### Modelling and computational simulation of optimal auction design and bidding strategies

Masiala Mavungu, Evan Hurwitz, Tshilidzi Marwala
Journal of Economic and Financial Sciences | Vol 12, No 1 | a415 | DOI: https://doi.org/10.4102/jef.v12i1.415 | © 2019 Masiala Mavungu, Evan Hurwitz, Tshilidzi Marwala | This work is licensed under CC Attribution 4.0
Submitted: 07 September 2018 | Published: 30 October 2019

Masiala Mavungu, Department of Electrical and Electronic Engineering, University of Johannesburg, Johannesburg, South Africa
Evan Hurwitz, Department of Electrical and Electronic Engineering, University of Johannesburg, Johannesburg, South Africa
Tshilidzi Marwala, Department of Electrical and Electronic Engineering, University of Johannesburg, Johannesburg, South Africa

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#### Abstract

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.

#### Keywords

auction design; bidding strategy; optimal auction; open ascending-bid auction; first-price bid auction; combinatorial auction; mathematical models; computational simulations

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