Social Distancing Equilibria in Games under Conventional SI Dynamics
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918386120785920 |
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| author | Olson, Connor D Reluga, Timothy C |
| author_facet | Olson, Connor D Reluga, Timothy C |
| contents | The mathematical characterization of social-distancing games in classical epidemic theory remains an important question, for their applications to both infectious-disease theory and memetic theory. We consider a special case of the dynamic finite-duration SI social-distancing game where payoffs are accounted using Markov decision theory with zero-discounting, while distancing is constrained by threshold-linear running-costs, and the running-cost of perfect-distancing is finite. In this special case, we are able construct strategic equilibria satisfying the Nash best-response condition explicitly by integration. Our constructions are obtained using a new change of variables which simplifies the geometry and analysis. As it turns out, there are no singular solutions, and a time-dependent bang-bang strategy consisting of a wait-and-see phase followed by a lock-down phase is always the unique strategic equilibrium. We also show that in a restricted strategy space the bang-bang Nash equilibrium is an ESS, and that the optimal public policy exactly corresponds with the equilibrium strategy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12107 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Social Distancing Equilibria in Games under Conventional SI Dynamics Olson, Connor D Reluga, Timothy C Computer Science and Game Theory Dynamical Systems Populations and Evolution 37N40 (Primary) 37N25, 91A23 (Secondary) The mathematical characterization of social-distancing games in classical epidemic theory remains an important question, for their applications to both infectious-disease theory and memetic theory. We consider a special case of the dynamic finite-duration SI social-distancing game where payoffs are accounted using Markov decision theory with zero-discounting, while distancing is constrained by threshold-linear running-costs, and the running-cost of perfect-distancing is finite. In this special case, we are able construct strategic equilibria satisfying the Nash best-response condition explicitly by integration. Our constructions are obtained using a new change of variables which simplifies the geometry and analysis. As it turns out, there are no singular solutions, and a time-dependent bang-bang strategy consisting of a wait-and-see phase followed by a lock-down phase is always the unique strategic equilibrium. We also show that in a restricted strategy space the bang-bang Nash equilibrium is an ESS, and that the optimal public policy exactly corresponds with the equilibrium strategy. |
| title | Social Distancing Equilibria in Games under Conventional SI Dynamics |
| topic | Computer Science and Game Theory Dynamical Systems Populations and Evolution 37N40 (Primary) 37N25, 91A23 (Secondary) |
| url | https://arxiv.org/abs/2603.12107 |