ASBS PhD student awarded IMA Catherine Richards Prize

ASBS PhD student awarded IMA Catherine Richards Prize

Issued: Thu, 22 Sep 2016 15:20:00 BST

Josue OrtegaThe panel of Mathematics Today, a publication from the Institute of Mathematics & its Applications (IMA), have awarded the Early Career Mathematicians (ECM) Catherine Richards Prize to Josue Ortega for his article entitled ‘Playing Tennis without Envy’.

Josue, a current Adam Smith Business School PhD student, is an economist whose research interests lie in game theory and market and mechanism design.  The Catherine Richards prize is awarded annually for the best article on any mathematical topic including pure, applied, teaching, and case studies.

Playing Tennis without Envy addresses a fair division problem from a different perspective.  In a standard fair division problem several agents attempt to divide some scarce objects and search for division procedures that are fair for everyone.  However, this division problem becomes more interesting when money can’t be used. 

In his article Josue studies a variant of this problem.  Think of a person who has to create the tennis schedule for a group of friends.  Her friends tell her on which days of the week they are available for her to create a schedule of double tennis matches.  She only has two constraints.  Firstly, no person plays on a day she is not available, and secondly, each person plays at most once a day.  What we try to find is an algorithm that produces a fair and non-envious outcome.  In classical assignment problems, such algorithms exist and we can compute them quickly. 

However, in this tennis problem such algorithms fail.  In fact, what Josue shows is that any algorithm is bounded to fail because those properties are not compatible.  This implies that many questions remain open about how to assign complimentary items using procedures that do not reply on money.  In this instance, the tennis problem is a mathematical metaphor that captures several real-world applications.  In a second article, together with Professor Herve Moulin, Josue studies further, more complex, alternatives.  This area of research lies between economics, mathematics and computer science.

Playing Tennis without Envy will appear in the December edition of Mathematics Today.


For further information please contact Emma Ferrier: business-marketing@glasgow.ac.uk

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