveness of various coordination arrangements between monetary and fiscal authorities within a monetary union if an economic shock has occurred. We address this problem using a multi-country New-Keynesian model of a monetary union cast in the framework of linear quadratic differential games. Using this model we study various coordination arrangements between fiscal and monetary players, including partial fiscal cooperation between only a subgroup of countries, which, to the best of our knowledge, has not been considered yet in the New-Keynesian literature. Using a simulation study we show that, in many cases and from the global point of view, partial fiscal cooperation between a subgroup of fiscal players is more efficient than non-coordination and that, in general, full cooperation without an appropriate transfer system is not a stable configuration. Furthermore, in case there is no full cooperation we show that the optimal configuration of the coordination structure depends on the type of shock that has occurred. We present a detailed analysis of the relationship between coordination structures and type of shock.
Tomasz Michalak; Jacob Engwerda; Joseph Plasmans. Interactions Between Fiscal and Monetary Authorities in a Three-Country New-Keynesian Model of a Monetary Union. Dynamic Modeling and Econometrics in Economics and Finance 2014, 16, 239 -288.
AMA StyleTomasz Michalak, Jacob Engwerda, Joseph Plasmans. Interactions Between Fiscal and Monetary Authorities in a Three-Country New-Keynesian Model of a Monetary Union. Dynamic Modeling and Econometrics in Economics and Finance. 2014; 16 ():239-288.
Chicago/Turabian StyleTomasz Michalak; Jacob Engwerda; Joseph Plasmans. 2014. "Interactions Between Fiscal and Monetary Authorities in a Three-Country New-Keynesian Model of a Monetary Union." Dynamic Modeling and Econometrics in Economics and Finance 16, no. : 239-288.
In this article we derive conditions for the existence of Pareto optimal solutions for linear quadratic infinite horizon cooperative differential games. First, we present a necessary and sufficient characterization for Pareto optimality which translates to solving a set of constrained optimal control problems with a special structure. Next, we show that if the dynamical system is controllable, certain transversality conditions hold true, and as a result all the Pareto candidates can be obtained by solving a weighted sum optimal control problem. Further, exploiting the linear structure we investigate the relationship between Pareto optimality and weighted sum minimization. Finally, for the scalar case, we present an algorithm to find all the Pareto optimal solutions assuming mild conditions on the control space.
Puduru Viswanadha Reddy; Jacob Christiaan Engwerda. Pareto optimality in infinite horizon linear quadratic differential games. Automatica 2013, 49, 1705 -1714.
AMA StylePuduru Viswanadha Reddy, Jacob Christiaan Engwerda. Pareto optimality in infinite horizon linear quadratic differential games. Automatica. 2013; 49 (6):1705-1714.
Chicago/Turabian StylePuduru Viswanadha Reddy; Jacob Christiaan Engwerda. 2013. "Pareto optimality in infinite horizon linear quadratic differential games." Automatica 49, no. 6: 1705-1714.
We present an algorithm and a corresponding MATLAB numerical toolbox to solve any form of infinite-planning horizon affine linear quadratic open-loop differential games. By rewriting a specific application into the standard framework one can use the toolbox to calculate and verify the existence of both the open-loop non-cooperative Nash equilibrium (equilibria) and cooperative Pareto equilibrium (equilibria). In case there is more than one equilibrium for the non-cooperative case, the toolbox determines all solutions that can be implemented as a feedback strategy. Alternatively, the toolbox can apply a number of choice methods in order to discriminate between multiple equilibria. The user can predefine a set of coalition structures for which they would like to calculate the non-cooperative Nash solution(s). It is also possible to specify the relative importance of each player in any coalition structure. Furthermore, the toolbox offers plotting facilities as well as other options to analyse the outcome of the game. For instance, it is possible to disaggregate each player’s total loss into its contributing elements. The toolbox is available as a freeware from the authors of this paper.
Tomasz Michalak; Jacob Engwerda; Joseph Plasmans. A Numerical Toolbox to Solve N-Player Affine LQ Open-Loop Differential Games. Computational Economics 2011, 37, 375 -410.
AMA StyleTomasz Michalak, Jacob Engwerda, Joseph Plasmans. A Numerical Toolbox to Solve N-Player Affine LQ Open-Loop Differential Games. Computational Economics. 2011; 37 (4):375-410.
Chicago/Turabian StyleTomasz Michalak; Jacob Engwerda; Joseph Plasmans. 2011. "A Numerical Toolbox to Solve N-Player Affine LQ Open-Loop Differential Games." Computational Economics 37, no. 4: 375-410.
This paper develops an endogenous coalition formation framework suitable for studying a design of international macroeconomic policy coordination between an arbitrary number of countries and monetary authorities in the presence of (possibly multiple) monetary unions. In analyzing the feasibility of policy cooperation, we follow the approach proposed by the recent literature on the non-cooperative theory of coalition formation, which includes Bloch (1995, 1996), Yi (1997), Ray and Vohra (1997, 1999), Finus (2001) and Finus and Rundshagen (2001, 2003). These models share the common framework of a two-stage structure. In the first stage, coalitions are formed. In the second stage of the game (the stabilization phase), assuming all coalition structures as given, the model is solved by methods of linear quadratic differential games.
Tomasz Michalak; Jacob Engwerda; Joseph Plasmans; Bas Van Aarle; Giovanni Di Bartolomeo; Reinhard Neck. Models of Endogenous Coalition Formation Between Fiscal and Monetary Authorities in the Presence of a Monetary Union. Advances in Computational Economics 2008, 20, 103 -136.
AMA StyleTomasz Michalak, Jacob Engwerda, Joseph Plasmans, Bas Van Aarle, Giovanni Di Bartolomeo, Reinhard Neck. Models of Endogenous Coalition Formation Between Fiscal and Monetary Authorities in the Presence of a Monetary Union. Advances in Computational Economics. 2008; 20 ():103-136.
Chicago/Turabian StyleTomasz Michalak; Jacob Engwerda; Joseph Plasmans; Bas Van Aarle; Giovanni Di Bartolomeo; Reinhard Neck. 2008. "Models of Endogenous Coalition Formation Between Fiscal and Monetary Authorities in the Presence of a Monetary Union." Advances in Computational Economics 20, no. : 103-136.
In this note we provide a characterization of a subclass of bargaining problems for which the Nash solution has the property of disagreement point monotonicity. While the original d-monotonicity axiom and its stronger notion, strong d-monotonicity, were introduced and discussed by Thomson (J Econ Theory, 42: 50–58, 1987), this paper introduces local strong d-monotonicity and derives a necessary and sufficient condition for the Nash solution to be locally strongly d-monotonic. This characterization is given by using the sensitivity matrix of the Nash bargaining solution w.r.t. the disagreement point d. Moverover, we present a sufficient condition for the Nash solution to be strong d-monotonic.
Jacob C. Engwerda; Rudy C. Douven. On the sensitivity matrix of the Nash bargaining solution. International Journal of Game Theory 2007, 37, 265 -279.
AMA StyleJacob C. Engwerda, Rudy C. Douven. On the sensitivity matrix of the Nash bargaining solution. International Journal of Game Theory. 2007; 37 (2):265-279.
Chicago/Turabian StyleJacob C. Engwerda; Rudy C. Douven. 2007. "On the sensitivity matrix of the Nash bargaining solution." International Journal of Game Theory 37, no. 2: 265-279.
A highly integrated area like the EMU features a large amount of interactions between the participating countries. In this context the interactions of monetary and fiscal policies are a crucial issue. This paper focuses on how coalitions among policymakers are formed and discusses their effects on the stabilization of output and price. We emphasize the role played by the institutional design of “cooperation forums” (as, e.g., the ECOFIN). If the coalition formation game is played without communication among the policymakers, full cooperation is an unlikely outcome. On the other hand, if policymakers can communicate, full cooperation becomes a possible equilibrium, while the complete non-cooperative solution is, in general, not a stable equilibrium. This supports the view that institutions for discussions can play a crucial role in achieving international cooperation even when these institutions are not endowed with enforcement powers.
Bas van Aarle; Giovanni Di Bartolomeo; Jacob Engwerda; Joseph Plasmans. Policymakers’ Coalitions and Stabilization Policies in the EMU. Journal of Economics 2003, 82, 1 -24.
AMA StyleBas van Aarle, Giovanni Di Bartolomeo, Jacob Engwerda, Joseph Plasmans. Policymakers’ Coalitions and Stabilization Policies in the EMU. Journal of Economics. 2003; 82 (1):1-24.
Chicago/Turabian StyleBas van Aarle; Giovanni Di Bartolomeo; Jacob Engwerda; Joseph Plasmans. 2003. "Policymakers’ Coalitions and Stabilization Policies in the EMU." Journal of Economics 82, no. 1: 1-24.
J.C. Engwerda; W.A. Van Den Broek; J.M. Schumacher. Soft-Constrained Feedback Nash Equilibria. Modeling and Control of Economic Systems 2001 2003, 23 -28.
AMA StyleJ.C. Engwerda, W.A. Van Den Broek, J.M. Schumacher. Soft-Constrained Feedback Nash Equilibria. Modeling and Control of Economic Systems 2001. 2003; ():23-28.
Chicago/Turabian StyleJ.C. Engwerda; W.A. Van Den Broek; J.M. Schumacher. 2003. "Soft-Constrained Feedback Nash Equilibria." Modeling and Control of Economic Systems 2001 , no. : 23-28.
J.C. Engwerda; W.A. Van Den Broek; J.M. Schumacher. Soft-Constrained Feedback Nash Equilibria. IFAC Proceedings Volumes 2001, 34, 23 -28.
AMA StyleJ.C. Engwerda, W.A. Van Den Broek, J.M. Schumacher. Soft-Constrained Feedback Nash Equilibria. IFAC Proceedings Volumes. 2001; 34 (20):23-28.
Chicago/Turabian StyleJ.C. Engwerda; W.A. Van Den Broek; J.M. Schumacher. 2001. "Soft-Constrained Feedback Nash Equilibria." IFAC Proceedings Volumes 34, no. 20: 23-28.