Network Cournot Competition

Cournot competition is a fundamental economic model that represents firms competing in a single market of a homogeneous good. Each firm tries to maximize its utility---a function of the production cost as well as market price of the product---by deciding on the amount of production. In today's dynamic and diverse economy, many firms often compete in more than one market simultaneously, i.e., each market might be shared among a subset of these firms. In this situation, a bipartite graph models the access restriction where firms are on one side, markets are on the other side, and edges demonstrate whether a firm has access to a market or not. We call this game \emph{Network Cournot Competition} (NCC). In this paper, we propose algorithms for finding pure Nash equilibria of NCC games in different situations. First, we carefully design a potential function for NCC, when the price functions for markets are linear functions of the production in that market. However, for nonlinear price functions, this approach is not feasible. We model the problem as a nonlinear complementarity problem in this case, and design a polynomial-time algorithm that finds an equilibrium of the game for strongly convex cost functions and strongly monotone revenue functions. We also explore the class of price functions that ensures strong monotonicity of the revenue function, and show it consists of a broad class of functions. Moreover, we discuss the uniqueness of equilibria in both of these cases which means our algorithms find the unique equilibria of the games. Last but not least, when the cost of production in one market is independent from the cost of production in other markets for all firms, the problem can be separated into several independent classical \emph{Cournot Oligopoly} problems. We give the first combinatorial algorithm for this widely studied problem

Market Efficiency and Coalition Structures

We consider a three-stage game in which symmetric firms decide whether to invest in a cost-reducing technology, then they have the possibility to merge (forming coalitions), and eventually, in the third stage, a Cournot oligopoly game is played by the resulting firms (coalitions). We show that, contrary to the existing literature, the monopoly market structure may fail to form even when the number of initial firms is just three. We then introduce a weighted sharing rule and show that a situation in which all firms acquire the cost-reducing asset cannot be sustained as a Subgame Perfect Equilibrium.

Market Efficiency and Coalition Structures

We consider a three-stage game in which symmetric firms decide whether to invest in a cost-reducing technology, then they have the possibility to merge (forming coalitions), and eventually, in the third stage, a Cournot oligopoly game is played by the resulting firms (coalitions). We show that, contrary to the existing literature, the monopoly market structure may fail to form even when the number of initial firms is just three. We then introduce a weighted sharing rule and show that a situation in which all firms acquire the cost-reducing asset cannot be sustained as a Subgame Perfect Equilibrium

Price Competition, Fluctuations, and Welfare Guarantees

In various markets where sellers compete in price, price oscillations are observed rather than convergence to equilibrium. Such fluctuations have been empirically observed in the retail market for gasoline, in airline pricing and in the online sale of consumer goods. Motivated by this, we study a model of price competition in which an equilibrium rarely exists. We seek to analyze the welfare, despite the nonexistence of an equilibrium, and present welfare guarantees as a function of the market power of the sellers. We first study best response dynamics in markets with sellers that provide a homogeneous good, and show that except for a modest number of initial rounds, the welfare is guaranteed to be high. We consider two variations: in the first the sellers have full information about the valuation of the buyer. Here we show that if there are $n$ items available across all sellers and $n_{\max}$ is the maximum number of items controlled by any given seller, the ratio of the optimal welfare to the achieved welfare will be at most $\log(\frac{n}{n-n_{\max}+1})+1$. As the market power of the largest seller diminishes, the welfare becomes closer to optimal. In the second variation we consider an extended model where sellers have uncertainty about the buyer's valuation. Here we similarly show that the welfare improves as the market power of the largest seller decreases, yet with a worse ratio of $\frac{n}{n-n_{\max}+1}$. The exponential gap in welfare between the two variations quantifies the value of accurately learning the buyer valuation. Finally, we show that extending our results to heterogeneous goods in general is not possible. Even for the simple class of $k$-additive valuations, there exists a setting where the welfare approximates the optimal welfare within any non-zero factor only for $O(1/s)$ fraction of the time, where $s$ is the number of sellers

Hotelling Games on Networks: Efficiency of Equilibria

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/Documents de travail du Centre d'Economie de la Sorbonne 2014.33 - ISSN : 1955-611XWe consider a Hotelling game where a finite number of retailers choose a location, given that their potential customers are distributed on a network. Retailers do not compete on price but only on location, therefore each consumer shops at the closest store. We show that when the number of retailers is large enough, the game admits a pure Nash equilibrium and we construct it. We then compare the equilibrium cost bore by the consumers with the cost that could be achieved if the retailers followed the dictate of a benevolent planner. We perform this comparison in term of the induced price of anarchy, i.e., the ratio of the worst equilibrium cost and the optimal cost, and the induced price of stability, i.e., the ratio of the best equilibrium cost and the optimal cost. We show that, asymptotically in the number of retailers, these ratios are two and one, respectively.On considère un jeu à la Hotelling où un nombre fini de magasins doivent choisir un emplacement sachant que leurs clients potentiels sont situés sur un réseau donné. Les magasins ne sont pas en compétition sur les prix, mais seulement sur les emplacements. Nous montrons de manière constructive que lorsque le nombre de magasins est suffisamment grand ce jeu admet un équilibre de Nash en stratégies pures. Ensuite, nous comparons le coût de déplacement des consommateurs à l'équilibre avec le coût engendré par la situation optimale qui aurait été décidée par un planificateur extérieur. Pour cela, nous calculons le prix de l'anarchie induit, c'est-à-dire le ratio entre le pire coût à l'équilibre et le coût à l'optimum. Nous regardons aussi le prix de la stabilité induit, le ratio entre le meilleur coût à l'équilibre et le coût à l'optimum. Nous montrons que lorsque le nombre de vendeurs devient grand ces ratios tendent respectivement vers 2 et 1

New economic sociology and new institutional economics

Abstract: This paper deals with similarities and differences between new economic sociology (NES) and new institu-tional economics (NIE). We start with brief reports on the basic ideas of NES and NIE. Regarding the latter, we concentrate on NIE in the sense of Oliver Williamson who introduced the term and whose work became the main target of sociologists’ critique. We show that the contrast between the two fields is less sharp than some social scien-tists might assume. We then present a review and assessment of the attack of seven sociologists on Oliver William-son’s ideas. The sociologists are Perrow, Fligstein, Freeland, Granovetter, Bradach & Eccles, and Powell. Their battering ram “social network theory” is briefly described and an attempt made to combine network analysis with new institutional economics as understood by Williamson, i.e., his transaction cost economics. The paper is con-cluded with some thoughts on the convergence of NES and NIE.New institutional economics; transaction cost economics; economic sociology

Online Learning in Multi-unit Auctions

We consider repeated multi-unit auctions with uniform pricing, which are widely used in practice for allocating goods such as carbon licenses. In each round, $K$ identical units of a good are sold to a group of buyers that have valuations with diminishing marginal returns. The buyers submit bids for the units, and then a price $p$ is set per unit so that all the units are sold. We consider two variants of the auction, where the price is set to the $K$-th highest bid and $(K+1)$-st highest bid, respectively. We analyze the properties of this auction in both the offline and online settings. In the offline setting, we consider the problem that one player $i$ is facing: given access to a data set that contains the bids submitted by competitors in past auctions, find a bid vector that maximizes player $i$'s cumulative utility on the data set. We design a polynomial time algorithm for this problem, by showing it is equivalent to finding a maximum-weight path on a carefully constructed directed acyclic graph. In the online setting, the players run learning algorithms to update their bids as they participate in the auction over time. Based on our offline algorithm, we design efficient online learning algorithms for bidding. The algorithms have sublinear regret, under both full information and bandit feedback structures. We complement our online learning algorithms with regret lower bounds. Finally, we analyze the quality of the equilibria in the worst case through the lens of the core solution concept in the game among the bidders. We show that the $(K+1)$-st price format is susceptible to collusion among the bidders; meanwhile, the $K$-th price format does not have this issue