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  ,  Applications accepted all year round  Competition Funded PhD Project (Students Worldwide)

About the Project

Algorithmic contract theory is a new research field aiming to align the well-established field of contract theory with the new reality of cryptocurrency-based contracts. Contracts of all types facilitate trust and cooperation among various entities including in multi-agent settings where agents operate in uncertain conditions by employing various AI techniques. This project aims to build that trust through the application of smart contracts.

Classic contract theory encapsulates mathematical depth and (naturally) many applications. In 2016, the Nobel Memorial Prize in Economic Sciences was awarded to Hart and Holmström for their ground-breaking work on this subject. However, most (in fact almost all) of the literature on the subject considers simple contracts that condition payments upon actions and/or outcomes. The cryptocurrency economy that has evolved in the last decade enables the actual implementation of more sophisticated `contractible contracts' via smart contracts. A simple realistic example is the popular ‘price-match guarantee’ that we see many times both online and in the physical reality where one contract contains a link to other contracts. In principle, even more complex links could be implemented. Recent research defines and analyses these new contract types allowing the possibility to condition payments/transactions on some aspects that are specified in other contracts, on top of conditioning on actions and outcomes. These new types of contracts are able to improve social efficiency and it has already been demonstrated that they can be constructed in a computationally-efficient way.

The proposed research project will examine implementations of the new theory and will deepen our theoretical/mathematical understanding of these new practical objects by examining the connections with the economic theory of contracts. In the first stage, it will demonstrate implementation of various (currently still theoretically proposed) types of contractible contracts via actual smart contracts. It will then aim to identify the limits (possibilities as well as impossibilities) of current Ethereum-based smart contracts as an implementation tool for the full class of contractible contracts that has been theoretically proposed. One possible application of such contracts is as a tool to implement an electronic auction environment, and in the advanced stages of the project we will further examine this research direction.

The Internet economy that has become such an important part of our society is an example of the way the connection between economics and computation can make a difference. This PhD project aims to add another hybrid component (namely, algorithmic contracts via smart contracts) to this ever evolving ecosystem. It will help in building trust in human-machine systems and will facilitate risk and decision making with AI since algorithmic contracts and smart contracts aim to support various automatic decision making.

The project will be carried out as part of an interdisciplinary integrated PhD in the UKRI Centre for Doctoral Training in Accountable, Responsible and Transparent AI (ART-AI). The ART-AI CDT aims at producing interdisciplinary graduates who can act as leaders and innovators with the knowledge to make the right decisions on what is possible, what is desirable, and how AI can be ethically, safely and effectively deployed. We value people from different life experiences with a passion for research. The CDT's mission is to graduate diverse specialists with perspectives who can go out in the world and make a difference.

Successful applicants will have, or expect to receive, a master's degree or first or upper-second bachelor's degree in a relevant subject and a strong mathematical background.

Formal applications should include a research proposal and be made via the University of Bath’s online application form. Enquiries about the application process should be sent to . Enquiries about the research should be directed to Dr Lavi.

Start date: 2 October 2023.

Funding Notes

ART-AI CDT studentships are available on a competition basis and applicants are advised to apply early as offers are made from January onwards. Funding will cover tuition fees and maintenance at the UKRI doctoral stipend rate (£17,668 per annum in 2022/23, increased annually in line with the GDP deflator) for up to 4 years.
We also welcome applications from candidates who can source their own funding.


1. Ron Lavi and Elisheva S. Shamash. "Principal-agent VCG contracts." Journal of Economic Theory 201 (2022)
2. Tal Alon, Ron Lavi, Elisheva S. Shamash, and Inbal Talgam-Cohen. “Incomplete Information VCG Contracts for Common Agency.” In Proceedings of the 22nd ACM Conference on Economics and Computation (2021)

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