How to think about Social Distancing and Containment using Network Formation Games

An unreliable test and tracing system risks becoming counter-productive once we consider how it may affect people’s behaviour, writes Dr. Fabrizio Adriani

When pandemics cannot be addressed by pharmaceutical solutions, policy makers need to find viable alternatives to indiscriminate lockdowns, which carry huge human and economic costs. At the time of writing, the most promising medium-term avenue to tackle the current COVID-19 crisis seems to be a combination of testing and contact tracing to ensure detection and isolation of cases.

Within this context, a common concern shared by many behavioural scientists is that the behavioural response to the containment policy might  (fully or partially) offset it — the so-called “crowding out” phenomenon. The idea is that, if people perceive that containment is doing its job, they might relax social distancing.  However, if everybody takes a more relaxed approach, the risk of infection may increase again.

We do not know much about this type of behavioural responses (at least within the context of an epidemic), as the lack of a counterfactual (what would have happened without intervention) makes it difficult to observe them empirically. In cases like this, theory can illuminate the qualitative features of the problem. In a recent paper, I use the tools of game theory and strategic network formation to look into the following questions.

When is crowding out an issue?

Crowding out is clearly irrelevant if new cases can be immediately identified and isolated before they can infect others. In reality, however, testing takes time, false negatives are possible, and contact tracing is only so fast. The more likely it is that an outbreak may go on undetected, the more crowding out becomes an issue, as social distancing is the only defence against outbreaks spreading off the radar.

Can the intervention crowd out social distance to the extent that the infection rate is actually higher than under no intervention?

At first glance, this seems absurd. After all, one is only going to relax social distancing if the intervention reduces risk, right? Unfortunately, there are two factors that work against this intuition: externalities and strategic complementarities.

Externalities. In the figure below, suppose that Alice and Bob meet frequently (the solid line), e.g. because they are co-workers.  Bob and Charles are close friends but they are currently only talking online because of social distancing (the dashed line).

What happens when the government unveils its latest mass testing and tracing plan? Bob and Charles may decide that, so long as they both test negative, it is ok to have a drink together now and then. This however increases Alice’s risk of infection: now that Bob and Charles meet regularly, if Charles is infected, Alice may catch the disease via Bob. Using economic jargon, Bob’s behaviour provides a negative externality to Alice. Although the meetings between Bob and Charles have indeed become less risky, the overall risk of infection may have increased when Alice is also taken into account.

Strategic complementarity. Suppose Alice and Charles are friends too. Upon hearing that Bob and Charles meet regularly, Alice might decide that it does not make sense for her to avoid seeing Charles while still bearing the risk of being infected by Charles via Bob. She might as well start meeting Charles too. As economists like to say, Bob’s and Alice’s propensities to meet Charles are strategic complements.

The presence of externalities and complementarities implies that a sufficiently inaccurate intervention may actually increase the infection rate.

How fast should the intervention be?

Policy makers worry that slow interventions may fall “one step behind” the outbreak. If a carrier is not identified quickly, he may go on to infect others, who then may infect others and so on. In the absence of behavioural responses, it is indeed always better to have interventions that are as fast as possible, as witnessed by the scramble to find technological solutions to speed up contact tracing.

Once behavioural responses are taken into account, however, the picture becomes murkier. Interventions that are too fast may actually become counterproductive.  Intuitively, a slightly slower intervention may weaken both the effect of the externality and strategic complementarity. To see this, suppose that contact tracing is not fast enough to prevent Bob from being infected if Charles is, but sufficiently fast to spare Alice provided she does not meet Charles directly. This has two effects. First, it weakens Bob and Charles’ incentives to resume their meetings in the first place, as these are as risky as without intervention. Second, even if Bob and Charles decide to meet, Alice’s incentive to join them is reduced, since there is a good chance that any outbreak may be contained before it reaches her.

This is good news. It suggests that it is unlikely that we need to worry both about containment falling one step behind and about crowding out. One tends to exclude the other.

Does the shape of the social network matter?

In dense networks, where everyone constantly meets everyone else, the risk of falling one step behind the outbreak is a real one. Also, if there are any individuals who are central in the network, they should be tested with high frequency. Consider for instance these two networks.

In the first, it makes sense to test everyone with the same frequency. In the second, a more sensible approach would be to concentrate testing on Alice, since any infection spreading to the others must pass through her. For instance, so long as visits are not allowed, staff are the main gateway for outbreaks hitting care homes. It thus makes sense to test them frequently.

To sum up, the nature and speed of the intervention shapes people’s social distancing choices. If we want fast reactions to outbreaks, we need to accept that crowding out may become an issue. This means stepping up testing frequency and accuracy to limit the chances of outbreaks spreading off the radar.

Dr. Fabrizio Adriani is Associate Professor of Economics in the University of Leicester School of Business.  His research interests are in Game Theory, Behavioural Economics, and Financial Economics.

Dr. Adriani’s full paper can be found at: Adriani, F. (2020) Social Distance, speed of containment and crowding in/out in a network model of contagion. CeDeX Discussion Paper 2020-10.