On cross-diffusion systemsfor two populations subject to a common congestion effect

In this paper, we investigate the existence of solution for systems of Fokker-Planck equations coupled through a common nonlinear congestion. Two different kinds of congestion are considered: a porous media congestion or \textit{soft} congestion and the \textit{hard} congestion given by the constraint $\rho_1+\rho_2 \leqslant 1$. We show that these systems can be seen as gradient flows in a Wasserstein product space and then we obtain a constructive method to prove the existence of solutions. Therefore it is natural to apply it for numerical purposes and some numerical simulations are included

On systems of continuity equations with nonlinear diffusion and nonlocal drifts

This paper is devoted to existence and uniqueness results for classes of nonlinear diffusion equations (or systems) which may be viewed as regular perturbations of Wasserstein gradient flows. First, in the case. where the drift is a gradient (in the physical space), we obtain existence by a semi-implicit Jordan-Kinderlehrer-Otto scheme. Then, in the nonpotential case, we derive existence from a regularization procedure and parabolic energy estimates. We also address the uniqueness issue by a displacement convexity argument

Why is the Doha development agenda failing? And what can be done?: A computable general equilibrium-game theoretical approach

"We herein use a world Computable General Equilibrium (CGE) model to simulate 143 potential trade reforms and seek solutions to the issues hampering progress in the Doha Development Agenda (DDA). Inside the domain defined by all these possible outcomes, we apply the axiomatic theory of bargaining and select the Nash solution of cooperative games. The solutions vary according to the objective functions adopted by the trade negotiators. When real income is the objective and services are excluded, or when optimizing terms of trade is the objective, the Nash solution is the status quo. Trade liberalization is feasible only when the negotiators focus on national exports or Gross Domestic Product (GDP). Our assessment of some possible solutions reveals that excluding members having a GDP below a certain threshold improves the bargaining process, regardless of the governments' objective. Formation of coalition, such as the G20, constitutes an option for its members to block outcomes imposed by rich members. We also find that side payments may be a solution, but represent a very high share of the global income gain." from authors' abstractTrade negotiations, Computable general equilibrium (CGE) modeling, Nash solution, Side payments, Cooperative games, Globalization, Markets, Doha Development Agenda,

The potential cost of a failed Doha Round:

"In times of economic turmoil, countries might decide to increase current tariff rates to protect domestic industries or raise revenues in order to finance domestic programs. Using the highest applied or bound rate imposed by countries from 1995 to 2008 as an indicator, this study presents several scenarios regarding the economic costs of a failed Doha Round and a subsequent rush into protectionism. For example, in a scenario where the applied tariffs of major economies would go all the way up to currently bound tariff rates, world trade would decrease by 7.7 percent. In a more modest scenario where countries would raise tariffs to maximum rates applied during the past 13 years, world trade would decrease by 3.2 percent. These increases in duties would reduce world welfare by US$353 billion under the first scenario, and by US$134 billion under the more modest scenario. While such an increase in duties would particularly impact agricultural exports (–6.9 percent), especially in developing countries (–11.5 percent), exports of industrial goods could also face a substantial reduction: 2 percent in developed countries and 4.8 percent in developing countries. This study concludes there would be a potential loss of US$1,064 billion in world trade if world leaders were to fail to conclude the Doha Development Round of trade negotiations in the next few weeks and if countries were to implement subsequently protectionist policies, as occurred after the end of the Uruguay Round. The failure of the negotiations would prevent a US$336 billion increase in world trade that would have come from a reduction in tariffs and domestic support, while a worldwide resort to protectionism would contract world trade by US$728 billion." from textAgricultural policies, WTO Doha round, International trade, exports, tariffs, Protectionism,