Abstract
We analyze the variation of prices in a model of an exchange market introduced by Kakade et al. [11], in which buyers and sellers are represented by vertices of a bipartite graph and trade is allowed only between neighbors. In this model the graph is generated probabilistically, and each buyer is connected via preferential attachment to v sellers. We show that even though the tail of the degree distribution of the sellers gets heavier as v increases, the prices at equilibrium decrease exponentially with v. This strengthens the intuition that as the number of vendors available to buyers increases, the prices of goods decrease.
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References
Arrow, K., Debreu, G.: Existence of an equilibrium for a competitive economy. Econometrica 22, 265–290 (1954)
Bollobás, B., Riordan, O.: Mathematical results on scale-free random graphs. In: Handbook of graphs and networks: from the genome to the internet, pp. 1–34. Wiley-VCH, Chichester (2002)
Chung, F., Lu, L.: Complex Graphs and Networks. In: Regional Conference Series in Mathematics, p. 107. American Mathematical Society, Providence, RI (2006)
Corominas-Bosch, M.: Bargaining in a network of buyers and sellers. Journal of Economic Theory 115, 35–77 (2004)
Even-Dar, E., Kearns, M., Suri, S.: A network formation game for bipartite exchange economies. In: ACM-SIAM Symposium on Discrete Algorithms (SODA) (2007)
I. Fisher. Ph.D. thesis, Yale University (1891)
Gale, D.: Theory of Linear Economic Models. McGraw-Hill, New York (1960)
Jackson, M.: The study of social networks in economics. In: Podolny, J., Rauch, J.E. (eds.) Forthcoming in The Missing Links: Formation and Decay of Economic Networks, Russell Sage Foundation, Thousand Oaks
Jackson, M.: The economics of social networks. Chapter 1 in Volume I of Advances in Economics and Econometrics. In: Blundell, R., Newey, W., Persson, T. (eds.) The economics of social networks., vol. 1, Cambridge University Press, Cambridge (2006)
Kakade, S., Kearns, M., Ortiz, L.: Graphical Economics. In: Shawe-Taylor, J., Singer, Y. (eds.) COLT 2004. LNCS (LNAI), vol. 3120, pp. 17–32. Springer, Heidelberg (2004)
Kakade, S., Kearns, M., Ortiz, L., Pemantle, R., Suri, S.: Economic properties of social networks. In: Saul, L.K., Weiss, Y., Bottou, L. (eds.) Advances in Neural Information Processing Systems, vol. 17, MIT Press, Cambridge (2005)
Kranton, R., Minehart, M.: A theory of buyer-seller networks. American Economic Review 91, 485–508 (2001)
Suri, S.: The effects of network topology on strategic behavior. Ph.D. thesis, University of Pennsylvania (2007)
Walras, L.: Éléments d’économie politique pure; ou, Théorie de la richesse sociale (Elements of Pure Economics, or the Theory of social wealth), Lausanne, Paris, vol. 4 (1874) (1899, 4th ed., 1954 Engl. transl.)
Wu, F., Zhang, L.: Proportional response dynamics leads to market equilibrium. In: Symposium on the Theory of Computing (STOC), pp. 354–363 (2007)
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Gradwohl, R. (2008). Price Variation in a Bipartite Exchange Network. In: Monien, B., Schroeder, UP. (eds) Algorithmic Game Theory. SAGT 2008. Lecture Notes in Computer Science, vol 4997. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79309-0_11
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DOI: https://doi.org/10.1007/978-3-540-79309-0_11
Publisher Name: Springer, Berlin, Heidelberg
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