# On the Cournot-Nash-Walras equilibria, the social equilibria, their stability and computation (Michal Outrata, University of Geneva)

25.02.2019 17:00

In 1997 the Kyoto protocol was concluded in Japan, proposing a new global way of addressing the greenhouse gas emissions problem. One of the major mechanism proposed was the greenhouse gas allowances system, which imposed on each of the signatories an upper bound for the production of these gases. On the other hand, if the upper bound was not reached or if some of the countries decided to do so, some of the allowances for the greenhouse gas production can be sold to other signatories of the Kyoto protocol.

This talk will be focused on a mathematical model of the "Kyoto protocol-like" situations where a multilevel market is established. That is, the participants of the market (in game theory often called agents) are producing goods, which require a certain rare resource. The rare resource is than traded on a separate market, crating a two-level market with the produced good on one hand and with the rare resources on the other. A natural question is how to introduce an equilibrium to this two-level system and what conditions should it meet.

The emphasis will be on easy to understand introduction of the so-called Cournot-Nash-Walras equilibrium - a concept proposed as an answer to this question, i.e., an equilibrium for hierarchical non-cooperative games. The mathematical formulation uses the terminology of non-smooth multi-valued functions in the framework of optimization problems. The existence, uniqueness and stability of these Cournot-Nash-Walras equilibria will be considered as well as the numerical side of the problem.

### Lieu

Room 17, Séminaire des doctorants

### Organisé par

Section de mathématiques### Intervenants

Michal Outrata, University of Genevaentrée libre

### Plus d'infos

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