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 ▲]

Carbon capture and storage and transboundary pollution: A differential game approach

in European Journal of Operational Research (2014)

We study the strategic behavior of two countries facing transboundary CO2 pollution under a differential game setting. In our model, the reduction of CO2 concentration occurs through the carbon capture ... [more ▼]

We study the strategic behavior of two countries facing transboundary CO2 pollution under a differential game setting. In our model, the reduction of CO2 concentration occurs through the carbon capture and storage process, rather than through the adoption of cleaner technologies. Furthermore, we first provide the explicit short-run dynamics for this dynamic game with symmetric open-loop and a special Markovian Nash strategy. Then, we compare these strategies at the games’ steady states and along some balanced growth paths. Our results show that if the initial level of CO2 is relatively high, state dependent emissions reductions can lead to higher overall environmental quality, hence, feedback strategy leads to less social waste. [less ▲]

On the dynamics of capital accumulation across space

in European Journal of Operational Research (2008), 186(2), 451-465

We solve an optimal growth model in continuous space, continuous and bounded time. The optimizer chooses the optimal trajectories of capital and consumption across space and time by maximizing an ... [more ▼]

We solve an optimal growth model in continuous space, continuous and bounded time. The optimizer chooses the optimal trajectories of capital and consumption across space and time by maximizing an objective function with both space and time discounting. We extract the corresponding Pontryagin conditions and prove their sufficiency. We end up with a system of two parabolic differential equations with the corresponding boundary conditions. We propose a simple numerical set-up to simulate PDE systems which we employ to study the roles of initial capital and technology distributions over space in various scenarios. [less ▲]