A note on Abreu-Matsushima mechanisms
Article Abstract:
D. Abreu and H. Matsushima's 1992 paper on the implementation of social choice functions in strategies that are iteratively undominated is criticized. The mechanisms used generate games wherein the iterative removal of strategies that are strongly dominated is subject to dispute. Analysis of examples of two-player coordination games with varying assumptions indicates that while Abreu and Matsushima's non-fine mechnism applies to a number of social-choice functions, it is based on a game in which the desired result is produced regardless of the existence of a countervailing focal point.
Publication Name: Econometrica
Subject: Mathematics
ISSN: 0012-9682
Year: 1992
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A response to Glazer and Rosenthal
Article Abstract:
J. Glazer and R.W. Rosenthal state that the mechnisms used to implement social-choice functions in iteratively undominated strategies lead to controversial games with iterative removal of strategies that are strictly dominated. However, iterative logic is accepted in conventional decision theory. Common knowledge of rationality, paradoxes of which are cited as criticisms, is necessary in the logic of iterative dominance, but the mechanisms in question are simultaneous and thus preclude the rationalization of iteratively dominated behavior.
Publication Name: Econometrica
Subject: Mathematics
ISSN: 0012-9682
Year: 1992
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Virtual implementation in iteratively undominated strategies: complete information
Article Abstract:
A study was done to analyze social choice functions (scf's) in complete information environments. The implementation of these functions in iteratively undominated strategies is examined. Results show that an scf is implementable in iteratively undominated strategies if there are three or more players with small domain constraints. The study focuses only on finite mechanisms.
Publication Name: Econometrica
Subject: Mathematics
ISSN: 0012-9682
Year: 1992
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