The Centre for Doctoral Training MAC-MIGS will provide advanced training in the formulation, analysis, and implementation of state-of-the-art mathematical and computational models. The vision for the training offered is that effective modern modelling must integrate data with laws framed in explicit, rigorous mathematical terms. The CDT will offer 76 PhD students an intensive 4-year training and research programme that equips them with the skills needed to tackle the challenges of data-intensive modelling. The new generation of successful modelling experts will be able to develop and analyse mathematical models, translate them into efficient computer codes that make best use of available data, interpret the results, and communicate throughout the process with users in industry, commerce and government. Mathematical and computational models are at the heart of 21st-century technology: they underpin science, medicine and, increasingly, social sciences, and impact many sectors of the economy including high-value manufacturing, healthcare, energy, physical infrastructure and national planning. When combined with the enormous computing power and volume of data now available, these models provide unmatched predictive tools which capture systematically the experimental and observational evidence available. Because they are based on sound deductive principles, they are also the only effective tool in many problems where data is either sparse or, as is often the case, acquired in conditions that differ from the relevant real-world scenarios. Developing and exploiting these models requires a broad range of skills - from abstract mathematics to computing and data science - combined with expertise in application areas. MAC-MIGS will equip its students with these skills through a broad programme that cuts across disciplinary boundaries to include mathematical analysis - pure, applied, numerical and stochastic - data-science and statistics techniques and the domain-specific advanced knowledge necessary for cutting-edge applications. MAC-MIGS students will join the broader Maxwell Institute Graduate School in its brand-new base located in central Edinburgh. They will benefit from (i) dedicated academic training in subjects that include mathematical analysis, computational mathematics, multi-scale modelling, model reduction, Bayesian inference, uncertainty quantification, inverse problems and data assimilation, and machine learning; (ii) extensive experience of collaborative and interdisciplinary work through projects, modelling camps, industrial sandpits and internships; (iii) outstanding early-career training, with a strong focus on entrepreneurship; and (iv) a dynamic and forward-looking community of mathematicians and scientists, sharing strong values of collaboration, respect, and social and scientific responsibility. The students will integrate a vibrant research environment, closely interacting with some 80 MAC-MIGS academics comprised of mathematicians from the universities of Edinburgh and Heriot-Watt as well as computer scientists, engineers, physicists and chemists providing their own disciplinary expertise. Students will benefit from MAC-MIGS's diverse network of more than 30 industrial and agency partners spanning a broad spectrum of application areas: energy, engineering design, finance, computer technology, healthcare and the environment. These partners will provide internships, development programmes and research projects, and help maximise the impact of our students' work. Our network of academic partners representing ten leading institutions in the US and Europe, will further provide opportunities for collaborations and research visits.

This proposal is motivated by the need to reduce the public deficit. One way to do this is by achieving efficiency savings in procurement for large public institutions such as the National Health Service, city councils, or the Ministry of Defence. We propose to contribute towards this goal by attempting to better align the stylised theoretical analysis of tendering - a form of trading mechanism - with the facts on the ground. The focus of our study is the provision and use of information in the tendering process, building on two recent methodological developments: "Information Design" and "Simple Auctions". Trading mechanisms have been the subject of a great deal of study, especially in the last half a century. More recently, the enormously successful sale of the 3G mobile phone licences by simultaneous auctions - £22.5 billion was raised for the public purse and the band of radio frequency was efficiently assigned - in 2000, provided vivid evidence of how useful this theory can be. The literature on "auctions" is focussed on finding the optimal trading mechanism, which maximizes expected benefits. However, on the one hand, this optimization assumes that the information available to the bidders is predetermined. This is often too strong an assumption as the bid taker may have significant leeway in choosing what information to gather and disclose. On the other hand, the optimization traditionally leaves both the complexity of the mechanism and its use of the information revealed by the bidders unconstrained. This often results in very complicated "optimal" mechanisms, which are hard to implement in practice. We propose to push out the research frontier by analysing what information, and in which form, is presented to the potential traders and how information revealed by them is used by the designer to determine prices and trades. The first of these novel ideas is information design: the optimal provision of information to a group of interacting agents by a designer with a certain objective. By strategically choosing its method for scoring the bids and by seeking out and revealing additional facts that might affect the cost of suppliers, the designer can create interdependence between the agents' information; this can then be exploited through the competitive bidding process, ultimately benefiting the designer's objective. The second idea is based on the observation that due to the complex objective of the buyer (quality, timing, transparency, sustainability etc. in addition to price) most actual tenders are multi-dimensional: the bids submitted include several different factors besides price. While a pre-announced scoring rule can transform these bids into readily comparable one-dimensional scores, it does not eliminate the complexity of bids and of the bidders' beliefs about the bids of others. For practical reasons, the designer needs to compensate for this innate complication by simplifying the mechanism, resulting in additional restrictions on the set of mechanisms she can choose from. These restrictions imply that families of mechanisms previously discarded as sub-optimal, now become relevant. To capture this scenario, we analyse decentralised mechanisms, where conditional on trading, prices are independent of the bids of competitors. In the context of scoring auctions, this would correspond to a discriminatory "first-score" auction. According to the existing theoretical literature, when the quantity traded is not set beforehand, these auctions are not optimal. Together, these two approaches make it possible to advance our understanding of issues like simultaneous bidding and realistic mechanisms that deal with interdependent valuations. While doing that we will also pay particular attention not to be hemmed in by the artificial boundary between micro- and macro-economic analyses, so that our insights can be exported to system-wide markets, such as the labour and credit markets.