Game theory is now routinely applied to quantitatively model the decision making of individuals presented with various voluntary actions that can prevent a given disease. Most models consider only a single preventive strategy and the case where multiple preventative actions are available is severely understudied. In our paper, we consider a very simple SI compartmental model of rabies in the domestic dog population. We study two choices of the dog owners: to vaccinate their dogs or to restrict the movements of unvaccinated dogs. We analyze the relatively rich patterns of Nash equilibria (NE). We show that there is always at least one NE at which the owners utilize only one form of prevention. However, there can be up to three different NEs at the same time: two NEs at which the owners use exclusively only the vaccination or movement restriction, and the third NE when the owners use both forms of prevention simultaneously. However, we also show that, unlike the first two types of NEs, the third kind of NE is not convergent stable.
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机译：博弈论现在通常用于定量模拟具有各种自愿行动的个体的决策，这些行动可以预防给定的疾病。大多数模型只考虑单一的预防策略，并且对多种预防措施的情况研究严重不足。在我们的论文中，我们考虑了家犬种群中狂犬病的非常简单的 SI 区室模型。我们研究了狗主人的两种选择：为他们的狗接种疫苗或限制未接种疫苗的狗的活动。我们分析了纳什均衡（NE）相对丰富的模式。我们表明，总是至少有一个 NE 所有者只使用一种预防形式。但是，最多可以同时有三个不同的 NE：两个 NE，业主仅使用疫苗接种或行动限制，第三个 NE，当业主同时使用两种形式的预防措施时。然而，我们也表明，与前两种类型的网元不同，第三类网元不是收敛稳定的。
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