Vaccine 28 (2010) 98–109 Contents lists available at ScienceDirect Vaccine journal homepage: www.elsevier.com/locate/vaccine Optimal vaccination choice, vaccination games, and rational exemption: An appraisal Piero Manfredi a,∗ , Pompeo Della Posta b , Alberto d’Onofrio c , Ernesto Salinelli d , Francesca Centrone d , Claudia Meo d , Piero Poletti e a Dipartimento di Statistica & Matematica Applicata all’Economia, Facoltà di Economia, Università di Pisa, Via Ridolfi 10, I-56124 Pisa, Italy b Dipartimento di Scienze Economiche, Facoltà di Economia, Università di Pisa, Via Ridolfi 10, I-56124 Pisa, Italy c Theoretical Biology and Medicine Unit, Department of Experimental Oncology, European Institute of Oncology, Via Ripamonti 435, 20141 Milano, Italy d Dipartimento di Scienze Economiche e Metodi Quantitativi, Università del Piemonte Orientale “A. Avogadro”, Via Perrone 18, 28100 Novara, Italy e Predictive Models for Biomedicine and Environment, Fondazione Bruno Kessler, Via Sommarive 18, 38100 Trento, Italy article info Article history: Received 11 April 2009 Received in revised form 19 September 2009 Accepted 25 September 2009 Available online 4 November 2009 Keywords: Vaccination choice Rational exemption Strategic behaviour Social planning abstract A threat for vaccination policies might be the onset of “rational” exemption, i.e. the family’s decision not to vaccinate children after a seemingly rational comparison between the perceived risk of infec- tion and the perceived risk of vaccine side effects. We study the implications of rational exemption by models of vaccination choice. By a simple model of individual choice we first prove the “elimination impossible” result in presence of informed families, i.e. aware of herd immunity, and suggest that limited information might explain patterns of universal vaccination. Next, we investigate vaccination choice in a game-theoretic framework for communities stratified into two groups, “pro” and “anti” vaccinators, having widely different perceived costs of infection and of vaccine side effects. We show that under informed families neither a Nash nor a Stackelberg behaviour (characterized, respectively, by players acting simultaneously and by an asymmetric situation with a “leader” and a “follower) allow elimina- tion, unless “pro-vaccinators” assign no costs to vaccine side effects. Elimination turns out to be possible when cooperation is encouraged by a social planner, provided, however, he incorporates in the “social loss function” the preferences of anti-vaccinators only. This allows an interpretation of the current Italian vaccination policy. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction Despite the fundamental role played in history by vaccines, second only to potable water in the reduction of mortality and morbidity, various forms of exemption to vaccination (conscien- cious, religious, philosophical) have always been documented [32]. In more recent times episodes of decline in vaccine uptake have been associated to vaccine scares, e.g. the cases of the whole-cell pertussis vaccine [19], of thimerosal and HBV vaccine [24], up to the MMR scare [17,35,39]. In such cases a significant role of anti- vaccinators’ movements in raising and spreading concerns about vaccine safety was also documented [19,28]. Today, developed countries are increasingly facing the chal- lenge of rational exemption (RE). By RE we mean, in regimes of voluntary vaccination, the parents’ decision not to immunize chil- dren after a seemingly rational comparison between the perceived utility of vaccination, i.e. protection from the risk of infection – per- ∗ Corresponding author. Tel.: +39 050 2216317; fax: +39 050 2216375. E-mail address: manfredi@ec.unipi.it (P. Manfredi). ceived as very low as a consequence of the high herd immunity due to decades of successful vaccination policies – with its disutility, i.e. the risk of vaccine-associated side effects. RE is often consid- ered as a form of “free riding” [36]. Such a behaviour, resulting from the optimization performed by rational agents, might well turn out to be “myopically” rational, since it considers only the current perceived risk of disease, and not the risk of its future resurgence due to declining coverage. Some evidence of rational exemption behaviour is documented by surveys of vaccination lifestyles [2,24,39,17]. Theoretical papers based on traditional epidemiological mod- els have investigated the implications of RE for the dynamics and control of vaccine preventable diseases [20,9,11]. This literature, which has pointed out the critical interplay between information and vaccinating as well as other disease-related behaviour [12], has shown that RE might make elimination a “mission impossible” unless the fraction of those who practice RE is small, i.e. below the susceptibility threshold ensuring endemic persistence. Moreover, it has shown that if the information set used by individuals includes past information, then the disease dynamics might yield epidemic waves with very long period. The negative implications for rubella 0264-410X/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.vaccine.2009.09.109