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Small Verifiability in Long-Term Relationships

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Author Info
Hitoshi Matsushima (Faculty of Economics, Universtiy of Tokyo)

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Abstract

This paper investigates a finitely repeated game at the beginning of which players agree to write an explicit contract with full commitment. This contract conditions the budget-balancing vector of side payments on the complete history of their action choices. However, this history is not always verifiable to the court, and each player's liability is severely limited. We show, in the general case, that even if the probability of the complete history being verifiable is small and the amount of possible fines is negligible compared with the differences in long-run payoffs, every efficient payoff vector induced by an action profile, which Pareto-dominates a Nash equilibrium action profile, is uniquely and exactly implementable either in terms of perfect equilibrium or in terms of perfect iterative undominance. Moreover, we show, in a wide class of component games, that even if this probability is close to zero and the amount of fines is negligible compared with the differences not only in long-run payoffs but also in instantaneous payoffs, every efficient payoff vector induced by an action profile, which Pareto-dominates a Nash equilibrium action profile, is uniquely and virtually implementable either in terms of perfect equilibrium or in terms of perfect iterative undominance.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-98.

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Length: 39 pages
Date of creation: Dec 2000
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Handle: RePEc:tky:fseres:2000cf98

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  20. Legros, Patrick & Matsushima, Hitoshi, 1991. "Efficiency in partnerships," Journal of Economic Theory, Elsevier, vol. 55(2), pages 296-322, December. [Downloadable!] (restricted)
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  26. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September. [Downloadable!] (restricted)
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  1. Hitoshi Matsushima, 2002. "Finitely Repeated Games with Small Side Payments," CIRJE F-Series CIRJE-F-179, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
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