Do multiple Nash equilibria in Markov strategies mitigate the tragedy of the commons?

In a seminal paper, Dockner and van Long [1993. International pollution control: cooperative versus non-cooperative strategies. Journal of Environmental Economics and Management 25, 13-29] argue that nonlinear strategies allow to protect the commons compared with the linear (and singular) strategy. This paper shows that the existence of multiple equilibria depends on preference characteristics and that multiple equilibria need not foster conservation. In particular, if the (absolute) elasticity of marginal utility is decreasing, then multiple equilibria aggravate the tragedy of the commons compared with the singular (or saddlepoint) strategy.