Designing Auctions: A Historical Perspective
DOI:
https://doi.org/10.26636/jtit.2011.3.1166Keywords:
auctions, game theory, mechanism designAbstract
Auction is a form of organization of competition that leads to the assignment and valuation of resources based on the information obtained from the competing agents. From the perspective of systems science it is a distributed resource allocation algorithm applied in the environment with information asymmetry, i.e., where the interconnected and interacting subsystems have different information about the system as a whole. This paper presents an overview of the historical development of mathematical theory underlying modern approach to auction design. Selected practical applications of the theory are also discussed.
Downloads
References
[1] V. Krishna, Auction Theory. Academic Press, 2002.
View in Google Scholar
[2] P. Milgrom, Putting Auction Theory to Work. Cambridge University Press, 2004.
View in Google Scholar
[3] J. R. Hicks, „Leon Walras”, Econometrica, vol. 2, no. 4, pp. 338-348, 1934.
View in Google Scholar
[4] A. Wald, „On some systems of equations of mathematical economics”, Econometrica, vol. 19, no. 4, pp. 368-404, 1951.
View in Google Scholar
[5] A. Wald, „On a relation between changes in demand and price changes”, Econometrica, vol. 20, no. 2, pp. 304-306, 1952.
View in Google Scholar
[6] O. Lange, „The foundations of welfare economics”, Econometrica, vol. 10, pp. 215-228, 1942.
View in Google Scholar
[7] K. J. Arrow and G. Debreu, „Existence of an equilibrium for a competitive economy”, Econometrica, vol. 22, no. 3, pp. 265-290, 1954.
View in Google Scholar
[8] A. Smith, An Inquiry into the Nature and Causes of the Wealth of Nations. Bantam Books, 2003.
View in Google Scholar
[9] T. Groves, R. Radner, and S. Reiter, Eds., Information, Incentives, and Economic Mechanisms: Essays in Honor of Leonid Hurwicz. Minneapolis: University of Minnesota Press, 1987.
View in Google Scholar
[10] P. A. Samuelson, „The stability of equilibrium: comparative statics and dynamics”, Econometrica, vol. 9, no. 2, pp. 97-120, 1941.
View in Google Scholar
[11] P. A. Samuelson, „The stability of equilibrium: linear and nonlinear systems”, Econometrica, vol. 10, no. 1, pp. 1-25, 1942.
View in Google Scholar
[12] P. A. Samuelson, „The relationship between Hicksian stability and true dynamic stability”, Econometrica, vol. 12, pp. 256-257, 1944.
View in Google Scholar
[13] J. R. Hicks, Value and Capital: An Inquiry into Some Fundamental Principles of Economic Theory. Oxford: Clarendon Press, 1946.
View in Google Scholar
[14] K. J. Arrow and L. Hurwicz, „On the stability of the competitive equilibrium, I”, Econometrica, vol. 26, no. 4, pp. 522-552, 1958.
View in Google Scholar
[15] K. J. Arrow and L. Hurwicz, „On the stability of the competitive equilibrium, II”, Econometrica, vol. 27, no. 1, pp. 82-109, 1959.
View in Google Scholar
[16] H. Uzawa, „The stability of dynamic process”, Econometrica, vol. 29, no. 4, pp. 617-631, 1961.
View in Google Scholar
[17] I. Ekeland and R. Temam, Convex Analysis and Variational Problems. SIAM, 1999.
View in Google Scholar
[18] H. Uzawa, „Market mechanisms and mathematical programming”, Econometrica, vol. 28, no. 4, pp. 872-881, 1960.
View in Google Scholar
[19] W. Findeisen et al., Control and Coordination in Hierarchical Systems. New York: Wiley, 1980.
View in Google Scholar
[20] D. G. Saari and C. P. Simon, „Effective price mechanisms”, Econometrica, vol. 46, no. 5, pp. 1097-1125, 1978.
View in Google Scholar
[21] D. G. Saari, „Iterative price mechanisms”, Econometrica, vol. 53, no. 5, pp. 1117-1131, 1985.
View in Google Scholar
[22] F. P. Kelly, A. K. Maulloo, and D. K. Tan, „Rate control for communication networks: shadow prices, proportional fairness, and stability”, J. Oper. Res. Soc., vol. 49, pp. 237-252, 1998.
View in Google Scholar
[23] R. Srikant, The Mathematics of Internet Congestion Control. Birkhäuser Boston, December 2003.
View in Google Scholar
[24] S. H. Low, „A duality model of TCP and queue management algorithms”, IEEE/ACM Trans. Netw., vol. 11, no. 4, pp. 525-536, 2003.
View in Google Scholar
[25] S. H. Low and D. E. Lapsley, „Optimization flow control, I: Basic algorithm and convergence”, IEEE/ACM Trans. Netw., vol. 7, no. 6, pp. 861-874, 1999.
View in Google Scholar
[26] S. H. Low, F. Paganini, and J. C. Doyle, „Internet congestion control”, IEEE Control Sys. Mag., vol. 22, no. 1, pp. 28-43, 2002.
View in Google Scholar
[27] J. Stiglitz, Globalization and Its Discontents. Penguin Books, 2002.
View in Google Scholar
[28] A. Mas-Colell, M. D. Whinston, and J. R. Green, Microeconomic Theory. Oxford University Press, 1995.
View in Google Scholar
[29] J. R. Green and J.-J. Laffont, Incentives in Public Decision-Making. North-Holland Publishing Company, 1979.
View in Google Scholar
[30] J.-J. Laffont and D. Martimort, The Theory of Incentives. Princeton University Press, 2002.
View in Google Scholar
[31] O. Lange, On the Economic Theory of Socialism. 1938.
View in Google Scholar
[32] C. H. Feinstein, Socialism, Capitalism and Economic Growth. Cambridge University Press, 1967.
View in Google Scholar
[33] O. Lange, „The practice of economic planning and the optimum allocation of resources”, Econometrica, 1949.
View in Google Scholar
[34] J. Stiglitz, Making globalization work. Penguin Books, 2006.
View in Google Scholar
[35] K. J. Arrow, Social Choice and Individual Values. Wiley, 1963.
View in Google Scholar
[36] L. Robbins, „Interpersonal comparisons and utility: A comment”, Econom. J., vol. 48, no. 192, pp. 635-641, 1938.
View in Google Scholar
[37] A. Sen, „Interpersonal aggregation and partial comparability”, Econometrica, 1970.
View in Google Scholar
[38] A. Sen, „Social choice theory: Re-examination”, Econometrica, 1977.
View in Google Scholar
[39] A. Sen, „On weights and measures: Informational constraints in social welfare”, Econometrica, vol. 45, no. 7, pp. 1539-1572, 1977.
View in Google Scholar
[40] A. Sen, Collective Choice and Social Welfare. Holden-Day, 1970.
View in Google Scholar
[41] S. J. Grossman and J. Stiglitz, „On the impossibility of informationally efficient markets”, American Econom. Rev., vol. 70, no. 3, pp. 393-408, 1980.
View in Google Scholar
[42] M. Rothschild and J. Stiglitz, „Equilibrium in competitive insurance markets: an essay on the economics of imperfect information”, Quarterly J. Econom., vol. 90, no. 4, pp. 630-649, 1976.
View in Google Scholar
[43] J. Stiglitz, „The theory of screening, education, and the distribution of income”, American Econom. Rev., vol. 65, no. 3, pp. 283-300, 1975.
View in Google Scholar
[44] G. A. Akerlof, „The market for „Lemons”: quality uncertainty and the market mechanism”, Quarterly J. Econom., vol. 84, no. 3, pp. 488-500, 1970.
View in Google Scholar
[45] M. Spence, „Job market signaling”, Quarterly J. Econom., vol. 87, no. 3, pp. 355-374, 1973.
View in Google Scholar
[46] L. Hurwicz, „On informationally decentralized systems”, in Studies in Resource Allocation Processes, K. Arrow and L. Hurwicz, Eds. Cambridge University Press, 1977, ch. 4, pp. 425-459.
View in Google Scholar
[47] R. Johari, „Efficiency loss in market mechanisms for resource allocation”, Ph.D. thesis, MIT, 2004.
View in Google Scholar
[48] R. Johari and J. N. Tsitsiklis, „Efficiency loss in a network resource allocation game”, Mathemat. Oper. Res., vol. 29, pp. 407-435, 2004.
View in Google Scholar
[49] R. Johari and J. N. Tsitsiklis, „Efficiency of scalar-parameterized mechanisms”, Oper. Res., vol. 57, no. 4, pp. 823-839, 2009.
View in Google Scholar
[50] T. Roughgarden and É. Tardos, „How bad is selfish routing?”, in Proc. 41st Ann. Symp. Foundat. Comp. Sci. FOCS 2000, Redondo Beach, USA, 2000, pp. 93-102.
View in Google Scholar
[51] T. Roughgarden, „The price of anarchy is independent of the network topology”, in Proc. 34th ACM Symp. Theory Comput. STOC 2002, Montréal, Canada, 2002, pp. 428-437.
View in Google Scholar
[52] S. Yang and B. Hajek, „VCG-Kelly mechanisms for allocation of divisible goods: adapting VCG mechanisms to one-dimensional signals”, IEEE J. Select. Areas Commun., vol. 25, no. 6, pp. 1237-1243, 2007.
View in Google Scholar
[53] B. Hajek and S. Yang, „Strategic buyers in a sum bid game for flat networks”, in Proc. IMA Worksh., March 2004.
View in Google Scholar
[54] M. Karpowicz, „Coordination in hierarchical systems with rational agents”, Ph.D. thesis, Politechnika Warszawska, 2009.
View in Google Scholar
[55] J.-J. Laffont and J. Tirole, Competition in Telecommunications. The MIT Press, 2000.
View in Google Scholar
[56] S. Laskowski, „Wspomaganie procesu ustalania cen na rynku usług telekomunikacyjnych”, Ph.D. thesis, Politechnika Warszawska, 2007 (in Polish).
View in Google Scholar
[57] W. B. Norton, „Internet service providers and peering”, in Proc. NANOG 19, Albuquerque, New Mexico, 2000.
View in Google Scholar
[58] P. Baake and T. Wichmann, „On the economics of Internet peering”, Netnomics, vol. 1, no. 1, pp. 89-105, 1999.
View in Google Scholar
[59] R. B. Myerson, Game Theory: Analysis of Conflict. Harvard University Press, 1991.
View in Google Scholar
[60] D. Fudenberg and J. Tirole, Game Theory. The MIT Press, 1991.
View in Google Scholar
[61] W. Vickrey, „Counterspeculation, auctions and competitive sealed tenders”, J. Finance, vol. 16, no. 1, pp. 8-37, 1961.
View in Google Scholar
[62] L. Hurwicz and M. Walker, „On the generic nonoptimality of dominant-strategy allocation mechanisms: a general theorem that includes pure exchange economies”, Econometrica, vol. 58, no. 3, pp. 683-704, 1990.
View in Google Scholar
[63] L. Hurwicz and D. Schmeidler, „Construction of outcome functions guaranteeing existence and Pareto-optimality of Nash-equilibria”, Econometrica, vol. 46, no. 6, 1978.
View in Google Scholar
[64] L. Hurwicz and S. Reiter, Designing Economic Mechanisms. Cambridge University Press, 2008.
View in Google Scholar
[65] L. Hurwicz, „The design of mechanisms for resource allocation”, American Econom. Rev., vol. 63, no. 2, pp. 1-30, 1973.
View in Google Scholar
[66] L. Hurwicz, „On allocations attainable through Nash equilibria”, J. Economic Theory, vol. 21, no. 1, pp. 140-165, 1979.
View in Google Scholar
[67] R. B. Myerson and M. A. Satterthwaite, „Efficient mechanisms for bilateral trading”, J. Econom. Theory, vol. 29, no. 2, 1983.
View in Google Scholar
[68] R. B. Myerson, „Optimal auction design”, Mathem. Operation Res., vol. 6, no. 1, 1981.
View in Google Scholar
[69] E. Maskin, „Nash equilibrium and welfare optimality”, Rev. Econom. Studies, vol. 66, no. 1, pp. 23-38, 1999.
View in Google Scholar
[70] J.-J. Laffont and E. Maskin, „A differential approach to dominant strategy mechanisms”, Econometrica, vol. 48, no. 6, pp. 1507-1520, 1980.
View in Google Scholar
[71] L. Hurwicz, E. Maskin, and A. Postlewaite, „Feasible implementation of social choice correspondences by Nash equilibria”, in Essays in Honor of Stanley Reiter, J. Ledyard, Ed. Kluwer, 1995.
View in Google Scholar
[72] P. Dasgupta and E. Maskin, „Efficient auctions”, Quarterly J. Econom., vol. 115, no. 2, pp. 341-388, 2000.
View in Google Scholar
[73] P. Dasgupta, P. Hammond, and E. Maskin, „The implementation of social choice rules: some general results on incentive compatibility”, Rev. Econom. Studies, 1978.
View in Google Scholar
[74] R. Wilson, „Auctions of shares”, Quart. J. Econom., vol. 93, no. 4, pp. 675-689, 1979.
View in Google Scholar
[75] K. Back and J. F. Zender, „Auctions of divisible goods: on the rationale for the treasury experiment”, The Rev. Financ. Studies, vol. 6, no. 4, pp. 733-764, 1993.
View in Google Scholar
[76] L. Ausubel and P. Cramton, „Demand reduction and inefficiency in multi-unit auctions”, Working paper. University of Maryland, 1996.
View in Google Scholar
[77] M. Karpowicz and K. Malinowski, „Efficiency loss and uniform-price mechanism”, in Proc. 47th IEEE Conf. Decision and Control, Cancun, Mexico, 2008.
View in Google Scholar
[78] G. J. Miller, „Debt management networks”, Public Adm. Rev., vol. 53, no. 1, pp. 50-58, 1993.
View in Google Scholar
[79] P. F. Malvey and C. M. Archibald, „Uniform-price auctions: update of the treasury experience”, Tech. rep., Office of Market Finance U.S. Treasury, 1998.
View in Google Scholar
[80] S. R. Umlauf, „An empirical study of the Mexican treasury bill auction”, J. Financ. Econom., vol. 33, pp. 313-340, 1993.
View in Google Scholar
[81] R. Tenorio, „Revenue equivalence and bidding behavior in a multi-unit auction market: an empirical analysis”, Rev. Econom. Statistics, vol. 75, pp. 302-314, 1993.
View in Google Scholar
[82] P. Milgrom, „Auction theory” in Advances in Economic Theory: Fifth World Congr., T. Bewley, Ed. Cambridge: Cambridge University Press, 1987.
View in Google Scholar
[83] M. Keloharju, K. G. Nyborg, and K. Rydqvist, „Strategic behavior and underpricing in uniform price auctions”, Working Papers 2003.25, Fondazione Eni Enrico Mattei, March 2003.
View in Google Scholar
[84] K. G. Nyborg and S. M. Sundaresan, „Discriminatory versus uniform treasury auctions: evidence from when-issued transactions”, J. Financ. Econom., vol. 42, pp. 63-104, 1996.
View in Google Scholar
[85] D. Goldreich, „Underpricing in discriminatory and uniform-price treasury auctions”, J. Financ. Quantitative Analysis (forthcoming).
View in Google Scholar
[86] H. Eggertsson, „The Scandinavian electricity power market and market power”, Master’s thesis, Technical University of Denmark, 2003.
View in Google Scholar
[87] A. Botterud, A. K. Bhattacharyya, and M. Ilic, „Futures and spot prices - an analysis of the Scandinavian electricity market”, in Proc. 34th Ann. North American Power Symp. NAPS 2002, Tempe, USA, 2002.
View in Google Scholar
[88] N. Fabra, N.-H. M. von der Fehr, and D. Harbord, „Designing electricity auctions”, Rand J. Econom., vol. 37, no. 1, pp. 23-46, 2006.
View in Google Scholar
[89] H. Gruenspecht and T. Terry, Horizontal market power in restructured electricity markets, Office of Policy, US Department of Energy, Washington, USA.
View in Google Scholar
[90] M. Kahn and L. Lynch, „California’s electricity options and challenges”, Report to the Governor, 2000.
View in Google Scholar
[91] S. Borenstein, „The trouble with electricity markets: understanding California’s restructuring disaster”, The J. Econom. Perspect., vol. 16, no. 1, pp. 191-211, 2002.
View in Google Scholar
[92] R. J. Green, „Increasing competition in the British electricity spot market”, J. Ind. Econom., vol. 44, no. 2, pp. 205-216, 1996.
View in Google Scholar
[93] J. R. Green and D. M. Newbery, „Competition in the British electricity spot market”, J. Polit. Economy, vol. 100, no. 5, pp. 929-953, 1992.
View in Google Scholar
[94] P. D. Klemperer and M. A. Meyer, „Supply function equilibria in oligopoly under uncertainty”, Econometrica, vol. 57, no. 6, pp. 1243-1277, 1989.
View in Google Scholar
[95] N.-H. M. von der Fehr and D. Harbord, „Spot market competition in the U.K. electricity industry”, Economic Journal, vol. 103, iss. 418, pp. 531-546, 1993.
View in Google Scholar
[96] P. Cramton, „Competitive bidding behavior in uniform-price auction markets”, in Proc. 37th Hawaii Int. Conf. Sys. Sci. HICSS 2004, Big Island, Hawaii, USA, 2004.
View in Google Scholar
[97] P. Cramton, „Electricity market design: the good, the bad, and the ugly”, in Proc. 36th Hawaii Int. Conf. Sys. Sci. HICSS 2003, Big Island, Hawaii, USA, 2003.
View in Google Scholar
[98] R. Engelbrecht-Wiggans and C. M. Kahn, „Multi-unit auctions with uniform prices”, Economic Theory, vol. 12, no. 2, pp. 227-258, 1998.
View in Google Scholar
[99] R. Engelbrecht-Wiggans and C. M. Kahn, „Multi-unit pay-your-bid auctions with variable award”, Games Econom. Behavior, vol. 23, pp. 25-42, 1998.
View in Google Scholar
[100] R. Baldick and W. Hogan, Capacity constrained supply function equilibrium models of electricity markets: Stability, nondecreasing constraints, and function space iterations. University of California Energy Institute, 2001.
View in Google Scholar
[101] C. J. Day and B. F. Hobbs, „Oligopolistic competition in power networks: a conjectured supply function approach”, IEEE Trans. Power Sys., 2002.
View in Google Scholar
[102] P. Cramton, „The FCC spectrum auctions: An early assessment”, J. Econom. Manage. Strategy, vol. 6, no. 3, pp. 431-495, 1997.
View in Google Scholar
[103] P. Cramton, „Spectrum auctions”, in Handbook of Telecommunications Economics, M. Cave, S. K. Majumdar, and I. Vogelsang, Eds. Elsevier, 2002, pp. 605-639.
View in Google Scholar
[104] J. Ledyard, D. Porter, and A. Rangel, „Experiments testing multiobject allocation mechanisms”, J. Econom. Manage. Strategy, vol. 6, no. 3, pp. 639-675, 1997.
View in Google Scholar
[105] C. R. Plott, „Laboratory experimental testbeds: application to the PCS auction”, J. Econom. Manage. Strategy, vol. 6, no. 3, pp. 605-638, 1997.
View in Google Scholar
[106] P. Milgrom and R. J. Weber, „A theory of auctions and competitive bidding”, Econometrica, vol. 50, no. 5, pp. 1089-1122, 1982.
View in Google Scholar
[107] P. Cramton, Combinatorial Auctions. MIT Press, 2006.
View in Google Scholar
[108] P. Cramton and J. A. Schwartz, „Collusive bidding in the FCC spectrum auctions”, The B.E. J. Economic Analysis and Policy, no. 1, 2002.
View in Google Scholar
[109] R. J. Weber, „Making more from less: Strategic demand reduction in the FCC spectrum auctions”, J. Econom. Manage. Strategy, vol. 6, no. 3, pp. 529-548, 1997.
View in Google Scholar
Downloads
Submitted
Published
Issue
Section
License
Copyright (c) 2023 Journal of Telecommunications and Information Technology
This work is licensed under a Creative Commons Attribution 4.0 International License.
