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Optimal coalition splitting with heterogenous strategies ; ; et al E-print/Working paper (2022) We consider a group of players initially members of a coalition managing cooperatively a public bad, in this case, the stock of pollution. Countries are technologically heterogeneous but the pollution ... [more ▼] We consider a group of players initially members of a coalition managing cooperatively a public bad, in this case, the stock of pollution. Countries are technologically heterogeneous but the pollution damage is uniform. We essentially attempt to characterize the conditions under which a country may eventually split and when it splits within an infinite horizon multi-stage differential game. In contrast to the existing literature, we do not assume that after splitting, the splitting player and the remaining coalition will adopt Markovian strategies. Instead, we assume that the latter will remain committed to the collective control of pollution and play open-loop, while the splitting player plays Markovian. Within a full linear-quadratic model, we characterize the optimal strategies. We later compare with the outcomes of the case where the splitting player and the remaining coalition play both Markovian. We highlight several interesting results in terms of the implications for long- term pollution levels and the duration of coalitions with heterogeneous strategies. [less ▲] Detailed reference viewed: 13 (0 UL)A dynamic programming approach to optimal pollution control under uncertain irreversibility: The Poisson case ; ; Zou, Benteng E-print/Working paper (2022) We solve a bimodal optimal control problem with a non-concavity and uncertainty through a Poisson process underlying the transition from a mode to another. We use a dynamic programming approach and are ... [more ▼] We solve a bimodal optimal control problem with a non-concavity and uncertainty through a Poisson process underlying the transition from a mode to another. We use a dynamic programming approach and are able to uncover the global optimal dynamics (including optimal non-monotonic paths) under a few linear-quadratic assumption, which do not get rid of the non-concavity of the problem. This is in contrast to the related literature on pollution control under irreversibility which usually explores local dynamics along monotonic solution paths to first order Pontryagin conditions. [less ▲] Detailed reference viewed: 16 (2 UL)Optimal lockdown and vaccination policies to contain the spread of a mutating infectious disease ; ; Zou, Benteng 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 ▲] Detailed reference viewed: 34 (8 UL)Why and when coalitions split? An alternative analytical approach with an application to environmental agreements ; ; 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 ▲] Detailed reference viewed: 99 (10 UL)The Irreversible Pollution Game ; ; Zou, Benteng 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 ▲] Detailed reference viewed: 97 (14 UL)Uncertainty-driven symmetry-breaking and stochastic stability in a generic differential game of lobbying ; ; 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 ▲] Detailed reference viewed: 77 (2 UL)Uncertainty-driven symmetry-breaking and stochastic stability in a generic differential game of lobbying ; ; 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 ▲] Detailed reference viewed: 157 (18 UL) |
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