Optimal coalition splitting with heterogenous strategies

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 ▲]

Why and when coalitions split? An alternative analytical approach with an application to environmental agreements

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 ▲]

Uncertainty-driven symmetry-breaking and stochastic stability in a generic differential game of lobbying

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 ▲]

Uncertainty-driven symmetry-breaking and stochastic stability in a generic differential game of lobbying

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 ▲]

A Pedagogical Note on Risk Sharing Versus Instability in International Financial Integration: When Obstfeld Meets Stiglitz

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 ▲]

Institutional dynamics under revenue volatility and revenue-dependent lobbying power: A stochastic differential game approach

E-print/Working paper (2015)

We propose an analysis of institutional dynamics under uncertainty by the means of a stochastic differential lobbying game with two main ingredients. The rst one is uncertainty inherent in the ... [more ▼]

We propose an analysis of institutional dynamics under uncertainty by the means of a stochastic differential lobbying game with two main ingredients. The rst one is uncertainty inherent in the institutional process itself. The second one has to do with the crucial role of resource windfalls in economic and political outcomes, shaping lobbying power and adding a second source of uncertainty. First, we focus on uncertainty surrounding the institutional process only and show that its main consequence is the existence of multiple equilibria with very distinct features: symmetric equilibria which lead the economy to reach almost surely a stable pointwise institutional steady state in the long run even in the absence of the retaliation motive put forward by the deterministic lobbying literature, and asymmetric equilibria which only show up under uncertainty and do no allow for stochastic convergence to a steady state. Second, when accounting for the two sources of uncertainty together with resource revenue-dependent lobbying power, we show that revenue volatility tends to stabilize institutional dynamics compared to the deterministic counterpart. [less ▲]

Stochastic stability of endogenous growth: The AK case

E-print/Working paper (2014)

This note studies the stochastic stability of the standard AK growth model un- der uncertain output technology. Capital accumulation follows a stochastic lin- ear homogenous differential equation. It’s ... [more ▼]

This note studies the stochastic stability of the standard AK growth model un- der uncertain output technology. Capital accumulation follows a stochastic lin- ear homogenous differential equation. It’s shown that exponential balanced paths, which characterize optimal trajectories in the absence of uncertainty, are not robust to uncertainty. Precisely, it’s demonstrated that the economy almost surely col- lapses at exponential speed even though productivity is initially arbitrarily high. [less ▲]