Game Theory

A crash course in implementation theory by Jackson M.O. PDF

By Jackson M.O.

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4, pp. 49 65. Barber a, S. and C. Bevia 1998, ," mimeo: Universitat Autonoma de Barcelona. Bergin, J. 1993, On Some Recent Results in Incomplete Information Implementation," mimeo: Queen's University. Bergin, J. and A. Sen 1996, Implementation in Generic Environments," Social Choice and Welfare, Vol. 13, pp. 467 478. Bergin, J. and A. Sen 1998, Extensive Form Implementation in Incomplete Information Environments," Journal of Economic Theory, Vol. 80, pp. 222 256. 48 Bergin, J. and J. Duggan 1999, An Implementation Theoretic Approach to Non- Cooperative Foundations," Journal of Economic Theory, Vol.

Short of this, we are lacking Again, Abreu and Matsushima 1992a provide a good deal of insight into this question for virtual implementation. The reason for considering the exact setting would be to loosen assumptions on preferences and sensitivity to small probability events under the lotteries. 61This holds provided one worries about mixed strategies, which Duggan and Roberts point to as another reason for accounting for mixed strategies in implementation. 60 43 even a basic understanding of the exact limitations that are imposed by requiring implementation by mechanisms that are robust to misspeci cations of the domain of preferences, beliefs, allocations, or even the number or role of various individuals in a society.

58See Jackson and Palfrey 1998b for a uni ed approach to dealing with renegotiation, outside options, and replay of the mechanism, in more abstract settings, with some applications to exchange economies. 59Including the planner as a player has an interesting theoretical byproduct: the planner is part of 57 41 which case one can explicitly account for the planner's preferences and behavior with regards to enforcing an outcome. In all of the above work there are two forces at work. On the one hand, allowing for movement away from ex-post undesirable outcomes can be improving just by itself since truly undesirable outcomes are eliminated automatically.

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