Coalition Formation and Price of Anarchy in Cournot Oligopolies

Immorlica, Nicole; Markakis, Evangelos; Piliouras, Georgios

doi:10.1007/978-3-642-17572-5_22

Cited by 16 publications

(11 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another line of research offers stronger performance guarantees using specific learning algorithms that employ equilibrium selection (e.g., in distributed load balancing [Kleinberg et al 2011a], in general congestion games [Kleinberg et al 2009], in evolutionary linguistic systems [Fox et al 2012]). The importance of such results that go beyond the analysis of performance of Nash equilibria has also been stressed in recent work [Kleinberg et al 2011b;Piliouras and Shamma 2014;Immorlica et al 2010;Nadav and Piliouras 2010] where, for example, it has been shown that even in simple and well-studied games, the performance of natural learning dynamics can be arbitrarily better than the social welfare of even the best Nash equilibria. A mini-review of this literature can be found in Ligett and Piliouras [2011].…”

Section: Related Workmentioning

confidence: 99%

Near-Optimality in Covering Games by Exposing Global Information

Balcan

Krehbiel

Piliouras

et al. 2014

ACM Trans. Econ. Comput.

Self Cite

View full text Add to dashboard Cite

Mechanism design for distributed systems is fundamentally concerned with aligning individual incentives with social welfare to avoid socially inefficient outcomes that can arise from agents acting autonomously. One simple and natural approach is to centrally broadcast nonbinding advice intended to guide the system to a socially near-optimal state while still harnessing the incentives of individual agents. The analytical challenge is proving fast convergence to near optimal states, and in this article we give the first results that carefully constructed advice vectors yield stronger guarantees.We apply this approach to a broad family of potential games modeling vertex cover and set cover optimization problems in a distributed setting. This class of problems is interesting because finding exact solutions to their optimization problems is NP-hard yet highly inefficient equilibria exist, so a solution in which agents simply locally optimize is not satisfactory. We show that with an arbitrary advice vector, a set cover game quickly converges to an equilibrium with cost of the same order as the square of the social cost of the advice vector. More interestingly, we show how to efficiently construct an advice vector with a particular structure with cost O(log n) times the optimal social cost, and we prove that the system quickly converges to an equilibrium with social cost of this same order.

show abstract

Section: Related Workmentioning

confidence: 99%

Near-Optimality in Covering Games by Exposing Global Information

Balcan

Krehbiel

Piliouras

et al. 2014

ACM Trans. Econ. Comput.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In a previous work [19], the author considered Cournot Competition on a network of firms and markets; however, assumed that inverse demand functions are linear and all the cost functions are quadratic function of the total production by the firm in all markets which is quite restrictive. Most of the results in other related works in Cournot Competition and Bertrand Network require linearity of the cost functions [3,20]. A brief summary of our results presented in three sections is given below.…”

Section: Results and Techniquesmentioning

confidence: 80%

Network Cournot Competition

Abolhassani

Bateni

Hajiaghayi

et al. 2014

Web and Internet Economics

View full text Add to dashboard Cite

Abstract. Cournot competition, introduced in 1838 by Antoine Augustin Cournot, is a fundamental economic model that represents firms competing in a single market of a homogeneous good. Each firm tries to maximize its utility-naturally a function of the production cost as well as market price of the product-by deciding on the amount of production. This problem has been studied comprehensively in Economics and Game Theory; however, 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 Network Cournot Competition (NCC). Computation of equilibrium, taking into account a network of markets and firms and the different forms of cost and price functions, makes challenging and interesting new problems. 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. This result lets us leverage optimization techniques for a single function rather than multiple utility functions of many firms. However, for nonlinear price functions, this approach is not feasible-there is indeed no single potential function that captures the utilities of all firms for the case of nonlinear price functions. 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 Cournot Oligopoly problems in which the firms compete over a single market. We give the first combinatorial algorithm for this widely studied problem. Interestingly, our algorithm is much simpler and faster than previous optimization-based approaches.

show abstract

“…The earliest and most well-known result in the area is the one on stable marriages by Gale and Shapley (Gale and Shapley 1962). Further works include (Aumann and Dreze 1974;Apt et al 2014;Banerjee, Konishi, and Sonmez 2001;Bogomolnaia and Jackson 2002;Chalkiadakis et al 2009;Feldman, Lewin-Eytan, and Naor 2012;Greenberg and Weber 1993;Hajdukova 2006;Hart and Kurz 1983;Immorlica, Markakis, and Piliouras 2010;Yi 1997).…”

Section: Related Workmentioning

confidence: 99%

You Get What You Share: Incentives for a Sharing Economy

Gollapudi

Kollias

Panigrahi

2019

AAAI

View full text Add to dashboard Cite

In recent years, a range of online applications have facilitated resource sharing among users, resulting in a significant increase in resource utilization. In all such applications, sharing one’s resources or skills with other agents increases social welfare. In general, each agent will look for other agents whose available resources complement hers, thereby forming natural sharing groups. In this paper, we study settings where a large population self-organizes into sharing groups. In many cases, centralized optimization approaches for creating an optimal partition of the user population are infeasible because either the central authority does not have the necessary information to compute an optimal partition, or it does not have the power to enforce a partition. Instead, the central authority puts in place an incentive structure in the form of a utility sharing method, before letting the participants form the sharing groups by themselves. We first analyze a simple equal-sharing method, which is the one most typically encountered in practice and show that it can lead to highly inefficient equilibria. We then propose a Shapley-sharing method and show that it significantly improves overall social welfare.

show abstract

Coalition Formation and Price of Anarchy in Cournot Oligopolies

Cited by 16 publications

References 21 publications

Near-Optimality in Covering Games by Exposing Global Information

Near-Optimality in Covering Games by Exposing Global Information

Network Cournot Competition

You Get What You Share: Incentives for a Sharing Economy

Contact Info

Product

Resources

About