Price Competition in Networked Markets: How Do Monopolies Impact Social Welfare?

Abstract

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 singlesink 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.

Toll caps in privatized road networks

“…The model of Xiao et al [48] studies competition in both tolls and capacities and finds that tolls are higher, but capacities are lower than socially desired. Other recent models of Bertrand competition in a network setting that use different ways of modelling congestion effects are Anshelevich and Sekar [3], Chawla and Niu [10], Chawla and Roughgarden [11], Papadimitriou and Valiant [37] and Caragiannis et al [8].…”

The Price of Fragmentation in Mobility-on-Demand Services

“…Finally we note that there is an extensive literature on competition between platforms [16,17,23], including in network settings [2,4,7] and power markets [9]. These are of less relevance to our work as we focus on the operational costs of demand fragmentation.…”

“…In order to build more complex synthetic examples that exhibit both regimes, we consider a four node network depicted in Fig. 3, comprising of 4 nodes, with inter-node average travel-times as indicated 4 . By varying the monopolist demands between the nodes, we use the network to verify the conditions for the two regimes given in Theorem 4.5.…”

Temporally Networked Cournot Platform Markets

“…Networked competition appears in various forms, including networked Bertrand competition, e.g., [18,19,20,21], networked Cournot competition, e.g., [8,9,22], and various other non-cooperative bargaining games where agents can trade via bilateral contracts and a network determines the set of feasible trades, e.g., [23,24,25,26,27].…”