Doping in Sport

A long standing interest of mine is doping in sport, or more specifically the game theoretic analysis of doping in sport. The game theory of doping in sport, building on the seminal analysis of Gunnar Breivik, recognizes that incentives to dope are inter-dependent. For instance, if others dope then an athlete has strong incentives to dope irrespective of how much they may intrinsically dislike doping. Here is some of my work in this area.

Cartwright, E. (2019) Guilt aversion and reciprocity in the performance-enhancing drug game, Journal of Sports Economics 20: 535-555.

Abstract: We revisit the performance-enhancing drug game by applying models of guilt aversion and reciprocity. Both models fit within the framework of psychological game theory in that they allow payoffs to depend on beliefs. We explore the extent to which social norms can help reduce or eliminate doping in sport. With reciprocity, we see that first-order beliefs on the prevalence of doping are key and a norm of clean sport would require a coordinated shift in such beliefs. With guilt aversion, by contrast, second-order beliefs are key and individuals may have an incentive to race clean even if they expect competitors will dope. Our results point to the importance for sports bodies and coaches to manage the beliefs of athletes.

Cartwright, E. and M. Leadbetter (2018) Coordinating on who dopes: An all pay auction approach to modelling doping in sport, SSRN3102350.

Abstract: We consider a two stage model of doping in sport in which athletes choose how much to dope and then how much effort to exert. Payoffs are determined by an all-pay auction where the bid or score depends on ability, doping and effort. In a very general setting we show that, in equilibrium, those with an ability level close to a clearly defined margin have most incentive to dope. Thus, it could be that the most able and least able athletes refrain from doping while those 'in the middle' dope. One can obtain, however, multiple equilibria. This results in a non-trivial coordination problem, analogous to that in market entry games, of who will dope.