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Secure Implementation in Production Economies

One thing that has been assumed for a long time is that whenever there is dominant strategy equilibrium in the game form of any mechanism and the outcome corresponding to that strategy profile is socially optimal, people will play that particular equilibrium strategy pro?le. The theory has been silent on why they will play that particular strategy pro?le when there are other (Nash) equilibria. The Nash/Bayes' Nash implementation being a possible solution to this problem suffers from the drawback of either the requirement of the designer knowing the (common) prior (in case of Bayes' Nash implementation) or the requirement of the players predicting the actions of other players and collaborate without pre-talk (in case of Nash implementation with absence of dominant strategy or unique Nash). Secure implementation [Saijo et al. (2007)] is a relatively new concept in the theory of mechanism design and implementation. This requires double implementation in Dominant Strategy Equilibrium and Nash Equi- librium by the same Mechanism. This concept has worked well in some particular environments and has been tested on data [Cason et al. (2006)]. Unsurprisingly, being stronger than both the two above said concepts of implementation, there are many impossibility results in specific environ- ments with richer domains. We look for secure implementability in pro- duction economies with divisible goods. We find that a very broad gener- alization of "Serial" Social Choice Function (SCF) [Moulin and Shenker (92)] as defined in [Shenker (92)] is securely implementable. We call such functions as Generalized Serial SCF (GSS). We also find that under cer- tain conditions the Fixed Path SCFs are special cases of GSS and thus they are also securely Implementable. We conjecture that these are the only securely impleme

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Paper provided by Department of Economics, Louisiana State University in its series Departmental Working Papers with number 2011-02.

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Handle: RePEc:lsu:lsuwpp:2011-02
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  1. Justin Leroux, 2007. "Cooperative production under diminishing marginal returns: interpreting fixed-path methods," Social Choice and Welfare, Springer, vol. 29(1), pages 35-53, July.
  2. Tatsuyoshi Saijo & Timothy N. Cason & Tomas Sjostrom, 2003. "Secure Implementation Experiments:Do Strategy-proof Mechanisms Really Work?," Discussion papers 03012, Research Institute of Economy, Trade and Industry (RIETI).
  3. Sjostrom, Tomas & Yamato, Takehiko & Saijo, Tatsuyoshi, 2007. "Secure implementation," Theoretical Economics, Econometric Society, vol. 2(3), September.
  4. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  5. Yuji Fujinaka & Takuma Wakayama, 2007. "Secure Implementation in Economies with Indivisible Objects and Money," ISER Discussion Paper 0699, Institute of Social and Economic Research, Osaka University.
  6. Friedman, Eric & Moulin, Herve, 1999. "Three Methods to Share Joint Costs or Surplus," Journal of Economic Theory, Elsevier, vol. 87(2), pages 275-312, August.
  7. Sprumont, Y., 1996. "Ordinal Cost Sharing," Cahiers de recherche 9624, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Satterthwaite, Mark A & Sonnenschein, Hugo, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Wiley Blackwell, vol. 48(4), pages 587-97, October.
  9. Watts, Alison, 1996. "On the Uniqueness of Equilibrium in Cournot Oligopoly and Other Games," Games and Economic Behavior, Elsevier, vol. 13(2), pages 269-285, April.
  10. Koster, M.A.L. & Tijs, S.H. & Borm, P.E.M., 1998. "Serial cost sharing methods for multi-commodity situations," Other publications TiSEM 6633be50-672a-42f3-a966-8, Tilburg University, School of Economics and Management.
  11. Leroux, Justin, 2008. "Profit sharing in unique Nash equilibrium: Characterization in the two-agent case," Games and Economic Behavior, Elsevier, vol. 62(2), pages 558-572, March.
  12. Maurice Koster, 2007. "The Moulin–Shenker rule," Social Choice and Welfare, Springer, vol. 29(2), pages 271-293, September.
  13. Bochet, Olivier & Sakai, Toyotaka, 2010. "Secure implementation in allotment economies," Games and Economic Behavior, Elsevier, vol. 68(1), pages 35-49, January.
  14. Kolpin, Van, 1996. "Multi-Product Serial Cost Sharing: An Incompatibility with the Additivity Axiom," Journal of Economic Theory, Elsevier, vol. 69(1), pages 227-233, April.
  15. repec:ner:tilbur:urn:nbn:nl:ui:12-78039 is not listed on IDEAS
  16. Eric Friedman & Scott Shenker, 1998. "Learning and Implementation on the Internet," Departmental Working Papers 199821, Rutgers University, Department of Economics.
  17. Friedman, Eric J., 2002. "Strategic properties of heterogeneous serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 145-154, November.
  18. Milgrom, Paul & Roberts, John, 1991. "Adaptive and sophisticated learning in normal form games," Games and Economic Behavior, Elsevier, vol. 3(1), pages 82-100, February.
  19. Dasgupta, Partha S & Hammond, Peter J & Maskin, Eric S, 1979. "The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 185-216, April.
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