×

zbMATH — the first resource for mathematics

Pigouvian pricing and stochastic evolutionary implementation. (English) Zbl 1142.91344
Summary: We study the implementation of efficient behavior in settings with externalities. A planner would like to ensure that a group of agents make socially optimal choices, but he only has limited information about the agents’ preferences, and can only distinguish individual agents through the actions they choose. We describe the agents’ behavior using a stochastic evolutionary model, assuming that their choice probabilities are given by the logit choice rule. We prove that there is a simple price scheme with the following property: regardless of the realization of preferences, a group of agents subjected to the price scheme will spend the vast majority of time in the long run behaving efficiently. The price scheme defines a game that may possess multiple equilibria, but we are able to obtain a unique and efficient selection from this set because of the stochastic nature of the agents’ choice rule. We conclude by comparing the performance of our price scheme with that of VCG mechanisms.

MSC:
91A22 Evolutionary games
91A10 Noncooperative games
91B14 Social choice
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Anderson, S.P.; de Palma, A.; Thisse, J.-F., Discrete choice theory of product differentiation, (1992), MIT Press Cambridge, MA · Zbl 0857.90018
[2] Benaı¨m, M.; Weibull, J., Deterministic approximation of stochastic evolution in games, Econometrica, 71, 873-903, (2003) · Zbl 1152.91350
[3] Beckmann, M.; McGuire, C.B.; Winsten, C.B., Studies in the economics of transportation, (1956), Yale University Press New Haven
[4] Binmore, K.G.; Samuelson, L.; Vaughan, R., Musical chairs: modeling noisy evolution, Games econ. behav., 11, 1-35, (1995) · Zbl 0839.90140
[5] Blume, L.E., The statistical mechanics of strategic interaction, Games econ. behav., 5, 387-424, (1993) · Zbl 0797.90123
[6] Blume, L.E., Population games, (), 425-460
[7] Clarke, E., Multipart pricing of public goods, Public choice, 11, 19-33, (1971)
[8] Cooper, R.J., Coordination games: complementarities and macroeconomics, (1999), Cambridge University Press Cambridge · Zbl 0941.91018
[9] Durlauf, S.N., Statistical mechanics approaches to socioeconomic behavior, (), 81-104
[10] R. Durrett, Probability: Theory and Examples, third ed., Thomson-Wadsworth-Brooks/Cole, Belmont, CA, 2005. · Zbl 1202.60002
[11] Ellison, G., Learning, local interaction, and coordination, Econometrica, 61, 1047-1071, (1993) · Zbl 0802.90143
[12] Ellison, G., Basins of attraction, long-run stochastic stability, and the speed of step-by-step evolution, Rev. econ. stud., 67, 17-45, (2000) · Zbl 0956.91027
[13] Foster, D.; Young, H.P., Stochastic evolutionary game dynamics, Theor. popul. biol., 38, 219-232, (1990) · Zbl 0703.92015
[14] Groves, T., Incentives in teams, Econometrica, 41, 617-631, (1973) · Zbl 0311.90002
[15] J. Hofbauer, W.H. Sandholm, Evolution in games with randomly disturbed payoffs, J. Econ. Theory, forthcoming. · Zbl 1142.91343
[16] Hofbauer, J.; Sigmund, K., Theory of evolution and dynamical systems, (1988), Cambridge University Press Cambridge
[17] P. Jehiel, M. Meyer-ter-Vehn, B. Moldovanu, Potentials and implementation, unpublished manuscript, University College London and University of Bonn, 2004. · Zbl 1153.91014
[18] Kandori, M.; Mailath, G.J.; Rob, R., Learning, mutation, and long run equilibria in games, Econometrica, 61, 29-56, (1993) · Zbl 0776.90095
[19] Kandori, M.; Rob, R., Bandwagon effects and long run technology choice, Games econ. behav., 22, 30-60, (1998) · Zbl 0892.90040
[20] Katz, M.L.; Shapiro, C., Systems competition and network effects, J. econ. lit., 8, 93-115, (1994)
[21] Monderer, D.; Shapley, L., Potential games, Games econ. behav., 14, 124-143, (1996) · Zbl 0862.90137
[22] Morris, S., Contagion, Rev. econ. stud., 67, 57-78, (2000) · Zbl 0960.91016
[23] Pigou, A.C., The economics of welfare, (1920), Macmillan London
[24] Rosenthal, R.W., A class of games possessing pure strategy Nash equilibria, Int. J. game theory, 2, 65-67, (1973) · Zbl 0259.90059
[25] Sandholm, W.H., Potential games with continuous player sets, J. econ. theory, 97, 81-108, (2001) · Zbl 0990.91005
[26] Sandholm, W.H., Evolutionary implementation and congestion pricing, Rev. econ. stud., 69, 667-689, (2002) · Zbl 1025.91002
[27] Sandholm, W.H., Negative externalities and evolutionary implementation, Rev. econ. stud., 72, 885-915, (2005) · Zbl 1136.91329
[28] W.H. Sandholm, Affine analysis and potential functions for population games, unpublished manuscript, University of Wisconsin, 2005.
[29] Sandholm, W.H.; Pauzner, A., Evolution, population growth, and history dependence, Games econ. behav., 22, 84-120, (1998) · Zbl 0892.90194
[30] Vickrey, W., Counterspeculation, auctions, and competitive sealed tenders, J. finance, 16, 8-37, (1961)
[31] Young, H.P., The evolution of conventions, Econometrica, 61, 57-84, (1993) · Zbl 0773.90101
[32] Young, H.P., Individual strategy and social structure, (1998), Princeton University Press Princeton, NJ
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.