Myerson's Lemma under Fuzzy Valuation

Abstract

The paper explores extending Myerson’s lemma, a key concept in mechanism design, to situations where participants' valuations are imprecise. Traditional game theory assumes precise valuations, but real-world scenarios often involve uncertainties. By introducing fuzzy set theory, the paper addresses this issue, allowing valuations to be represented as fuzzy numbers. The study proves that even under fuzzy valuations, the auction mechanism can still satisfy dominant strategy incentive compatibility (DSIC). Practical applications are discussed, including auctions in online advertising where click-through rates (CTR) are uncertain. The paper demonstrates how fuzzy valuation can ensure fairness and efficiency in these auctions, offering a more realistic approach to mechanism design in uncertain environments.