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See detailOptimal lockdown and vaccination policies to contain the spread of a mutating infectious disease
Prieur, Fabien; Ruan, Weihua; Zou, Benteng UL

E-print/Working paper (2022)

We develop a piecewise deterministic control model to study optimal lockdown and vaccination policies to manage a pandemic. Lockdown is modeled as an impulse control that allows the system to switch from ... [more ▼]

We develop a piecewise deterministic control model to study optimal lockdown and vaccination policies to manage a pandemic. Lockdown is modeled as an impulse control that allows the system to switch from one restriction regime of restrictions to another. Vaccination policy is a continuous control. Decisions are taken under the risk of mutations of the disease, with repercussions on the transmission rate. The decision maker follows a cost minimization objective. We first characterize the optimality conditions for impulse control and show how the prospect of a mutation affects the decision maker's choice by inducing her to anticipate the relative benefit of a regime change after a mutation has occurred. Under some parametric conditions, our problem admits infinitely many value functions. We show the existence of a minimum value function that is a natural candidate to the solution given the nature of the problem. Focusing on this specific value function, we finally study the features of the optimal policy, especially the timing of impulse control. We prove that uncertainty surrounding future \bad" vs. \good" mutation of the disease expedites vs. delays the adoption of lockdown measures. [less ▲]

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See detailWhy and when coalitions split? An alternative analytical approach with an application to environmental agreements
Boucekkine, Raouf; Camacho, Carmen; Ruan, Weihua et al

E-print/Working paper (2022)

We use a parsimonious two-stage differential game setting where the duration of the first stage, the coalition stage, depends on the will of a particular player to leave the coalition through an explicit ... [more ▼]

We use a parsimonious two-stage differential game setting where the duration of the first stage, the coalition stage, depends on the will of a particular player to leave the coalition through an explicit timing variable. By specializing in a standard linear-quadratic environmental model augmented with a minimal constitutional setting for the coalition (payoff share parameter), we are able to analytically extract several nontrivial findings. Three key aspects drive the results: the technological gap as an indicator of heterogeneity across players, the constitution of the coalition and the intensity of the public bad (here, the pollution damage). We provide with a full analytical solution to the two-stage differential game. In particular, we characterize the intermediate parametric cases leading to optimal nite time splitting. A key characteristic of these finite-time-lived coalitions is the requirement of the payoff share accruing to the splitting country to be large enough. Incidentally, our two-stage differential game setting reaches the conclusion that splitting countries are precisely those which use to benefit the most from the coalition. Constraining the payoff share to be low by Constitution may lead to optimal everlasting coalitions only provided initial pollution is high enough, which may cover the emergency cases we are witnessing nowadays. [less ▲]

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See detailPandemic Impacts on Sustainability and Hartwick’s Rule
Mavi, Can; Zou, Benteng UL

E-print/Working paper (2022)

In this study, we present a modified Hartwick rule encompassing the dynamics of pandemic, such as COVID-19. In our setting, the labor productivity gradually improves after the pandemic shock and may even ... [more ▼]

In this study, we present a modified Hartwick rule encompassing the dynamics of pandemic, such as COVID-19. In our setting, the labor productivity gradually improves after the pandemic shock and may even go beyond its pre-pandemic level due to the remote work and digitalization as also suggested by the empirical evidence. We demonstrate that a gradual labor productivity increase helps to conserve natural resources. We provide a theoretical foundation for a“sooner-the-better" strategy to control a pandemic, and we show that policy maker should implement a “whatever it costs” response to ensure that the transmission rate of the virus is below the recovery rate from the very beginning of the pandemic. Otherwise, the economy cannot have a sustained utility. We also analyze the implications of an “uncertain” pandemic on the intertemporal dynamics of natural resource and capital accumulation under the maximin criterion. Another important finding is that there exists a new economic and public health trade-off since a strong prevention policy is shown to decrease capital accumulation. [less ▲]

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See detailThe Irreversible Pollution Game
Boucekkine, Raouf; Ruan, Weihua; Zou, Benteng UL

E-print/Working paper (2022)

We study a 2-country differential game with irreversible pollution. Irresability is of a hard type: above a certain threshold level of pollution, the self-cleaning capacity of Nature drops to zero ... [more ▼]

We study a 2-country differential game with irreversible pollution. Irresability is of a hard type: above a certain threshold level of pollution, the self-cleaning capacity of Nature drops to zero. Accordingly, the game includes a non-concave feature, and we characterize both the cooperative and non-cooperative versions with this general non-LQ property. We deliver full analytical results for the existence of Markov Perfect Equilibria. We first demonstrate that when pollution costs are equal across players (symmetry), irreversible pollution regimes are more frequently reached than under cooperation. Second, we study the implications of asymmetry in the pollution cost. We find far nontrivial results on the reachability of the irreversible regime. However, we unambiguously prove that, for the same total cost of pollution, provided the irreversible regime is reached in both the symmetric and asymmetric cases, long-term pollution is larger in the symmetric case, reflecting more intensive free-riding under symmetry. [less ▲]

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See detailUncertainty-driven symmetry-breaking and stochastic stability in a generic differential game of lobbying
Boucekkine, Raouf; Fabien, Prieur; Ruan, Weihua et al

in Economic Theory (2022)

We study a 2-players stochastic differential game of lobbying. Players invest in lobbying activities to alter the legislation in her own benefit. The payoffs are quadratic and uncertainty is driven by a ... [more ▼]

We study a 2-players stochastic differential game of lobbying. Players invest in lobbying activities to alter the legislation in her own benefit. The payoffs are quadratic and uncertainty is driven by a Wiener process. We consider the Nash symmetric game where players face the same cost and extract symmetric payoffs, and we solve for Markov Perfect Equilibria (MPE) in the class of affine functions. First, we prove a general sufficient (catching up) optimality condition for two-players stochastic games with uncertainty driven by Wiener processes. Second, we prove that the number and nature of MPE depend on the extent of uncertainty (i.e the variance of the Wiener processes). In particular, we prove that while a symmetric MPE always exists, two asymmetric MPE emerge if and only if uncertainty is large enough. Third, we study the stochastic stability of all the equilibria. We notably find, that the state converges to a stationary invariant distribution under asymmetric MPE. Fourth, we study the implications for rent dissipation asymptotically and compare the outcomes of symmetric vs asymmetric MPE in this respect, ultimately enhancing again the role of uncertainty. [less ▲]

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See detailThe U.S.–China Supply Competition for Rare Earth Elements: A Dynamic Game View
Zou, Benteng UL; Poncin, Stephane; Bertinelli, Luisito UL

in Environmental Modeling and Assessment (2022)

Rare earth elements govern today’s high-tech world and are deemed to be essential for the attainment of sustainable development goals. Since the 1990s, these elements have been predominantly supplied by ... [more ▼]

Rare earth elements govern today’s high-tech world and are deemed to be essential for the attainment of sustainable development goals. Since the 1990s, these elements have been predominantly supplied by one single actor, China. However, due to the increasing relevance of their availability, the United States, who imports 80% of its rare earths from China, recently announced its plan to (re-)enter the rare earths supply market. This paper analyzes the strategic interactions among these two countries in open-loop and Markovian strategy spaces. Particular interest is devoted to the impact of heterogeneous supply concepts on (1) the theoretical optimal timing for the U.S. to enter the non-renewable resource market, (2) China’s optimal supply reaction to the U.S.’ entry announcement, (3) the central planner outcome, and (4) the profitability of the suppliers’ extraction behavior. By setting up a continuous-time differential game model, we show that in the absence of arbitrage opportunity, (1) the U.S. should always postpone the production launch until its rare earths reserves coincide with those of China, (2) China’s monopolistic supply is not shaped by the selected strategy, (3) while the duopolistic Markovian behavior is initially more lucrative than open-loop commitment, the opposite situation emerges as the competition proceeds, and (4) on balance, both countries are financially better off when committing to an open-loop supply path. [less ▲]

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See detailIs a dynamic approach to tax games relevant?
Paulus, Nora; Pieretti, Patrice UL; Zou, Benteng UL

in Annals of Economics and statistics (2021), 144

In this paper, we argue that static models provide an incomplete analysis of interjurisdictional tax competition. Accordingly, one can doubt whether a one-shot view is suitable for analyzing real world ... [more ▼]

In this paper, we argue that static models provide an incomplete analysis of interjurisdictional tax competition. Accordingly, one can doubt whether a one-shot view is suitable for analyzing real world tax competition. Contrary to previous contributions in tax competition, we are able to model the interplay between changing tax rates and sluggish factor adjustments. We demonstrate that the intensity of tax competition is impacted by the temporal nature of the game. The commitment of governments to stick to their tax policies for a given period (open-loop behavior) leads to less intense competition relative to a static approach. If the policymakers continuously update their tax rates (Markovian behavior), competition is fiercer than in a static game, except for the case where capital adjustment is relatively sluggish and the governments' marginal valuation of public goods is high enough. [less ▲]

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See detailStochastic petropolitics: The dynamics of institutions in resource-dependent economies
Boucekkine, Raouf; Prieur, Fabien; Vasilakis, Chrysovalantis et al

in European Economic Review (2021)

We investigate the link between resource revenues volatility and institutions. We build a stochastic differential game with two players (conservatives vs . liberals) lobbying for changing the institutions ... [more ▼]

We investigate the link between resource revenues volatility and institutions. We build a stochastic differential game with two players (conservatives vs . liberals) lobbying for changing the institutions in their preferred directions. First, uncertainty surrounds the dynamics of institutions and the resource revenues. Second, the lobbying power is asymmetric, the conservatives’ power being increasing with resource revenues. We show the existence of a unique equilibrium in the set of affine strategies. We then examine to which extent uncertainty leads to more liberal institutions in the long run, compared to the deterministic case. We finally explore the institutional impact of volatility using a database covering 91 countries over the period 1973–2005. Focusing on financial liberalization, we find that as oil revenue volatility increases, liberalization goes down. This result is robust to different specifications and sample distinctions. [less ▲]

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See detailUncertainty-driven symmetry-breaking and stochastic stability in a generic differential game of lobbying
Boucekkine, Raouf; Prieur, Fabien; Ruan, Weihua et al

E-print/Working paper (2021)

We study a 2-players stochastic differential game of lobbying. Players have opposite interests; at any date, each player invests in lobbying activities to alter the legislation, the continuous state ... [more ▼]

We study a 2-players stochastic differential game of lobbying. Players have opposite interests; at any date, each player invests in lobbying activities to alter the legislation, the continuous state variable of the game, in her own benefit. The payoffs are quadratic and uncertainty is driven by a Wiener process. We prove that while a symmetric Markov Perfect Equilibrium (MPE) always exists, (two) asymmetric MPE only emerge when uncertainty is large enough. In the latter case, the legislative state converges to a stationary invariant distribution. We fully characterize existence and stochastic stability of the legislative state for both types of MPE. We finally study the implications for rent dissipation asymptotically. We show in particular that while the average rent dissipation is lower with asymmetric equilibria relative to the symmetric, the former yield larger losses at the most likely asymptotic states for large enough but moderate uncertainty. [less ▲]

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See detailOptimal Switching from Competition to Cooperation: A Preliminary Exploration
Boucekkine, Raouf; Camacho, Carmen; Zou, Benteng UL

in Haunschmied, Josef; Kovacevic, Raimund; Semmler, Willi (Eds.) et al Dynamic economic problems with regime switches (2020)

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 ... [more ▼]

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. [less ▲]

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See detailefugee Mobility: Evidence from Phone Data in Turkey
Beine, Michel UL; Bertinelli, Luisito UL; Cömertpay, Rana UL et al

in Salah, Albert Ali; Pentland, Alex; Lepri, Bruno (Eds.) et al Guide to Mobile Data Analytics in Refugee Scenarios: The 'Data for Refugees Challenge' Study (2019)

Our research report employs the D4R data and combines it with several other sources to study one of the multiple aspects of integration of refugees, namely the mobility of refugees across provinces in ... [more ▼]

Our research report employs the D4R data and combines it with several other sources to study one of the multiple aspects of integration of refugees, namely the mobility of refugees across provinces in Turkey. In particular, we employ a standard gravity model to empirically estimate a series of determinants of refugee movements. These include the standard determinants such as province characteristics, distances across provinces, levels of income, network effects as well as some refugee-specific determinants such as the presence of refugee camps and the intensity of phone call interaction among refugees. Importantly, we explore the effect of certain categories of news events, notably protests, violence, and asylum grants. Considering news as an indicator of policy implemented at the provincial level, we gain a better understanding as to how policy can facilitate refugee mobility and thus enhance integration. To benchmark our findings, we estimate the same model for the mobility of individuals with a non-refugee status. [less ▲]

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See detailA Pedagogical Note on Risk Sharing Versus Instability in International Financial Integration: When Obstfeld Meets Stiglitz
Boucekkine, Raouf; Zou, Benteng UL

in Open Economies Review (2019)

The pure risk sharing mechanism implies that financial liberalization is growth enhancing for all countries as the world portfolio shifts from safe low-yield capital to riskier high-yield capital. This ... [more ▼]

The pure risk sharing mechanism implies that financial liberalization is growth enhancing for all countries as the world portfolio shifts from safe low-yield capital to riskier high-yield capital. This result is typically obtained under the assumption that the volatilities for risky assets prevailing under autarky are not altered after liberalization. We relax this assumption within a simple two-country model of intertemporal portfolio choices. By doing so, we put together the risk sharing effect and a well defined instability effect. We identify the conditions under which liberalization may cause a drop in growth. These conditions combine the typical threshold conditions outlined in the literature, which concern the deep characteristics of the economies, and size conditions on the instability effect induced by liberalization. [less ▲]

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See detailClimate politics: how public persuasion affects the trade-off between environmental and economic performance
Prieur, Fabien; Zou, Benteng UL

in Mathematical Social Sciences (2019)

This paper aims at studying the impact of public persuasion, through information dissemination, on environmental and economic performance. A differential game in which opposite interest groups compete for ... [more ▼]

This paper aims at studying the impact of public persuasion, through information dissemination, on environmental and economic performance. A differential game in which opposite interest groups compete for bringing the majority’s environmental concern closer to their views is developed. The results show a strong asymmetry in the impact of public persuasion. It may bring the median voter economy closer to the social optimum in the long run, thereby reducing environmental and economic distorsions. But this only occurs when the environmental group exhibits a radical ideology and people are initially closer to the industrialists’ views. By contrast, economies where industrial groups are powerful and strongly opposed to environmental protection never benefit from the outcome of the game of persuasion. This may explain why the US have failed to take action on global warming up to now. [less ▲]

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See detailThe War of Rare Earth Elements: A Dynamic Game Approach
Bertinelli, Luisito UL; Poncin, Stéphane Louis Maxim UL; Zou, Benteng UL

E-print/Working paper (2019)

Rare earth elements govern today’s high-tech world and are deemed to be essential for the attainment of sustainable development goals. Since the 1990s, these elements have been predominantly supplied by ... [more ▼]

Rare earth elements govern today’s high-tech world and are deemed to be essential for the attainment of sustainable development goals. Since the 1990s, these elements have been predominantly supplied by one single actor, China. However, due to the increasing global relevance of their availability, other countries are now encouraged to enter the market. The objective of this paper is to analyze the strategic interactions among (potential) suppliers. In particular, we are interested in (1) the optimal timing for a newcomer (e.g. the U.S.) to enter the market, (2) the incumbent’s (i.e. China’s) optimal behavior, and (3) the cost-efficiency of cooperative vs. competitive market relations. By setting up a continuous-time dynamic game model, we show that (1) the newcomer should postpone the production launch until its rare earth reserves coincide with those of the incumbent, (2) the incumbent should strive for a late market entry and therefore keep its monopolistic resource extraction at the lowest possible level, (3) compared to the payoffs under competition, cooperation leads to a Pareto improvement when started at an early stage. The findings of our model are particularly relevant for the rational strategic positioning of the two great powers, America and China. [less ▲]

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See detailRefugee Mobility: Evidence from Phone Data in Turkey
Beine, Michel UL; Bertinelli, Luisito UL; Cömertpay, Rana UL et al

in Ali Salah, Albert; Pentland, Alex; Lepri, Bruno (Eds.) et al Guide to Mobile Data Analytics in Refugee Scenarios (2019)

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See detailTo MigrateWith orWithout Ones’ Children in China - That is the Question
Chen, Yiwen UL; Fromentin, Vincent; Zou, Benteng UL

in Annals of Eceonomcis and statistics (2019)

Where should Chinese internal migrant parents locate their school-aged children: migrate with them or leave them behind? And should they invest in private education of their children? We investigate ... [more ▼]

Where should Chinese internal migrant parents locate their school-aged children: migrate with them or leave them behind? And should they invest in private education of their children? We investigate whether migrant parents can afford to take their children to migrate and thus provide theoretical optimum that maximizes migrant parents’ utility which includes the children’s educational performance. Depending on the educational investment parents make and the relocation cost of children, we provide necessary and sufficient conditions under which migrant parents should take their children to migrate and conditions under which migrant parents should provide their children with private education. [less ▲]

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See detailMean growth and stochastic stability in endogenous growth models
Boucekkine, Raouf; Pintus, Patrick; Zou, Benteng UL

in Economics Letters (2018)

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See detailDoes tax competition increase disparity among jurisdictions?
Han, Yutao; Pieretti, Patrice UL; Zou, Benteng UL

in Review of International Economics (2018)

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See detailThe Impact of Unilateral Commitment on Transboundary Pollution
Bertinelli, Luisito UL; Marchiori, Luca; Tabakovic, Amer et al

in Environmental Modeling & Assessment (2017)

To reach a common target of environmental quality, countries can choose to commit to a stream of pollution abatement right from the beginning of the game or decide upon abatement at each moment of time ... [more ▼]

To reach a common target of environmental quality, countries can choose to commit to a stream of pollution abatement right from the beginning of the game or decide upon abatement at each moment of time. Though most of the previous literature studies homogeneous strategies where no country or all countries commit to a (same) predefined policy, reality goes along a different way: some countries make more efforts than others to reduce pollutant emission. The main novelty of this paper resides in the introduction of this kind of heterogeneous strategic behavior currently observed among large pollution nations. We find that the pollution level can be lower under heterogeneous than under homogeneous strategies. A stringent environmental quality target will induce the committed player to produce an abatement effort that more than compensates the free-riding attitude of the non-committed player. [less ▲]

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