Report on Master’s Thesis “A Model of Oligopoly Based on Network Approach”
by Tsyganov Kirill Vasilyevich


The thesis examines a problem of competition of firms in a single-product market by means of game-theoretic modeling. The firms compete in quantities, and firm’s costs depend on the number of collaborators the firm has. The structure of collaborations is described by a network. The study covers two different concepts: non-cooperative behavior of firms and cooperation.

The first concept is related to the concept of Nash equilibrium. Here the author finds all equilibrium collaborators-outputs profiles stating that any “pairwise network” is always an equilibrium network structure. He also compares different networks with respect to firms’ profits and provides an analysis of how a removal/formation of a link affects the profits. Similar analysis is then applied to a special type of networks—regular networks.

In case of cooperation, the total profit of firms is allocated among them in accordance with two cooperative solutions: the Shapley value and the CIS-value. It is proved that if the characteristic function is determined by the definition of von Neumann and Morgenstern, the Shapley value and the CIS-value coincide. Moreover for regular networks, firms will not benefit from cooperation. The thesis also contains expressions for the values of the characteristic function determined by two other definitions.

As a natural extension of the model, an additional type of firm’s costs—the offering costs—is considered where the author characterizes all equilibrium collaborators-outputs profiles and performs an analysis of how a removal/formation of a link affects firms’ profits in this case. In contrast to the model without offering cost, here a “pairwise network” will be an equilibrium network structure only if a condition on firms’ collaborators is satisfied. However no analysis is performed for the cooperative case of the extended model.

I consider the Master’s Thesis “A Model of Oligopoly Based on Network Approach” by Tsyganov Kirill Vasilyevich to be prepared according to the instructions for the structure, the content, and the format of graduation theses. The model, propositions and their proofs are mathematically precisely formulated. The results of the service for plagiarism detection show few matches, however the matches are insignificant: they are either standard terms, notations and phrases, or matches resulted from incorrect processing of mathematical expressions. The related literature is properly cited. Thus I can conclude that there was no plagiarism detected in the thesis. I would grade the thesis as “excellent”.


Artem Sedakov,
Research advisor,
PhD, Associate Professor