Solving deterministic and stochastic equilibrium problems via augmented Walrasian

TL;DR

This paper introduces an augmented bifunction method to solve deterministic and stochastic Walras equilibrium models, providing a convergent numerical procedure applicable to dynamic settings with intertemporal goods transfer.

Contribution

It presents a novel augmentation approach for bifunctions to find equilibrium points, with proven convergence, applicable to both static and dynamic stochastic models.

Findings

Convergence of the method is established via lopsided convergence.

The approach effectively handles dynamic models with intertemporal goods transfer.

The method applies to both deterministic and stochastic equilibrium problems.

Abstract

We described a method to solve deterministic and stochastic Walras equilibrium models based on associating with the given problem a bifunction whose maxinf-points turn out to be equilibrium points. The numerical procedure relies on an augmentation of this bifunction. Convergence of the proposed procedure is proved by relying on the relevant lopsided convergence. In the dynamic versions of our models, deterministic and stochastic, we are mostly concerned with models that equip the agents with a mechanism to transfer goods from one time period to the next, possibly simply savings, but also allows for the transformation of goods via production