Networks of Complements

We consider a network of sellers, each selling a single product, where the graph structure represents pair-wise complementarities between products. We study how the network structure affects revenue and social welfare of equilibria of the pricing game between the sellers. We prove positive and negative results, both of "Price of Anarchy" and of "Price of Stability" type, for special families of graphs (paths, cycles) as well as more general ones (trees, graphs). We describe best-reply dynamics that converge to non-trivial equilibrium in several families of graphs, and we use these dynamics to prove the existence of approximately-efficient equilibria.Comment: An extended abstract will appear in ICALP 201

A demonstration of an application of the Bertrand Network: Guessing the distribution of buyers within the market

Bertrand and the Cournot model are one of the most used model for modeling competition between companies. This paper presents a work-in-progress that studies the application of the recently developed Bertrand Network model by using it in a reverse manner: first it is considered that firms are competing in equilibrium, then, after analyzing how companies are choosing prices, it is calculated which distribution of buyers would lead to that equilibrium. An unreal example is presented to help to understand the model. Furthermore, a formula is suggested to expand the networked model to allow a mix of duopolies and oligopolies

Evaluating market pricing competition with the Bertrand Network

Mestrado de dupla diplomação com a UTFPR - Universidade Tecnológica Federal do ParanáRecently in the literature, there have been many attempts to expand classic models of market competition analysis. Considering firms are competing globally against many different sellers over different markets, recent works proposed a model where it is possible to represent competition among companies where they compete against each other directly and indirectly, using a hypergraph to represent the competition structure. This document presents an attempt to demonstrate how the young and maturing networked price competition model, which allows finding the best price for the companies from the competition structure and market sizes, can be used in any case of study. This work continues the recent demand to adapt the famous Bertrand competition model, where sellers ask for prices. Since there are no recent works which use the recent model, it has been presented how to use it in such a way that is possible to guess the competition structure and the distribution of the buyers by only by observing how companies are pricing. To better understand the applications of the existing method, the first real case of study which has used the Bertrand Network model is presented: a competition among 6 flight companies, where prices were collected by using the Google Flight tracking service, concluding that the proofs and claims developed in this work are useful to enhance market analysis