×

Optimal contracting in networks. (English) Zbl 1422.91612

Summary: We study optimal contracting between a firm selling a divisible good that exhibits positive externality and a group of agents in a social network. The extent of externality that each agent receives from the consumption of neighboring agents is privately held and is unknown to the firm. By explicitly characterizing the optimal multilateral contract, we demonstrate how inefficiency in an agent’s trade propagates through the network and creates unequal and network-dependent downward distortion in other agents’ trades. Furthermore, we describe bilateral contracts (nonlinear pricing schemes) and characterize their explicit dependence on the network structure. We show that the firm will benefit from uncertainty in an agent’s valuation of other agents’ externality. We describe the profit gap between multilateral and bilateral contracts and analyze the consequences of the explicit dependence of the contracts on network structure. When the network is balanced in terms of homogeneity of agents’ influence, network structure has no impact on the firm’s profit for bilateral contracts. On the other hand, when the influences are heterogeneous with high dispersion (as in core-periphery networks) the restriction to bilateral contracts can result in profit losses that grow unbounded with the size of networks.

MSC:

91D30 Social networks; opinion dynamics
91B40 Labor market, contracts (MSC2010)
91A43 Games involving graphs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Acemoglu, D.; Carvalho, V.; Ozdaglar, A.; Tahbaz-Salehi, A., The network origins of aggregate fluctuations, Econometrica, 80, 5, 1977-2016 (2012) · Zbl 1274.91317
[2] Acemoglu, D.; Dahleh, M.; Lobel, I.; Ozdaglar, A., Bayesian learning in social networks, Rev. Econ. Stud., 78, 1201-1236 (2011) · Zbl 1274.91354
[3] Ajorlou, A.; Jadbabaie, A.; Kakhbod, A., Dynamic pricing in social networks: the word of mouth effect, Manag. Sci., 64, 971-979 (2018)
[4] Ballester, C.; Calvo-Armengol, A.; Zenou, Y., Who’s who in networks. Wanted: the key player, Econometrica, 74, 1403-1417 (2006) · Zbl 1138.91590
[5] Belhaj, M.; Bervoets, S.; Deroian, F., Efficient networks in games with local complementarities, Theor. Econ., 11, 1, 357-380 (2016) · Zbl 1395.91074
[6] Bernstein, S.; Winter, E., Contracting with heterogeneous externalities, Am. Econ. J. Microecon., 4, 2, 50-76 (2012)
[7] Bimpikis, K.; Ozdaglar, A.; Yildiz, E., Competitive targeted advertising over networks, Oper. Res., 64, 3, 705-720 (2016) · Zbl 1348.90366
[8] Bloch, F., Targeting and pricing in social networks, (Bramoullé, Y.; Galeotti, A.; Rogers, B., Oxford Handbook of the Economics of Networks (2016), Oxford University Press: Oxford University Press Oxford)
[9] Bloch, F.; Quérou, N., Pricing in social networks, Games Econ. Behav., 80, 263-281 (2013)
[10] Bramoullé, Y.; Kranton, R., Public goods in networks, J. Econ. Theory, 135, 478-494 (2007) · Zbl 1186.91099
[11] Bramoullé, Y.; Kranton, R.; D’Amours, M., Strategic interaction and networks, Am. Econ. Rev., 104, 3, 898-930 (2014)
[12] Candogan, O.; Bimpikis, K.; Ozdaglar, A., Optimal pricing in networks with externalities, Oper. Res., 60, 4, 883-905 (2012) · Zbl 1260.91095
[13] Chen, Y.; Zenou, Y.; Zhou, J., Competitive pricing strategies in social networks, Rand J. Econ., 49, 3, 672-705 (2018)
[14] Corbo, J.; Calvo-Armengol, A.; Parkes, D., The importance of network topology in local contribution games, (Proceedings of the 3rd International Workshop on Internet and Network Economics (2007))
[16] Fainmesser, I. P.; Galeotti, A., Pricing network effects, Rev. Econ. Stud., 83, 1, 165-198 (2016) · Zbl 1405.91198
[17] Fainmesser, I. P.; Galeotti, A., Pricing Network Effects: Competition (2016), Working paper · Zbl 1405.91198
[18] Farrell, J.; Saloner, G., Standardization, compatibility, and innovation, Rand J. Econ., 16, 1, 70-83 (1985)
[19] Galeotti, A.; Goyal, S., Influencing the influencers: a theory of strategic diffusion, Rand J. Econ., 40, 3, 509-532 (2009)
[20] Galeotti, A.; Goyal, S.; Jackson, M.; Vega-Redondo, F.; Yariv, L., Network games, Rev. Econ. Stud., 77, 1, 218-244 (2010) · Zbl 1197.91168
[21] Galeotti, A.; Mattozzi, A., Personal influence: social context and political competition, Am. Econ. J. Microecon., 3, 1, 307-327 (2011)
[22] Golub, B.; Jackson, M. O., Naive learning in social networks: convergence, influence, and the wisdom of crowds, Am. Econ. J. Microecon., 2, 112-149 (2010)
[23] Golub, B.; Jackson, M. O., How homophily affect the speed of learning and best response dynamics, Q. J. Econ., 127, 1287-1338 (2012) · Zbl 1400.91465
[24] Horn, R.; Johnson, C., Matrix Analysis (2012), Cambridge University Press
[25] Jackson, M., Social and Economic Networks (2008), Princeton University Press: Princeton University Press Princeton, NJ · Zbl 1149.91051
[26] Jackson, M.; Zenou, Y., Games on networks, (Young, P.; Zamir, S., Handbook of Game Theory, vol. 4 (2015), Elsevier Publisher: Elsevier Publisher Amsterdam) · Zbl 1304.91001
[27] Katz, M.; Shapiro, C., Technology adoption in the presence of network externalities, J. Polit. Econ., 94, 4, 822-841 (1986)
[28] Laffont, J.; Martimort, D., The Theory of Incentives: The Principal-Agent Model (2002), Princeton University Press
[29] Laffont, J.; Tirole, J., Optimal bypass and cream skimming, Am. Econ. Rev., 80, 1040-1061 (1990)
[30] Leduc, M. V.; Jackson, M. O.; Johari, R., Pricing and referrals in diffusion on networks, Games Econ. Behav., 104, 568-594 (2017) · Zbl 1393.91069
[31] Lovász, L., Eigenvalues of Graphs (2007)
[32] Maskin, E.; Riley, J., Monopoly with incomplete information, Rand J. Econ., 15, 171-196 (1984)
[33] Mussa, M.; Rosen, C., Monopoly and product quality, J. Econ. Theory, 18, 301-317 (1978) · Zbl 0403.90007
[34] Probst, F.; Grosswiele, L.; Pfleger, R., Who will lead and who will follow: identifying influential users in online social networks, Bus. Inf. Syst. Eng., 5, 3, 179-193 (2013)
[35] Segal, I., Contracting with externalities, Q. J. Econ., 114, 337-388 (1999) · Zbl 0953.91026
[36] Segal, I., Coordination and discrimination in contracting with externalities: divide and conquer, J. Econ. Theory, 113, 147-181 (2003) · Zbl 1059.91055
[37] Shin, E., Monopoly pricing and diffusion of social network goods, Games Econ. Behav., 102, 162-178 (2017) · Zbl 1409.91112
[38] Sundararajan, A., Local network effects and complex network structure, B.E. J. Theor. Econ., 7, 1 (2008)
[39] Zhou, J.; Chen, Y., Key leaders in social networks, J. Econ. Theory, 157, 212-235 (2015) · Zbl 1330.91169
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.