Elsevier

Games and Economic Behavior

Volume 115, May 2019, Pages 247-264
Games and Economic Behavior

Price dispersion in stationary networked markets

https://doi.org/10.1016/j.geb.2019.03.005Get rights and content

Abstract

Different sellers often sell the same good at different prices. Using a strategic bargaining model, I characterize how the equilibrium prices of a good depend on the interaction between its sellers' costs, its buyers' values, and a network capturing various frictions associated with trading it. In contrast to the standard random-matching model of bargaining in stationary markets, I allow agents to strategically choose whom to make offers to, which qualitatively changes how the network shapes prices. As in the random-matching model, the market decomposes into different submarkets, and—in the limit as bargaining frictions vanish—the law of one price holds within but not across them. But strategic choice of partners changes both how the market decomposes into different submarkets and the determinants of each submarket's price.

Section snippets

The market M

There is a finite set B of types of buyers and a finite set S of types of sellers of a homogenous good. The type i of a buyer is determined by her value vi0 for the good and the set of sellers that she can trade with. Similarly, the type j of a seller is determined by her cost cj0 of producing the good and the set of buyers that she can trade with. I let N denote the set of all types of agents—that is, the union of the set B and the set S—and I let n denote the cardinality of the set N.10

Equilibrium: arbitrary bargaining frictions

In this section, I investigate the subgame-perfect equilibrium of the game Γ(M,δ) for an arbitrary discount factor δ.15 After describing the sense in which this game admits an essentially unique equilibrium, I investigate what determines the equilibrium terms of trade in

Equilibrium: arbitrarily-small bargaining frictions

In this section, I characterize the equilibrium prices in the game Γ(M,δ) in the limit as the discount factor δ goes to 1. The only trading frictions that remain in this limit are those generated by the underlying trading network g. Hence, this characterization isolates the effect of the trading network g on the equilibrium terms of trade. After showing that the limit in question is well defined, I leverage the results of the previous section to (i) provide a necessary and sufficient joint

Related literature

This article contributes to the emerging literature on strategic bargaining in networked markets.29 An important part of this literature studies the conditions under which decentralized bargaining in markets without inflows of traders can be efficient and/or feature the law of one price.30

Conclusion

The widespread phenomenon of price dispersion is the result of different frictions that prevent the traders who buy at high prices from reaching out to the traders that sell at low prices. In this paper, I take these frictions as given—in the form of a buyer–seller network that determines which agents can trade with each other—and I show how they shape the prices that emerge when buyers and sellers engage in decentralized strategic bargaining in a stationary market.

The main distinction between

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  • Cited by (6)

    • Bargaining in small dynamic markets

      2023, Journal of Economic Theory
      Citation Excerpt :

      In these papers, either there is no arrival, or traders are immediately replaced by copies of themselves upon transaction; furthermore, traders are heterogeneous because of their different valuations and/or different positions in the network. Both Talamàs and Elliott and Nava show that the network incompleteness and trader heterogeneity generate inefficiency, price dispersion, and delay. Here, we instead study an endogenously evolving unstructured market (i.e., with a complete network) with homogeneous traders and ask how the endogenous arrival determines—and is determined by—the bargaining outcome.

    1

    The guidance of Benjamin Golub throughout the process of conducting and presenting this research has been essential. I thank Eduardo Azevedo, Matthew Elliott, Edward Glaeser, Sanjeev Goyal, Jerry Green, Mihai Manea, Eric Maskin, Pau Milán and Rakesh Vohra, as well as several audiences and anonymous referees, for useful feedback. This work was supported by the Warren Center for Network & Data Sciences, and the Rockefeller Foundation (#2017PRE301). All errors are my own.

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