# zbMATH — the first resource for mathematics

Price competition in networked markets: how do monopolies impact social welfare? (English) Zbl 1406.91141
Markakis, Evangelos (ed.) et al., Web and internet economics. 11th international conference, WINE 2015, Amsterdam, The Netherlands, December 9–12, 2015. Proceedings. Berlin: Springer (ISBN 978-3-662-48994-9/pbk; 978-3-662-48995-6/ebook). Lecture Notes in Computer Science 9470, 16-30 (2015).
Summary: 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 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 buyer demand functions, equilibrium always exists and allocations can often be close to optimal. In the process, we characterize the structure and properties of equilibria using techniques from min-cost flows, and obtain tight bounds on efficiency in terms of the various parameters governing the market, especially the number of monopolies $$M$$.
Although 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 $$1+\frac{M}{2}$$ 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. 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.
For the entire collection see [Zbl 1326.68026].

##### MSC:
 91B24 Microeconomic theory (price theory and economic markets) 91B15 Welfare economics 90B10 Deterministic network models in operations research
##### Keywords:
price competition; networked markets; monopoly; social welfare
Full Text:
##### References:
 [1] Abolhassani, M., Bateni, M.H., Hajiaghayi, M.T., Mahini, H., Sawant, A.: Network cournot competition. In: Liu, T.-Y., Qi, Q., Ye, Y. (eds.) WINE 2014. LNCS, vol. 8877, pp. 15–29. Springer, Heidelberg (2014) · Zbl 1406.91243 · doi:10.1007/978-3-319-13129-0_2 [2] Acemoglu, D., Ozdaglar, A.: Competition and efficiency in congested markets. Math. Oper. Res. 32(1), 1–31 (2007) · Zbl 1276.91032 · doi:10.1287/moor.1060.0231 [3] Acemoglu, D., Ozdaglar, A.: Competition in parallel-serial networks. IEEE J. Sel. Areas Commun. 25(6), 1180–1192 (2007) · doi:10.1109/JSAC.2007.070812 [4] Amir, R.: Cournot oligopoly and the theory of supermodular games. Games Econ. Behav. 15(2), 132–148 (1996) · Zbl 0859.90034 · doi:10.1006/game.1996.0062 [5] Anshelevich, E., Sekar, S.: Price competition in networked markets: how do monopolies impact social welfare? arXiv preprint arXiv:1410.1113 (2015) · Zbl 1406.91141 [6] Azevedo, E.M., Weyl, E.G., White, A.: Walrasian equilibrium in large, quasilinear markets. Theor. Econ. 8(2), 281–290 (2013) · Zbl 1395.91294 · doi:10.3982/TE1060 [7] Babaioff, M., Leme, R.P., Sivan, B.: Price competition, fluctuations and welfare guarantees. In: Proceedings of EC (2015) · doi:10.1145/2764468.2764493 [8] Babaioff, M., Lucier, B., Nisan, N.: Bertrand networks. In: Proceedings of EC (2013) · doi:10.1145/2492002.2482564 [9] Babaioff, M., Lucier, B., Nisan, N., Leme, R.P: On the efficiency of the walrasian mechanism. In: Proceedings of EC (2014) · doi:10.1145/2600057.2602850 [10] Babaioff, M., Nisan, N., Leme, R.P: Price competition in online combinatorial markets. In: Proceedings of WWW (2014) · doi:10.1145/2566486.2568016 [11] Bulow, J.I., Pfleiderer, P.: A note on the effect of cost changes on prices. J. Polit. Econ. 91, 182–185 (1983) · doi:10.1086/261135 [12] Cabon-Dhersin, M.-L., Drouhin, N.: Tacit collusion in a one-shot game of price competition with soft capacity constraints. J. Econ. Manage. Strategy 23(2), 427–442 (2014) · doi:10.1111/jems.12049 [13] Chawla, S., Niu, F.: The price of anarchy in bertrand games. In: Proceedings of EC (2009) · doi:10.1145/1566374.1566418 [14] Chawla, S., Roughgarden, T.: Bertrand competition in networks. In: Monien, B., Schroeder, U.-P. (eds.) SAGT 2008. LNCS, vol. 4997, pp. 70–82. Springer, Heidelberg (2008) · Zbl 1136.91340 · doi:10.1007/978-3-540-79309-0_8 [15] Chawla, S., Sivan, B.: Bayesian algorithmic mechanism design. SIGecom Exch. 13(1), 5–49 (2014) · doi:10.1145/2692375.2692378 [16] Correa, J.R., Figueroa, N., Lederman, R., Stier-Moses, N.E.: Pricing with markups in industries with increasing marginal costs. Math. Program., 1–42 (2008) · Zbl 1302.90029 [17] Hassidim, A., Kaplan, H., Mansour, Y., Nisan, N.: Non-price equilibria in markets of discrete goods. In: Proceedings of EC (2011) · doi:10.1145/1993574.1993619 [18] Kuleshov, V., Wilfong, G.: On the efficiency of the simplest pricing mechanisms in two-sided markets. In: Goldberg, P.W. (ed.) WINE 2012. LNCS, vol. 7695, pp. 284–297. Springer, Heidelberg (2012) · Zbl 06153236 · doi:10.1007/978-3-642-35311-6_21 [19] Lev, O., Oren, J., Boutilier, C., Rosenschein, J.S.: The pricing war continues: on competitive multi-item pricing. In: Proceedings of AAAI (2015) [20] Papadimitriou, C.H., Valiant, G: A new look at selfish routing. In: Proceedings of ICS (2010) [21] Shenker, S., Clark, D., Estrin, D., Herzog, S.: Pricing in computer networks: reshaping the research agenda. ACM SIGCOMM Comput. Commun. Rev. 26(2), 19–43 (1996) · doi:10.1145/231699.231703 [22] Tullock, G.: The welfare costs of tariffs, monopolies, and theft. Econ. Inq. 5(3), 224–232 (1967) · doi:10.1111/j.1465-7295.1967.tb01923.x
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.