Social Distancing Equilibria in Games under Conventional SI Dynamics
A new mathematical model shows the best public policy for pandemics is a delayed, sharp lockdown.
Researchers Connor Olson and Timothy Reluga have published a significant paper applying game theory to epidemic modeling. Their work, 'Social Distancing Equilibria in Games under Conventional SI Dynamics,' tackles a classic problem: mathematically defining the optimal social distancing strategy during an outbreak. They analyzed a finite-duration Susceptible-Infected (SI) model where individuals make strategic distancing choices based on costs and infection risk, using a Markov decision process framework with zero discounting.
Their key finding is a definitive mathematical proof. For this specific model, the only strategic equilibrium—a state where no individual can benefit by changing their strategy—is a time-dependent 'bang-bang' control strategy. This means the optimal behavior isn't gradual adjustment, but a sharp switch: first, a period of normal activity ('wait-and-see'), followed abruptly by perfect distancing ('lockdown'). The model shows no other singular solutions exist.
Furthermore, the researchers demonstrated that this individual Nash equilibrium strategy is also an Evolutionarily Stable Strategy (ESS), meaning it resists invasion by alternative behavioral strategies. Crucially, their analysis reveals that the optimal public health policy—the one a central planner would impose—exactly corresponds to this emergent individual equilibrium. This provides a rigorous, game-theoretic justification for a specific, two-phase pandemic response policy.
- Proves the unique strategic equilibrium for a finite-duration SI epidemic game is a 'bang-bang' strategy: wait-then-lockdown.
- Uses Markov decision theory with zero-discounting and threshold-linear costs to model individual distancing choices.
- Shows the optimal public policy aligns perfectly with the individual Nash equilibrium, which is also an Evolutionarily Stable Strategy (ESS).
Why It Matters
Provides a mathematical foundation for pandemic policy, showing delayed, decisive lockdowns can be the strategically sound approach for both individuals and governments.