Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Implementation Theory

  • Luis C. Corchón
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_283-2

Glossary

Equilibrium concept

A mapping (or a collection of them) from the set of states of the world into allocations yielded by equilibrium messages. This equilibrium is a game-theoretical notion of how agents behave, e.g., Nash equilibrium, Bayesian equilibrium, dominant strategies, etc.

Implementable social choice rule in an equilibrium concept (e.g., Nash equilibrium)

A social choice rule is implementable in an equilibrium concept (e.g., Nash equilibrium) if there is a mechanism such that for each state of the world, the allocations prescribed by the social choice rule and those yielded by the equilibrium concept coincide.

Mechanism

A list of message spaces and an outcome function mapping messages into allocations. It represents the communication and decision aspects of the organization.

Social choice rule

A correspondence mapping the set of states of the world in the set of allocations. It represents the social objectives that the society or its representatives want to achieve.

Sta...
This is a preview of subscription content, log in to check access.

Notes

Acknowledgments

I am grateful to Pablo Amorós, Claude d’Aspremont, Carmen Beviá, Luis Cabral, Eric Maskin, Bernardo Moreno, Carlos Pimienta, Socorro Puy, Tömas Sjöstrom, William Thomson, Matteo Triossi, Galina Zudenkova, and an anonymous referee for helpful suggestions and to the Spanish Ministry of Education for financial support under grant SEJ2005-06167. I also thank the Department of Economics, Stern School of Business, NYU, for their hospitality while writing the first draft of this survey. This survey was dedicated to Leo Hurwicz to celebrate his Nobel Prize and to the memory of those who contributed to the area and are no longer with us: Louis-André Gerard-Varet, Jean-Jacques Laffont, Richard McKelvey, and Murat Sertel.

Bibliography

  1. Abreu D, Sen A (1990) Virtual implementation in Nash equilibrium. Econometrica 59:997–1021MathSciNetzbMATHCrossRefGoogle Scholar
  2. Abreu D, Sen A (1991) Subgame perfect implementation: a necessary and almost sufficient condition. J Econ Theory 50:285–299MathSciNetzbMATHCrossRefGoogle Scholar
  3. Akerlof G The market for lemons: qualitative uncertainty and the market mechanism. Q J Econ 84:488–500Google Scholar
  4. Alcalde J, Corchón L, Moreno B (1999) Pigouvian taxes: a strategic approach. J Public Econ Theory 1(2):271–281CrossRefGoogle Scholar
  5. Amoros P (2004) Nash implementation and uncertain renegotiation. Game Econ Behav 49:424–434MathSciNetzbMATHCrossRefGoogle Scholar
  6. Amorós P (2009) Eliciting socially optimal rankings from unfair jurors. J Econ Theory 144:1211–1226MathSciNetzbMATHCrossRefGoogle Scholar
  7. Amorós P (2016) Subgame perfect implementation of the deserving winner of a competition with natural mechanisms. Math Soc Sci 83:44–57MathSciNetzbMATHCrossRefGoogle Scholar
  8. Amoros P, Corchón L, Moreno B (2002) The scholarship assignment problem. Game Econ Behav 38:1–18MathSciNetzbMATHCrossRefGoogle Scholar
  9. Arrow K (1977) The property rights doctrine and demand revelation under incomplete information. Technical report No. 243, IMSSS. Stanford University, Aug 1977Google Scholar
  10. Artemov G, Kunimoto T, Serrano R (2007) Robust virtual implementation with incomplete information: towards a reinterpretation of the Wilson doctrine. W.P. 2007-06. Brown UniversityGoogle Scholar
  11. Baliga S, Sjöström T (2007) Mechanism design: recent developments. In: Blume L, Durlauf S (eds) The new palgrave dictionary of economics, 2nd ednGoogle Scholar
  12. Baliga S, Corchón L, Sjöström T (1997) The theory of implementation when the planner is a player. J Econ Theory 77:15–33MathSciNetzbMATHCrossRefGoogle Scholar
  13. Barberá S (1983) Strategy-proofness and pivotal voters: a direct proof of the Gibbard-Satterthwaite theorem. Int Econ Rev 24:413–417MathSciNetzbMATHCrossRefGoogle Scholar
  14. Barberá S, Peleg B (1990) Strategy-proof voting schemes with continuous preferences. Soc Choice Welf 7:31–38MathSciNetzbMATHCrossRefGoogle Scholar
  15. Barberá S, Sonnenschein H, Zhou L (1991) Voting by committees. Econometrica 59(3):595–609MathSciNetzbMATHCrossRefGoogle Scholar
  16. Barberà S, Berga D, Moreno B (2010) Individual versus group strategy-proofness: when do they coincide? J Econ Theory 145:1648–1674MathSciNetzbMATHCrossRefGoogle Scholar
  17. Barberà S, Berga D, Moreno B (2016) Group strategy-proofness in private good economies. Am Econ Rev 106(4):1073–1099CrossRefGoogle Scholar
  18. Barone E (1908) The ministry of production in a collectivist state. Translated from the italian and reprinted in F. A. von Hayek Collectivist Economic Planning, Routledge and Keegan, 1935Google Scholar
  19. Benoit J-P (2000) The Gibbard-Satterthwaite theorem: a simple proof. Econ Lett 69:319–322ADSMathSciNetzbMATHCrossRefGoogle Scholar
  20. Bergemann D, Morris S (2005) Robust mechanism design. Econometrica 73:1771–1813MathSciNetzbMATHCrossRefGoogle Scholar
  21. Beviá C, Corchón L (1995) On the generic impossibility of truthful behavior. Economic Theory 6:365–371zbMATHCrossRefGoogle Scholar
  22. Beviá C, Corchón L, Wilkie (2003) Implementation of the Walrasian correspondence by market games. Rev Econ Des 7:429–442zbMATHGoogle Scholar
  23. Burguet R (1990) Revelation in informational dynamic settings. Econ Lett 33:237–239. Corrigendum (1994), 44:451–452ADSMathSciNetzbMATHGoogle Scholar
  24. Cabrales A (1999) Adaptive dynamics and the implementation problem with complete information. J Econ Theory 86:159–184MathSciNetzbMATHCrossRefGoogle Scholar
  25. Candel F (2004) Dynamic provision of public goods. Economic Theory 23:621–641MathSciNetzbMATHCrossRefGoogle Scholar
  26. Chakravorty B, Corchón L, Wilkie S (2006) Credible implementation. Game Econ Behav 57:18–36MathSciNetzbMATHCrossRefGoogle Scholar
  27. Chattopadhyay S, Corchón L, Naeve J (2000) Contingent commodities and implementation. Econ Lett 68:293–298zbMATHCrossRefGoogle Scholar
  28. Clarke E (1971) Multipart pricing of public goods. Public Choice 19–33Google Scholar
  29. Conitzer V, Sandholm T (2002) Complexity of mechanism design. In: Proceedings of the 18th annual conference on uncertainty in artificial intelligence (UAI-02), EdmontonGoogle Scholar
  30. Corchón L (1996) The theory of implementation of socially optimal decisions in economics. St. Martin’s Press, New YorkCrossRefGoogle Scholar
  31. Corchón L, Faulí-Oller R (2004) To merge or not to merge: that is the question. Rev Econ Des 9:11–30zbMATHGoogle Scholar
  32. Corchón L, Herrero C (2004) A decent proposal. Span Econ Rev 6(2):107–125CrossRefGoogle Scholar
  33. Corchón L, Ortuño-Ortín I (1995) Robust implementation under alternative information structures. Econ Des 1:159–171Google Scholar
  34. Corchón L, Puy S (2002) Existence and Nash implementation of efficient sharing rules for a commonly owned technology. Soc Choice Welf 19:369–379MathSciNetzbMATHCrossRefGoogle Scholar
  35. Corchón L, Triossi M (2011) Implementation with renegotiation when preferences and feasible sets are state dependent. Soc Choice Welf 36(2):179–198MathSciNetzbMATHCrossRefGoogle Scholar
  36. Corchón L, Wilkie S (1996) Doubly implementing the ratio correspondence by a market mechanism. Rev Econ Des 2:325–337Google Scholar
  37. d’Aspremont C, Gerard-Varet L-A (1975) Individual incentives and collective efficiency for an externality game with incomplete information. CORE DP 7519Google Scholar
  38. d’Aspremont C, Gerard-Varet L-A (1979) Incentives and incomplete information. J Public Econ 11:25–45CrossRefGoogle Scholar
  39. Dagan N, Serrano R, Volij O (1999) Feasible implementation of taxation methods. Rev Econ Des 4:57–72Google Scholar
  40. Danilov V (1992) Implementation via Nash equilibria. Econometrica 60(1):43–56MathSciNetzbMATHCrossRefGoogle Scholar
  41. Dasgupta P, Hammond P, Maskin E (1979) The implementation of social choice rules: some results on incentive compatibility. Rev Econ Stud 46:185–216MathSciNetzbMATHCrossRefGoogle Scholar
  42. Dutta B, Sen A (1991a) Implementation under strong equilibrium. A complete characterization. J Math Econ 20:49–67MathSciNetzbMATHCrossRefGoogle Scholar
  43. Dutta B, Sen A (1991b) A necessary and sufficient condition for two-person Nash implementation. Rev Econ Stud 58:121–128MathSciNetzbMATHCrossRefGoogle Scholar
  44. Dutta B, Sen A (2012) Nash implementation with partially honest individuals. Game Econ Behav 74(1):154–169MathSciNetzbMATHCrossRefGoogle Scholar
  45. Dutta B, Sen A, Vohra R (1995) Nash implementation through elementary mechanisms in economic environments. Econ Des 1:173–204Google Scholar
  46. Eliaz K (2002) Fault tolerant implementation. Rev Econ Stud 69:589–610MathSciNetzbMATHCrossRefGoogle Scholar
  47. Freixas X, Guesnerie R, Tirole J (1985) The ratchet effect. Rev Econ Stud 52:173–191zbMATHCrossRefGoogle Scholar
  48. Gerardi D, McLean R, Postlewaite A (2005) Aggregation of expert opinions. Cowles Foundation Discussion Paper # 1503Google Scholar
  49. Gibbard A (1973) Manipulation of voting schemes: a general result. Econometrica 41:587–602MathSciNetzbMATHCrossRefGoogle Scholar
  50. Green J, Laffont J-J (1979) Incentives in public decision making. North Holland, AmsterdamzbMATHGoogle Scholar
  51. Gresik T, Satterthwaite M (1989) The rate at which a simple market converges to efficiency as the number of traders increases. J Econ Theory 48:304–332zbMATHCrossRefGoogle Scholar
  52. Groves T (1973) Incentives in teams. Econometrica 41:617–631MathSciNetzbMATHCrossRefGoogle Scholar
  53. Hammond P (1987) Markets as constraints: multilateral incentive compatibility in continuum economies. Rev Econ Stud 54:399–412MathSciNetzbMATHCrossRefGoogle Scholar
  54. Harris M, Townsend R (1981) Resource allocation under asymmetric information. Econometrica 49:33–64MathSciNetzbMATHCrossRefGoogle Scholar
  55. Harsanyi J (1967/1968) Games with incomplete information played by ‘Bayesian’ players. Parts I, II and III. Manag Sci 14:159–182. 320–334 and 486–502Google Scholar
  56. Hong L (1998) Feasible Bayesian implementation with state dependent feasible sets. J Econ Theory 80:201–221MathSciNetzbMATHCrossRefGoogle Scholar
  57. Hurwicz L (1959) Optimality and informational efficiency in resource allocation processes. In: Arrow KJ (ed) Mathematical methods in the social sciences. Stanford University Press, Stanford, pp 27–46Google Scholar
  58. Hurwicz L (1972) On informationally decentralized systems. In: Radner R, McGuire CB (eds) Decision and organization: a volume in honor of Jacob Marshak. North-Holland, Amsterdam, pp 297–336Google Scholar
  59. Hurwicz L (1979) On allocations attainable through Nash equilibria. J Econ Theory 21:40–65MathSciNetzbMATHCrossRefGoogle Scholar
  60. Hurwicz L, Walker M (1990) On the generic non-optimality of dominant strategy mechanisms. Econometrica 58(3):683–704zbMATHCrossRefGoogle Scholar
  61. Hurwicz L, Maskin E, Postlewaite A (1995) Feasible Nash implementation of social choice rules when the designer does not know endowments or production set. In: Ledyard J (ed) The economics of informational decentralization: complexity, efficiency and stability. Kluwer, DordrechtGoogle Scholar
  62. Jackson M (1991) Bayesian implementation. Econometrica 59:461–477MathSciNetzbMATHCrossRefGoogle Scholar
  63. Jackson M (1992) Implementation in undominated strategies: a look to bounded mechanisms. Rev Econ Stud 59:757–775MathSciNetzbMATHCrossRefGoogle Scholar
  64. Jackson MO (2001) A crash course in implementation theory. Soc Choice Welf 18:655–708MathSciNetzbMATHCrossRefGoogle Scholar
  65. Jackson MO, Palfrey T (2001) Voluntary implementation. J Econ Theory 98:1–25MathSciNetzbMATHCrossRefGoogle Scholar
  66. Jackson MO, Palfrey T, Srivastava S (1994) Undominated Nash implementation in bounded mechanisms. Game Econ Behav 6:474–501MathSciNetzbMATHCrossRefGoogle Scholar
  67. Kalai E, Ledyard J (1988) Repeated implementation. J Econ Theory 83:308–317zbMATHCrossRefGoogle Scholar
  68. Klemperer P (1999) Auction theory, a guide to the literature. J Econ Surv 13:227–268CrossRefGoogle Scholar
  69. Koray S (2005) The need of regulating a Bayesian regulator. J Regul Econ 28:5–21CrossRefGoogle Scholar
  70. Krishna V (2002) Auction theory. Academic, San DiegoGoogle Scholar
  71. Krishna V, Perry M (1997) Efficient mechanism design. Unpublished paper, Penn State UniversityGoogle Scholar
  72. Laffont J-J, Martimort D (2001) The theory of incentives: the principal-agent model. Princeton University Press, PrincetonGoogle Scholar
  73. Laffont J-J, Maskin E (1982) The theory of incentives: an overview. In: Hildenbrand W (ed) Advances in economic theory, 4th World Congress of the Econometric Society. Cambridge University Press, New YorkGoogle Scholar
  74. Lange O (1936/1937) On the economic theory of socialism. Rev Econ Stud 4:53–71. 123–142Google Scholar
  75. Ledyard J, Roberts J (1974) On the incentive problem with public goods. Discussion Paper 116, Centre for Mathematical Studies in Economics and Management Science. Northwestern UniversityGoogle Scholar
  76. Lee J, Sabourian H (2011) Efficient repeated implementation. Econometrica 79(6):1967–1994MathSciNetzbMATHCrossRefGoogle Scholar
  77. Loeb M, Magath W (1979) A decentralized method for utility regulation. J Law Econ 22:399–404CrossRefGoogle Scholar
  78. Ma A, Moore J, Turnbull S (1988) Stop agents from cheating. J Econ Theory 46:355–372zbMATHCrossRefGoogle Scholar
  79. Macho-Stadler I, Pérez-Castrillo D, Wettstein D (2007) Sharing the surplus: an extension of the Shapley value for environments with externalities. J Econ Theory 135(1):339–356MathSciNetzbMATHCrossRefGoogle Scholar
  80. Makowski L, Mezzetti C (1993) The possibility of efficient mechanisms for trading an indivisible object. J Econ Theory 59:451–465zbMATHCrossRefGoogle Scholar
  81. Maskin E (1985) The theory of implementation in Nash equilibrium: a survey. In: Hur-wicz L, Schmeidler D, Sonnenschein H (eds) Social goals and social organization. Cambridge University Press, Cambridge, UK, pp 173–204Google Scholar
  82. Maskin E (1999) Nash equilibrium and welfare optimality. Rev Econ Stud 66(1):23–38. Circulating in working paper version since 1977MathSciNetzbMATHCrossRefGoogle Scholar
  83. Maskin E, Moore J (1999) Implementation with renegotiation. Rev Econ Stud 66:39–56MathSciNetzbMATHCrossRefGoogle Scholar
  84. Maskin E, Sjöström T (2002) Implementation theory, Chapter 5. In: Arrow KJ, Sen AK (eds) Handbook of social choice and welfare. ElsevierGoogle Scholar
  85. Matsushima H (1988) A new approach to the implementation problem. J Econ Theory 45:128–144MathSciNetzbMATHCrossRefGoogle Scholar
  86. Matsushima H (2008) Role of honesty in full implementation. J Econ Theory 139:353–359MathSciNetzbMATHCrossRefGoogle Scholar
  87. McKelvey R (1989) Game forms for Nash implementation of general social choice correspondences. Soc Choice Welf 6:139–156MathSciNetzbMATHCrossRefGoogle Scholar
  88. Mirless J (1971) An exploration in the theory of optimum income taxation. Rev Econ Stud 38:175–208CrossRefGoogle Scholar
  89. Mookherjee D, Reichelstein S (1990) Implementation via augmented revelation mechanisms. Rev Econ Stud 57:453–475MathSciNetzbMATHCrossRefGoogle Scholar
  90. Moore J (1992). Implementation, contracts and renegotiation in environments with complete information. In: Laffont J-J (ed) Advances in economic theory, 4th World Congress of the Econometric Society, vol I. Cambridge University Press, Cambridge, UK, pp 182–282Google Scholar
  91. Moore J, Repullo R (1988) Subgame perfect implementation. Econometrica 56:1191–1220MathSciNetzbMATHCrossRefGoogle Scholar
  92. Moore J, Repullo R (1990) Nash implementation: a full characterization. Econometrica 58:1083–1089MathSciNetzbMATHCrossRefGoogle Scholar
  93. Moulin H (1979) Dominance solvable voting schemes. Econometrica 47(6):1337–1351MathSciNetzbMATHCrossRefGoogle Scholar
  94. Muller E, Satterthwaite M (1977) The equivalence of strong positive association and strategy-proofness. J Econ Theory 14:412–418MathSciNetzbMATHCrossRefGoogle Scholar
  95. Myerson R (1979) Incentive compatibility and the bargaining problem. Econometrica 47:61–73MathSciNetzbMATHCrossRefGoogle Scholar
  96. Myerson R (1981) Optimal auction design. Math Oper Res 6:58–73MathSciNetzbMATHCrossRefGoogle Scholar
  97. Myerson R (1985) Bayesian equilibrium and incentive compatibility: an introduction, Chapter 8. In: Hurwicz L, Schmeidler D, Sonnenschein H (eds) Social goals and social organization. Cambridge University Press, Cambridge, UKGoogle Scholar
  98. Myerson R, Satterthwaite MA (1983) Efficient mechanisms for bilateral trading. J Econ Theory 29:265–281MathSciNetzbMATHCrossRefGoogle Scholar
  99. Palfrey TR (2002) Implementation theory. In: Aumann RJ, Hart S (eds) Handbook of game theory with economic applications, vol III. Elsevier Science, New York, pp 2271–2326Google Scholar
  100. Palfrey T, Srivastava S (1987) On Bayesian implementable allocations. Rev Econ Stud 54:193–208MathSciNetzbMATHCrossRefGoogle Scholar
  101. Palfrey T, Srivastava S (1989) Implementation with incomplete information in exchange economies. Econometrica 57:115–134MathSciNetzbMATHCrossRefGoogle Scholar
  102. Palfrey T, Srivastava S (1991) Nash implementation using undominated strategies. Econometrica 59:479–501MathSciNetzbMATHCrossRefGoogle Scholar
  103. Peleg B (1996) Double implementation of the Lindahl equilibrium by a continuous mechanism. Rev Econ Des 2(1):311–324Google Scholar
  104. Pérez-Castrillo D, Wettstein D (2002) Choosing wisely: a multi-bidding approach. Am Econ Rev 92:1577–1587CrossRefGoogle Scholar
  105. Postlewaite A. Manipulation via endowments. Rev Econ Stud 46:255–262Google Scholar
  106. Postlewaite A, Schmeidler D (1986) Implementation in differential information economies. J Econ Theory 39:14–33MathSciNetzbMATHCrossRefGoogle Scholar
  107. Prize Committee of the Royal Swedish Academy of Sciences (2007) Mechanism design theory. Royal Swedish Academy of Sciences, StockholmGoogle Scholar
  108. Reiter S (1977) Information and performance in the (new) welfare economics. Am Econ Rev 67:226–234Google Scholar
  109. Repullo R (1986) On the revelation principle under complete and incomplete information. In: Binmore K, Dasgupta P (eds) Economics organizations as games. Basil Blackwell, OxfordGoogle Scholar
  110. Repullo R (1987) A simple proof of Maskin theorem on Nash implementation. Soc Choice Welf 4:39–41MathSciNetzbMATHCrossRefGoogle Scholar
  111. Roth AE (2008) What have we learned from market design? Econ J 118:285–310Google Scholar
  112. Rothchild M, Stiglitz J (1976) Equilibrium in competitive insurance markets: an essay on the economics of imperfect information. Q J Econ 90:629–650CrossRefGoogle Scholar
  113. Rubinstein A, Wolinsky A (1992) Renegotiation-proof implementation and time preferences. Am Econ Rev 82:600–614Google Scholar
  114. Saari D (1987) The source of some paradoxes from social choice and probability. J Econ Theory 41:1–22ADSMathSciNetzbMATHCrossRefGoogle Scholar
  115. Saijo T (1988) Strategy space reduction in Maskin’s theorem. Econometrica 56:693–700MathSciNetzbMATHCrossRefGoogle Scholar
  116. Saijo T (1991) Incentive compatibility and individual rationality in public good economies. J Econ Theory 55:103–112MathSciNetzbMATHCrossRefGoogle Scholar
  117. Saijo T, Tatamitani Y, Yamato T (1996) Toward natural implementation. Int Econ Rev 37(4):949–980zbMATHCrossRefGoogle Scholar
  118. Saijo T, Sjöström T, Yamato T (2007) Secure implementation. Theor Econ 2:203–229Google Scholar
  119. Samuelson PA (1954) The pure theory of public expenditure. Rev Econ Stat 36:387–389CrossRefGoogle Scholar
  120. Sandholm W (2007) Pigouvian pricing and stochastic evolutionary implementation. J Econ Theory 132:367–382MathSciNetzbMATHCrossRefGoogle Scholar
  121. Satterthwaite (1975) Strategy-proofness and arrows conditions: existence and correspondence theorems for voting procedures and social choice functions. J Econ Theory 10:187–217MathSciNetzbMATHCrossRefGoogle Scholar
  122. Schmeidler D (1980) Walrasian analysis via strategic outcome functions. Econometrica 48:1585–1593MathSciNetzbMATHCrossRefGoogle Scholar
  123. Sen A (2001) Another direct proof of the Gibbard-Satterthwaite theorem. Econ Lett 70:381–385ADSMathSciNetzbMATHCrossRefGoogle Scholar
  124. Serizawa S (2002) Inefficiency of strategy-proof rules for pure exchange economies. J Econ Theory 106:219–241MathSciNetzbMATHCrossRefGoogle Scholar
  125. Serizawa S, Weymark J (2003) Efficient strategy-proof exchange and minimum consumption guarantees. J Econ Theory 109:246–263MathSciNetzbMATHCrossRefGoogle Scholar
  126. Serrano R (2004) The theory of implementation of social choice rules. SIAM Rev 46:377–414ADSMathSciNetzbMATHCrossRefGoogle Scholar
  127. Serrano R, Vohra R (1997) Non cooperative implementation of the core. Soc Choice Welf 14:513–525MathSciNetzbMATHCrossRefGoogle Scholar
  128. Serrano R, Vohra R (2001) Some limitation of Bayesian virtual implementation. Econometrica 69:785–792MathSciNetzbMATHCrossRefGoogle Scholar
  129. Sertel M, Samver R (1999) Equilibrium outcomes of Lindahl-endowment pretension games. Eur J Polit Econ 15:149–162CrossRefGoogle Scholar
  130. Shin S, Suh S-C (1997) Double implementation by a simple game form in the commons problem. J Econ Theory 77:205213MathSciNetCrossRefGoogle Scholar
  131. Sjöström T (1993) Implementation in perfect equilibria. Soc Choice Welf 10:97–106MathSciNetzbMATHCrossRefGoogle Scholar
  132. Sjöström T (1994) Implementation in undominated Nash equilibrium without integer games. Game Econ Behav 6:502–511MathSciNetzbMATHCrossRefGoogle Scholar
  133. Sjöström T (1996) Implementation by demand mechanisms. Econ Des 1:343–354Google Scholar
  134. Spence M (1973) Job market signalling. Q J Econ 87:355–374CrossRefGoogle Scholar
  135. Taylor FM (1929) The guidance of production in a socialist state. Am Econ Rev 19:1–8Google Scholar
  136. Thomson W (1985) Manipulation and implementation in economics. Unpublished manuscript, RochesterGoogle Scholar
  137. Thomson W (1987) The vulnerability to manipulative behavior of economic mechanisms designed to select equitable and efficient outcomes, Chapter 14. In: Groves T, Radner R, Reiter S (eds) Information, incentives and economic mechanisms. University of Minnesota Press, pp 375–396Google Scholar
  138. Thomson W (1996) Concepts of implementation. Jpn Econ Rev 47:133–143CrossRefGoogle Scholar
  139. Thomson W (2005) Divide and permute. Game Econ Behav 52:186–200MathSciNetzbMATHCrossRefGoogle Scholar
  140. Tian G (1996) On the existence of optimal truth-dominant mechanisms. Econ Lett 53:17–24zbMATHCrossRefGoogle Scholar
  141. Tian G, Li Q (1995) On Nash-implementation in the presence of withholding. Game Econ Behav 9:222–233MathSciNetzbMATHCrossRefGoogle Scholar
  142. Vickrey W (1961) Counterspeculation, auctions and competitive sealed tenders. J Financ 16:8–37MathSciNetCrossRefGoogle Scholar
  143. Walker M (1981) A simple incentive compatible scheme for attaining Lindahl allocations. Econometrica 49:65–73MathSciNetzbMATHCrossRefGoogle Scholar
  144. Williams S (1986) Realization of Nash implementation: two aspects of mechanism design. Econometrica 54:139–151MathSciNetzbMATHCrossRefGoogle Scholar
  145. Williams S (1999) A characterization of efficient, Bayesian incentive compatible mechanisms. Economic Theory 14:155–180MathSciNetzbMATHCrossRefGoogle Scholar
  146. Yamato T (1993) Double implementation in Nash and undominated Nash equilibria. J Econ Theory 59(2):311–323MathSciNetzbMATHCrossRefGoogle Scholar
  147. Yamato T (1994) Equivalence of Nash implementability and robust implementability with incomplete information. Soc Choice Welf 11:289–303MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  1. 1.Departamento de EconomíaUniversidad Carlos IIIMadridSpain