Existence of optimal auctions in general environments
Article Abstract:
A general existence result for a specific Stackelberg revelation game is established to arrive at a standard approach to the problem of existence of optimal auctions for a a wide array of auction environments. When systematically specializing the revelation game to include different types of auctions, the presence of optimal Bayesian auction mechanisms for single and multiple unit auctions and for contract auctions with moral hazard and adverse selection are deduced.
Publication Name: The Journal of Mathematical Economics
Subject: Mathematics
ISSN: 0304-4068
Year: 1998
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Unified treatment of the problem of existence of maximal elements in binary relations: a characterization
Article Abstract:
Analysis of maximal elements in binary relations reveals that there is an existence result that covers both convexity and acyclicity analyses of non-transitive binary relation maximal elements. The study also reveals that there is an abstract convexity structure that generalizes the notion of usual convexity. The study reveals that the statement covering maximal elements and the concept may be used as a powerful tool in solving maximal element problems.
Publication Name: The Journal of Mathematical Economics
Subject: Mathematics
ISSN: 0304-4068
Year: 1998
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Variations on the measure representation approach
Article Abstract:
Analysis of the measure representation approach reveals that additive utility theorems of Debreu and Gorman allows for the existence of a measure representation theorem for increasing and continuous real-valued functions. The proof may be modified to yeild another measure representation theorem for functions of bounded variation when considering preference relation epigraphs or hypographs.
Publication Name: The Journal of Mathematical Economics
Subject: Mathematics
ISSN: 0304-4068
Year: 1998
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