@ARTICLE{Olson2026-tl,
  title         = "Social distancing equilibria in games under conventional
                   {SI} dynamics",
  author        = "Olson, Connor D and Reluga, Timothy C",
  abstract      = "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.",
  month         =  mar,
  year          =  2026,
  copyright     = "http://creativecommons.org/licenses/by/4.0/",
  archivePrefix = "arXiv",
  primaryClass  = "cs.GT",
  eprint        = "2603.12107"
}