We consider optimal group testing of individuals with heterogeneous risks for an infectious disease. Our algorithm significantly reduces the number of tests needed compared to Dorfman (Ann Math Stat 14(4):436-440, 1943). When both low-risk and high-risk samples have sufficiently low infection probabilities, it is optimal to form heterogeneous groups with exactly one high-risk sample per group. Otherwise, it is not optimal to form heterogeneous groups, but homogeneous group testing may still be optimal. For a range of parameters including the U.S. Covid-19 positivity rate for many weeks during the pandemic, the optimal size of a group test is four. We discuss the implications of our results for team design and task assignment.

We analyze the role of disease containment policy in the form of treatment in a stochastic economic-epidemiological framework in which the probability of the occurrence of random shocks is state-dependent, namely it is related to the level of disease prevalence. Random shocks are associated with the diffusion of a new strain of the disease which affects both the number of infectives and the growth rate of infection, and the probability of such shocks realization may be either increasing or decreasing in the number of infectives. We determine the optimal policy and the steady state of such a stochastic framework, which is characterized by an invariant measure supported on strictly positive prevalence levels, suggesting that complete eradication is never a possible long run outcome where instead endemicity will prevail. Our results show that: (i) independently of the features of the state-dependent probabilities, treatment allows to shift leftward the support of the invariant measure; and (ii) the features of the state-dependent probabilities affect the shape and spread of the distribution of disease prevalence over its support, allowing for a steady state outcome characterized by a distribution alternatively highly concentrated over low prevalence levels or more spread out over a larger range of prevalence (possibly higher) levels.

A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Programming approach and prove some continuity properties of the value function of the associated optimization problem. We study the corresponding Hamilton-Jacobi-Bellman equation and show that the value function solves it in the viscosity sense. Finally, we discuss some optimality conditions. Our paper represents a first contribution towards a complete analysis of non-convex dynamic optimization problems, within a Dynamic Programming approach.

We propose a model, which nests a susceptible-infected-recovered-deceased (SIRD) epidemic model into a dynamic macroeconomic equilibrium framework with agents' mobility. The latter affect both their income and their probability of infecting and being infected. Strategic complementarities among individual mobility choices drive the evolution of aggregate economic activity, while infection externalities caused by individual mobility affect disease diffusion. The continuum of rational forward-looking agents coordinates on the Nash equilibrium of a discrete time, finite-state, infinite-horizon Mean Field Game. We prove the existence of an equilibrium and provide a recursive construction method for the search of an equilibrium(a), which also guides our numerical investigations. We calibrate the model by using Italian experience on COVID-19 epidemic and we discuss policy implications.

We propose and solve an optimal vaccination problem within a deterministic compartmental model of SIRS type: the immunized population can become susceptible again, e.g. because of a not complete immunization power of the vaccine. A social planner thus aims at reducing the number of susceptible individuals via a vaccination campaign, while minimizing the social and economic costs related to the infectious disease. As a theoretical contribution, we provide a technical non-smooth verification theorem, guaranteeing that a semiconcave viscosity solution to the Hamilton-Jacobi-Bellman equation identifies with the minimal cost function, provided that the closed-loop equation admits a solution. Conditions under which the closed-loop equation is well-posed are then derived by borrowing results from the theory of . From the applied point of view, we provide a numerical implementation of the model in a case study with quadratic instantaneous costs. Amongst other conclusions, we observe that in the long-run the optimal vaccination policy is able to keep the percentage of infected to zero, at least when the natural reproduction number and the reinfection rate are small.

We analyze the optimal lockdown in an economic-epidemic model with realistic infectiveness distribution. The model is described by Volterra integral equations and accurately depicts the COVID-19 infectivity pattern from clinical data. A maximum principle is derived, and a qualitative dynamic analysis of the optimal lockdown problem is provided over finite and infinite horizons. We analytically prove and economically justify the possibility of an endemic scenario when the infection rate begins to climb after the lockdown ends.

This paper studies continuing optimal lockdowns (can also be interpreted as quarantines or self-isolation) in the long run if a disease (Covid-19) is endemic and immunity can fail, that is, the disease has SIRS dynamics. We model how disease related mortality affects the optimal choices in a dynamic general equilibrium neoclassical growth framework. An extended welfare function that incorporates loss from mortality is used. In a disease endemic steady state, without this welfare loss even if there is continuing mortality, it is not optimal to impose even a partial lockdown. We characterize how the optimal restriction and equilibrium outcomes vary with the effectiveness of the lockdown, the productivity of working from home, the rate of mortality from the disease, and failure of immunity. We provide the sufficiency conditions for economic models with dynamics with disease related mortality-a class of models which are non-convex and have endogenous discounting so that no existing results are applicable.

This paper is concerned with cross-dependencies between endogenous market structure and tax policy. We extend the Mirrlees (Rev Econ Stud 38:175-208, 1971) model of income taxation with a monopolistic competition framework with general additively separable consumer preferences. We show that quantity and variety distortions resulting from the market structure require adjustments to income tax policy, which also needs to be complemented with commodity or firm taxation to achieve the constrained social optimum. We calibrate the model and find that in policy design the failure to account for the market structure results in a welfare loss of 1.77%. Motivated by practical cases, we study a policy regime that is solely based on income taxation. We show that departures from the social optimum can be compensated by lower and less regressive income taxes and a smaller government compared to the regime with income and commodity taxes. We also examine the role of consumer preferences for policy outcomes and show that it is substantially amplified by an endogenous market structure.

We analyze the relation between individuals' risk aversion and their willingness to expose themselves to infection when faced with an asymptomatic infectious disease. We show that in a high prevalence environment, increasing individuals' risk aversion increases their propensity to engage in transmissive behavior. The reason for this result is that as risk aversion increases, exposure which leads to infection with certainty becomes relatively more attractive than the uncertain payoffs from protected behavior. We provide evidence from a laboratory experiment which is consistent with our theoretical findings.

Motivated by the Covid-19 epidemic, we build a SIR model with private decisions on social distancing and population heterogeneity in terms of infection-induced fatality rates, and calibrate it to UK data to understand the quantitative importance of these assumptions. Compared to our model, the calibrated benchmark version with constant mean contact rate significantly over-predicts the mean contact rate, the death toll, herd immunity and prevalence peak. Instead, the calibrated counterfactual version with endogenous social distancing but no heterogeneity massively under-predicts these statistics. We use our calibrated model to understand how the impact of mitigating policies on the epidemic may depend on the these policies induce across the population segments. We find that policies that shut down some of the essential sectors have a stronger impact on the death toll than on infections and herd immunity compared to policies that shut down non-essential sectors. Furthermore, there might not be an after-wave after policies that shut down some of the essential sectors are lifted. Restrictions on social distancing can generate welfare gains relative to the case of no intervention. Milder but longer restrictions on less essential activities might be better in terms of these welfare gains than stricter but shorter restrictions, whereas the opposite might be the case for restrictions on more essential activities. Finally, shutting down some of the more essential sectors might generate larger welfare gains than shutting down the less essential sectors.

We examine a two-player game with two-armed exponential bandits à la (Keller et al. in Econometrica 73:39-68, 2005), where players operate different technologies for exploring the risky option. We characterise the set of Markov perfect equilibria and show that there always exists an equilibrium in which the player with the inferior technology uses a cut-off strategy. All Markov perfect equilibria imply the same of experimentation but differ with respect to the expected speed of the resolution of uncertainty. If and only if the degree of asymmetry between the players is high enough, there exists a Markov perfect equilibrium in which both players use cut-off strategies. Whenever this equilibrium exists, it welfare dominates all other equilibria. This contrasts with the case of symmetric players, where there never exists a Markov perfect equilibrium in cut-off strategies.

Considered are imperfectly discriminating contests in which players may possess private information about the primitives of the game, such as the contest technology, valuations of the prize, cost functions, and budget constraints. We find general conditions under which a given contest of incomplete information admits a unique pure-strategy Nash equilibrium. In particular, provided that all players have positive budgets in all states of the world, existence requires only the usual concavity and convexity assumptions. Information structures that satisfy our conditions for uniqueness include independent private valuations, correlated private values, pure common values, and examples of interdependent valuations. The results allow dealing with inactive types, asymmetric equilibria, population uncertainty, and the possibility of resale. It is also shown that any player that is active with positive probability ends up with a positive net rent.

A group of experts, for instance climate scientists, is to advise a decision maker about the choice between two policies and . Consider the following decision rule. If all experts agree that the expected utility of is higher than the expected utility of , the unanimity rule applies, and is chosen. Otherwise, the precautionary principle is implemented and the policy yielding the highest minimal expected utility is chosen. This decision rule may lead to time inconsistencies when adding an intermediate period of partial resolution of uncertainty. We show how to coherently reassess the initial set of experts' beliefs so that precautionary choices become dynamically consistent: new beliefs should be added until one obtains the smallest "rectangular set" that contains the original one. Our analysis offers a novel behavioral characterization of rectangularity and a prescriptive way to aggregate opinions in order to avoid sure regret.