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52See Dutta and Sen 1991c for more on the necessary and su cient conditions for Bayesian implementation. 53See also Matsushima 1993. 54Other natural extensions of complete information implementation to incomplete information set49 39 generalization, but instead several. This is due to the variety of alternative formulations of sequential rationality under incomplete information. In particular, varying assumptions about how individuals update beliefs o the equilibrium path results in alternative solution concepts to be used in implementation.

1998, Coalition-Proof Implementation," Journal of Economic Theory, Vol. 82, pp. 132 143. Brusco, S. 1995, Perfect Bayesian Implementation," Economic Theory, Vol. 5, pp. 419 444. Brusco, S. 1997a, Implementing Action Pro les when Agents Collude," Journal of Economic Theory, Vol. 73, pp. 395 424. Brusco, S. 1997b, Implementation with Extensive Form Games: One Round of Signaling is not Enough," forthcoming in the Journal of Economic Theory. Brusco, S. 1998a, Implementing Action Pro les with Sequential Mechanisms," Review of Economic Design, Vol.

73, pp. 460 472. Bagnoli, M. and B. Lipman 1989, Provision of Public Goods: Fully Implementing the Core through Private Contributions," Review of Economic Studies, Vol. 56, pp. 583 601. Baliga, S. 1999, Implementation in Economic Environments with Incomplete Information: The Use of Multi-Stage Games," Games and Economic Behavior, Vol. 27, pp. 173 183. Baliga, S. and S. Brusco 1996, Collusion, Renegotiation, and Implementation," mimeo. , L. Corchon, and T. Sjostrom 1997, The Theory of Implementation When the Planner is a Player," Journal of Economic Theory, Vol.

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