This chapter forms the first part of the monograph and presents key concepts and results in mechanism design. The second part of the monograph explores application of mechanism design to contemporary problems in network economics. The chapter comprises 21 sections that can be logically partitioned into four groups. Sections 2.1 through 2.5 constitute Group 1, and they set the stage by describing essential aspects of game theory for understanding mechanism design. The five sections deal with strategic form games, dominant strategy equilibria, pure strategy Nash equilibria, mixed strategy Nash equilibria, and Bayesian games. Sections 2.6 through 2.12 constitute the next group of sections, and they deal with fundamental notions and results of mechanism design. The sections include a description of the mechanism design environment, social choice functions, implementation of social choice functions by mechanisms, incentive compatibility and revelation theorem, properties of social choice functions, the Gibbard-Satterthwaite impossibility theorem, and the Arrow’s impossibility theorem. Following this, the sections in the third group (Sections 2.13 – 2.20) present useful mechanisms that provide the building blocks for solving mechanism design problems. The sections here include: The quasilinear environment, Groves mechanisms, Clarke mechanisms, examples of VCG mechanisms, the dAGVA mechanism, Bayesian mechanisms in linear environment, revenue equivalence theorem, and optimal auctions. Finally, in Section 2.21, we provide a sprinkling of further key topics in mechanism design. The chapter uses a fairly large number of stylized examples of network economics situations to illustrate the notions and the results.
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References
R.B. Myerson. Game Theory: Analysis of Conflict. Harvard University Press, Cambridge, Massachusetts, 1997.
J. von Neumann and O. Morgenstern. Theory of Games and Economic Behavior. Princeton University Press, 1944.
R. Aumann. Agreeing to disagree. The Annals of Statistics, 4(6):1236–1239, 1976.
E. Tardos and V.V. Vazirani. Basic solution concepts and computational issues. In N. Nisan, T. Roughgarden, E. Tardos, and V.V. Vazirani, (eds.), Algorithmic Game Theory, pages 3–28. Cambridge University Press, New York, 2007.
J. Bertrand. Book review of theorie mathematique de la richesse sociale and of recherches sur les principles mathematiques de la theorie des richesses. Journal de Savants, 67:499–508, 1883.
A. Mas-Colell, M.D. Whinston, and J.R. Green. Microeconomic Theory. Oxford University Press, New York, 1995.
R.D. McKelvey and A. McLennan. Computation of equilibria in finite games. In J. Rust H.M. Amman, D.A. Keudrick, (eds.), Handbook of Computational Economics, Handbooks in Economics (13), Volume 1, pages 87–142. North-Holland, Amsterdam, 1996.
C.H. Papadimitriou. The complexity of finding nash equilibria. In N. Nisan, T. Roughgarden, E. Tardos, and V.V. Vazirani, (eds.), Algorithmic Game Theory, pages 29–52. Cambridge University Press, New York, 2007.
B.V. Stengel. Equilibrium computation for two-player games in strategic and extensive form. In N. Nisan, T. Roughgarden, E. Tardos, and V.V. Vazirani, (eds.), Algorithmic Game Theory, pages 53–78. Cambridge University Press, New York, 2007.
L. Hurwicz. On informationally decentralized systems. In C.B. McGuire and R. Radner, (eds.), Decision and Organization, North-Holland, Amsterdam, 1972.
L. Hurwicz. Optimality and informational efficiency in resource allocation processes. In K.J. Arrow, S. Karlin and P. Suppes (eds.), Mathematical Methods in the Social Sciences. Stanford University Press, Palo Alto, California, USA, 1960.
B. Holmstrom and R.B. Myerson. Efficient and durable decision rules with incomplete information. Econometrica, 51(6):1799–1819, 1983.
A. Gibbard. Manipulation of voting schemes. Econometrica, 41:587–601, 1973.
M.A. Satterthwaite. Strategy-proofness and Arrow's conditions: Existence and correspondence theorem for voting procedure and social welfare functions. Journal of Economic Theory, 10:187–217, 1975.
W. Vickrey. Counterspeculation, auctions, and competitive sealed tenders. Journal of Finance, 16(1):8–37, 1961.
E. Clarke. Multi-part pricing of public goods. Public Choice, 11:17–23, 1971.
T. Groves. Incentives in teams. Econometrica, 41:617–631, 1973.
J.R. Green and J.J. Laffont. Incentives in Public Decision Making. North-Holland, Amsterdam, 1979.
L.M. Ausubel and P. Milgrom. The lovely but lonely vickrey auction. In P. Cramton, Y. Shoham, and R. Steinberg, (eds.), Combinatorial Auctions, pages 17–40. The MIT Press, Cambridge, Massachusetts, 2006.
M. Rothkopf. Thirteen reasons why the Vickrey-Clarke-Groves process is not practical. Operations Research, 55(2):191–197, 2007.
C. Caplice and Y. Sheffi. Combinatorial auctions for truckload transportation. In P. Cramton, Y. Shoham, and R. Steinberg, (eds.), Combinatorial Auctions, pages 539–572. The MIT Press, Cambridge, Massachusetts, 2005.
C. d'Aspremont and L.A. G'erard-Varet. Incentives and incomplete information. Journal of Public Economics, 11:25–45, 1979.
K. Arrow. The property rights doctrine and demand revelation under incomplete information. In M. Boskin, (eds.), Economics and Human Welfare. Academic Press, New York, 1979.
R.B. Myerson. Optimal auction design. Mathematics of Operations Research, 6(1):58–73, 1981.
P.R. McAfee and J. McMillan. Auctions and bidding. Journal of Economic Literature, 25(2):699–738, 1987.
P. Klemperer. Why every economist should learn some auction theory. In M. Dewatripont, L. Hansen, and S. Turnovsky, (eds.), Advances in Economics and Econometrics: Invited Lectures to 8th World Congress of the Econometric Society. Cambridge University Press, Cambridge, UK, 2003.
P. Milgrom. Putting Auction Theory to Work. Cambridge University Press, Cambridge, UK, 2004.
V. Krishna. Auction Theory. Academic Press, San Diego, California, USA, 2002.
D. Garg, Y. Narahari, and S. Gujar. Foundations of mechanism design: A tutorial – Part 1: Key Concepts and Classical Results. Sadhana — Indian Academy Proceedings in Engineering Sciences, 33(2):83–130, 2008.
J.G. Riley and W.F. Samuelson. Optimal auctions. American Economic Review, 71(3):383–92, 1981.
K. Roberts. The characterization of implementable choice rules. In J.J. Laffont, (eds.), Aggregation and Revelation of Preferences, pages 321–349, Amsterdam, 1979.
R. Lavi, A. Mu'alem, and N. Nisan. Two simplified proofs for Roberts' theorem. Technical report, Working Paper, School of Computer Science and Engineering, The Hebrew University of Jerusalem, Israel, 2004.
D. Mookherjee and S. Reichelstein. Dominant strategy implementation of Bayesian incentive compatible allocation rules. Journal of Economic Theory, 56(2):378–399, 1992.
E. Maskin. Nash equilibrium and welfare optimality. Review of Economic Studies, 66:23–38, 1999.
P. Dasgupta, P. Hammond, and E. Maskin. The implementation of social choice rules: some general results on incentive compatibility. Review of Economic Studies, 46:181–216, 1979.
J. Cremer and R.P McLean. Optimal selling strategies under uncertainty for a discriminating monopolist when demands are interdependent. Econometrica, 53(2):345–61, 1985.
The Nobel Foundation. The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2007: Scientific Background. Technical report, The Nobel Foundation, Stockholm, Sweden, December 2007.
J.K. Kalagnanam and D.C. Parkes. Auctions, bidding, and exchange design. In D. Simchi-Levi, S.D. Wu, and Z.J. Shen, (eds.), Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era. Kluwer Academic Publishers, New York, 2005.
T. Sandholm. Computing in mechanism design. In S.N. Durlauf and L.E. Blume, (eds.), The New Palgrave Dictionary of Economics. Second Edition, Palgrave Macmillan, 2008.
S. de Vries and R.V. Vohra. Combinatorial auctions: A survey. INFORMS Journal of Computing, 15(1):284–309, 2003.
S. de Vries and R.V. Vohra. Design of combinatorial auctions. In Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era, pages 247–292. International Series in Operations Research and Management Science, Kluwer Academic Publishers, Norwell, MA, USA, 2005.
J.J. Laffont. Fundamentals of Public Economics. The MIT Press, Cambridge, Massachusetts, 1988.
N. Nisan. Introduction to mechanism design (for computer scientists). In N. Nisan, T. Roughgarden, E. Tardos, and V.V. Vazirani (eds.), Algorithmic Game Theory, pages 209–242. Cambridge University Press, New York, 2007.
R. Myerson. Mechanism design. In J. Eatwell, M. Milgate, and P. Newman (eds.), The New Palgrave Dictionary of Economics, pages 191–206. Norton, New York, 1989.
R. Serrano. The theory of implementation of social choice rules. SIAM Review, 46:377–414, 2004.
M.O. Jackson. A crash course in implementation theory. Social Choice and Welfare, 18:655–708, 2001.
M.O. Jackson. Mechanism theory. In U. Derigs (ed.), Encyclopedia of Life Support Systems. EOLSS Publishers, Oxford, U.K., 2003.
N. Nisan, T. Roughgarden, E. Tardos, and V.V. Vazirani (eds.). Algorithmic Game Theory. Cambridge University Press, New York, 2007.
P. Milgrom. Auctions and bidding: A primer. Journal of Economic Perspectives, 3(3):3–22, 1989.
P. Klemperer. Auctions: Theory and Practice. The Toulouse Lectures in Economics. Princeton University Press, Princeton, NJ, USA, 2004.
E. Wolfstetter. Auctions: An introduction. Economic Surveys, 10:367–421, 1996.
A. Pekec and M.H. Rothkopf. Combinatorial auction design. Management Science, 49:1485–1503, 2003.
P. Klemperer Auctions: Theory and Practice. Princeton University Press, Princeton, NJ, USA, 2004.
Y. Narahari and P. Dayama. Combinatorial auctions for electronic business. Sadhana — Indian Academy Proceedings in Engineering Sciences, 30(2-3):179–212, 2005.
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Narahari, Y., Narayanam, R., Garg, D., Prakash, H. (2009). Foundations of Mechanism Design. In: Game Theoretic Problems in Network Economics and Mechanism Design Solutions. Advanced Information and Knowledge Processing. Springer, London. https://doi.org/10.1007/978-1-84800-938-7_2
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