Modelling and computational simulation of optimal auction design and bidding strategies

Abstract

Orientation: This article is related to Finances and Optimisation. The auctioneer designs every auction mechanism such that utility is maximised and cost is minimised. Research purpose: This article proposes an optimal auction mechanism through which auctioneers can assign fairly and efficiently assets to the highest bidders and maximise utility and/or minimise cost. Motivation for the study: One of the tasks of my PhD was about spectrum auction from which I got a vision to design mathematical models and related computational simulations for any asset underlying an auction. Research approach/design and method: Firstly, a study was conducted to model the way auctioneers could analyse and estimate bidders’ (buyers’) valuations, and then, accordingly, set the prices of the underlying assets or services. An open ascending-bid auction mechanism was also considered. Finally, a first-price sealed-bid auction mechanism for utility maximisation and cost minimisation is investigated. Main findings: The substantive contribution of this article is in the set of mathematical models and computational simulations designed and proposed for the bidders’ valuations and the considered open ascending-bid auction. For the investigated first-price sealed-bid auction mathematical models are developed in terms of a combinatorial optimisation problem. The formula computing the expected utility for the auctioneer was designed. Practical/managerial implications: The research provides rigorous ways for optimal auction design to auctioneers and any financial operators or managers. Contribution/value-add: The contributions are in the set of mathematical models and computational simulations. This article models the optimal auction design strategy mechanism as a combinatorial optimisation problem.