On the Lagrangian branched transport model and the equivalence with its Eulerian formulation

First we present two classical models of Branched Transport: the Lagrangian model introduced by Bernot, Caselles, Morel, Maddalena, Solimini, and the Eulerian model introduced by Xia. An emphasis is put on the Lagrangian model, for which we give a complete proof of existence of minimizers in a --hopefully-- simplified manner. We also treat in detail some $\sigma$-finiteness and rectifiability issues to yield rigorously the energy formula connecting the irrigation cost I$\alpha$ to the Gilbert Energy E$\alpha$. Our main purpose is to use this energy formula and exploit a Smirnov decomposition of vector flows, which was proved via the Dacorogna-Moser approach by Santambrogio, to establish the equivalence between the Lagrangian and Eulerian models

Stochastic differential utility as the continuous-time limit of recursive utility

We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus (1978), converges to stochastic differential utility, as introduced by Dufffie and Epstein (1992), in the continuous-time limit of vanishing grid size

A Unified View of Large-scale Zero-sum Equilibrium Computation

The task of computing approximate Nash equilibria in large zero-sum extensive-form games has received a tremendous amount of attention due mainly to the Annual Computer Poker Competition. Immediately after its inception, two competing and seemingly different approaches emerged---one an application of no-regret online learning, the other a sophisticated gradient method applied to a convex-concave saddle-point formulation. Since then, both approaches have grown in relative isolation with advancements on one side not effecting the other. In this paper, we rectify this by dissecting and, in a sense, unify the two views.Comment: AAAI Workshop on Computer Poker and Imperfect Informatio

Cournot-Nash Competition in a General Equilibrium Model of International Trade.

We use the two-factor, two-sector, two-country model of Melvin and Warne (1973) and Markusen (1981), in which the production of one good is monopolized in each country, in order to investigate the role of the price normalization. We illustrate several puzzling effects that occur if the price normalization is changed. However, we show that Markusen’s result on the direction of the trade flow between two proportional countries with constant returns to scale is robust with respect to the choice of the normalization rule. To overcome the price normalization problem in international trade we suggest to use the concept of real wealth maximization.international trade with imperfect competition; price normalization; real wealth maximization