A fundamental question about a market is under what conditions, and then how rapidly, does price signaling cause price equilibration. Qualitatively, this ought to depend on how well-connected the market is. We address this question quantitatively for a certain class of Arrow-Debreu markets with continuous-time proportional t ^ a tonnement dynamics. We show that the algebraic connectivity of the market determines the effectiveness of price signaling equilibration. This also lets us study the rate of external noise that a market can tolerate and still maintain near-equilibrium prices.
In a different vein, researchers have been interested in other market structure effects: as these works do not directly impact ours, we do not attempt a survey, but only provide a few pointers: @cite_1 looks at markets in which buyer-seller pairs can trade only along established links, at the incentives to form such links, and at the efficiency of trade in such networks; @cite_36 considers Arrow-Debreu markets in which, again, direct trade can occur only along established links, thus enabling the same commodity to have different prices in different places; and @cite_43 looks at markets in which buyer-seller pairs can only interact through intermediary traders, and studies the power of these traders and how equilibrium prices are affected by the connectivity structure.
@cite_36 @cite_43 @cite_1
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We study the efficiency of allocations in large markets with a network structure where every seller owns an edge in a graph and every buyer desires a path connecting some nodes. While it is known that stable allocations in such settings can be very inefficient, the exact properties of equilibria in markets with multiple sellers are not fully understood even in single-source single-sink networks. In this work, we show that for a large class of natural buyer demand functions, we are guaranteed the existence of an equilibrium with several desirable properties. The crucial insight that we gain into the equilibrium structure allows us to obtain tight bounds on efficiency in terms of the various parameters governing the market, especially the number of monopolies M. All of our efficiency results extend to markets without the network structure. While it is known that monopolies can cause large inefficiencies in general, our main results for single-source single-sink networks indicate that for several natural demand functions the efficiency only drops linearly with M. For example, for concave demand we prove that the efficiency loss is at most a factor 1+M 2 from the optimum, for demand with monotone hazard rate it is at most 1+M, and for polynomial demand the efficiency decreases logarithmically with M. In contrast to previous work that showed that monopolies may adversely affect welfare, our main contribution is showing that monopolies may not be as evil' as they are made out to be; the loss in efficiency is bounded in many natural markets. Finally, we consider more general, multiple-source networks and show that in the absence of monopolies, mild assumptions on the network topology guarantee an equilibrium that maximizes social welfare. In a wide range of markets, individual buyers and sellers trade through intermediaries, who determine prices via strategic considerations. Typically, not all buyers and sellers have access to the same intermediaries, and they trade at correspondingly different prices that reflect their relative amounts of power in the market. We model this phenomenon using a game in which buyers, sellers, and traders engage in trade on a graph that represents the access each buyer and seller has to the traders. We show that the resulting game always has a subgame perfect Nash equilibrium, and that all equilibria lead to an efficient allocation of goods. Finally, we analyze trader profits in terms of the graph structure -- roughly, a trader can command a positive profit if and only if it has an "essential" connection in the network, thus providing a graph-theoretic basis for quantifying the amount of competition among traders. This paper introduces a new model of exchange: networks, rather than markets, of buyers and sellers. It begins with the empirically motivated premise that a buyer and seller must have a relationship, a "link," to exchange goods. Networks--buyers, sellers, and the pattern of links connecting them--are common exchange environments. This paper develops a methodology to study network structures and explains why agents may form networks. In a model that captures characteristics of a variety of industries, the paper shows that buyers and sellers, acting strategically in their own self-interests, can form the network structures that maximize overall welfare. We study the efficiency implications of competition among profit-maximizing service providers in communication networks. Service providers set prices for transmission of flows through their (sub)network. The central question is whether the presence of prices will help or hinder network performance. We investigate this question by considering the difference between users' willingness to pay and delay costs as the efficiency metric. Previous work has demonstrated that in networks consisting of parallel links, efficiency losses from competition are bounded. Nevertheless, parallel-link networks are special, and in most networks, traffic has to simultaneously traverse links (or subnetworks) operated by independent service providers. The simplest network topology allowing this feature is the parallel-serial structure, which we study in this paper. In contrast to existing results, we show that in the presence of serial links, the efficiency loss relative to the social optimum can be arbitrarily large. The reason for this degradation of performance is the double marginalization problem, whereby each serial provider charges high prices not taking into account the effect of this strategy on the profits of other providers along the same path. Nevertheless, when there are no delay costs without transmission (i.e., latencies at zero are equal to zero), irrespective of the number of serial and parallel providers, the efficiency of strong oligopoly equilibria can be bounded by 1 2, where strong oligopoly equilibria are equilibria in which each provider plays a strict best response and all of the traffic is transmitted. However, even with strong oligopoly equilibria, inefficiency can be arbitrarily large when the assumption of no delay costs without transmission is relaxed.