A Game Theoretical Analysis of Sexually Transmitted Disease Epidemics

Abstract

Social scientists who study sexual behavior have consistently found that some HIV-infected individuals continue to have unprotected sex with uninfected partners. In this article, we address three questions that stem from this empirical finding. First, what can game theory contribute to the study of sexual behavior? Second, can a person deduce the HIV status of a potential sexual partner from observed behavior? Third, what are the implications of a game theoretic analysis for infection rate dynamics? Briefly, we argue that game theory models capture the interactive aspects of sexual behavior such as signalign status through behavior. We then go on to show that some simple signaling game models predict that behavior does not distinguish infected from uninfected partners. In those models, uninfected individuals will engage in high-risk sex with potentially infected partners if the perceived rate of infection is sufficiently low. Otherwise, they engage in low-risk sex. The final section of the article analyses an epidemiological model where individuals play the signaling game in discrete time periods. Simulations of the model under varying conditions show that the most virulent epidemics occur when individuals randomly select partners but base their estimate of the infection rate on the percentage of socially close individuals who are infected. Simulations also show that epidemics where individuals restrict partners slow the spread of disease more than other models but that the epidemic lasts longer. Another implication is that with replacement, infection rates will oscillate because individuals will switch from low- to high-risk sex as the percentage of infected individuals changes. We conclude by discussing empirically testable predictions of the model.