We are interested in how to develop policy in the presence of a simple (SIR) epidemic in which the population consists of identical, rational individuals without added uncertainty. Individuals and government are bestowed with an objective function that, e.g. balances the cost of social distancing with the benefit of a reduced chance of infection. Governments are able to impose taxes or offer incentives to change individual behaviour so as to target the maximum of their own objective function. This represents a novel form of control theory with two hierarchies of control - for individuals and government. Although this is a highly stylised setting we believe that it tests an important proof-of-principle: that rational policies can be developed in this way. We discuss the insights that this formalism provides and what would be needed to develop a genuine policy tool. Within our formulation the objective function, or utility, completely determines the behaviour. In the final part of my talk I will consider the inverse problem, in which behaviour is observed and a hidden objective function is to be inferred. We discuss our progress towards this goal using a new machine learning methodology we call “Nash Neural Networks”. We flag possible applications of this approach beyond epidemiology.

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