Price Competition in Online Combinatorial Markets

We consider a single buyer with a combinatorial preference that would like to purchase related products and services from different vendors, where each vendor supplies exactly one product. We study the general case where subsets of products can be substitutes as well as complementary and analyze the game that is induced on the vendors, where a vendor's strategy is the price that he asks for his product. This model generalizes both Bertrand competition (where vendors are perfect substitutes) and Nash bargaining (where they are perfect complements), and captures a wide variety of scenarios that can appear in complex crowd sourcing or in automatic pricing of related products. We study the equilibria of such games and show that a pure efficient equilibrium always exists. In the case of submodular buyer preferences we fully characterize the set of pure Nash equilibria, essentially showing uniqueness. For the even more restricted "substitutes" buyer preferences we also prove uniqueness over {\em mixed} equilibria. Finally we begin the exploration of natural generalizations of our setting such as when services have costs, when there are multiple buyers or uncertainty about the the buyer's valuation, and when a single vendor supplies multiple products.Comment: accept to WWW'14 (23rd International World Wide Web Conference

The Pricing War Continues: On Competitive Multi-Item Pricing

We study a game with \emph{strategic} vendors who own multiple items and a single buyer with a submodular valuation function. The goal of the vendors is to maximize their revenue via pricing of the items, given that the buyer will buy the set of items that maximizes his net payoff. We show this game may not always have a pure Nash equilibrium, in contrast to previous results for the special case where each vendor owns a single item. We do so by relating our game to an intermediate, discrete game in which the vendors only choose the available items, and their prices are set exogenously afterwards. We further make use of the intermediate game to provide tight bounds on the price of anarchy for the subset games that have pure Nash equilibria; we find that the optimal PoA reached in the previous special cases does not hold, but only a logarithmic one. Finally, we show that for a special case of submodular functions, efficient pure Nash equilibria always exist

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

Efficiency and complexity of price competition among single-product vendors

Motivated by recent progress on pricing in the AI literature, we study marketplaces that contain multiple vendors offering identical or similar products and unit-demand buyers with different valuations on these vendors. The objective of each vendor is to set the price of its product to a fixed value so that its profit is maximized. The profit depends on the vendor's price itself and the total volume of buyers that find the particular price more attractive than the price of the vendor's competitors. We model the behavior of buyers and vendors as a two-stage full-information game and study a series of questions related to the existence, efficiency (price of anarchy) and computational complexity of equilibria in this game. To overcome situations where equilibria do not exist or exist but are highly inefficient, we consider the scenario where some of the vendors are subsidized in order to keep prices low and buyers highly satisfied

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