Efficiency Loss in a Network Resource Allocation Game
Mathematics of Operations Research
Competition and Efficiency in Congested Markets
Mathematics of Operations Research
Bertrand Competition in Networks
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
MINT: a Market for INternet Transit
CoNEXT '08 Proceedings of the 2008 ACM CoNEXT Conference
Efficiency and stability of Nash equilibria in resource allocation games
GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
Pricing with markups under horizontal and vertical competition
Proceedings of the Behavioral and Quantitative Game Theory: Conference on Future Directions
On the efficiency of markets with two-sided proportional allocation mechanisms
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
A scalable network resource allocation mechanism with bounded efficiency loss
IEEE Journal on Selected Areas in Communications
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We study the price of anarchy of a trading mechanism for divisible goods in markets containing both producers and consumers (i.e. in two-sided markets). Each producer is asked to submit a linear pricing function (or, equivalently, a linear supply function) that specifies a per-unit price p(d) as a function of the demand d that they face. Consumers then buy their preferred resource amounts at these prices. We prove that having three producers for every resource guarantees the price of anarchy is bounded. In general, the price of anarchy depends heavily on the level of horizontal and vertical competition in the market, on the producers' cost functions, and on the elasticity of consumer demand. We show how these characteristics affect economic efficiency and in particular, we find that the price of anarchy equals 2/3 in a perfectly competitive market, 3/4 in a monopsony, and 2ε(2−ε)/(4−ε) in a monopoly where consumer valuations have a fixed elasticity of ε. These results hold in markets with multiple goods, particularly in bandwidth markets over arbitrary graphs. Pricing mechanisms are used in several real-world applications; our results suggest how to add formal efficiency guarantees to these mechanisms. On the theory side, we show that near-optimal efficiency can be achieved within two-sided markets by simple mechanisms in the spirit of Bertrand and Cournot. This result extends to the two-sided setting the analyses for fixed-supply and fixed-demand markets of Johari and Tsitsiklis (2005), Acemoglu and Ozdaglar (2007), and Correa et al. (2010).