Abstract

Abstract
The problem of the consumption or provision of common and public goods is a well known and well studied problem in economic sciences. The nature of the problem is the existence of non-excludable externalities which gives rise to incentives to free-riding behaviour. There are several economical frameworks trying to deal with the problem such as coalition theory or mechanism design and implementation theory to ensure a Pareto efficient consumption or provision of such good. Baliga and Maskin considered an environmental game where several communities face a problem of pollution reduction. They show that all communities except one of them have incentives to act as a free-rider, i.e. only one community is willing to face the costs that air cleaning implies, namely the one with greatest preference for the good. In this work we introduce an adaptive evolutionary dynamics for the generalization of the Baliga-Maskin model to quasi-linear utility functions. We show that the Baliga-Maskin equilibrium is the only asymptotically stable dynamical equilibrium, all others being unstable. This result reasserts the problem of free-riding and externalities for the case of a common good in a dynamically/evolutionary setting, and reiterates the relevance of mechanism design and coalition formation in the context of dynamical models.

Abstract
In this work, we introduce the concept of maximum curvature to separate the low from high reinfection levels. For each temporary immunity transition rate, the threshold value is the infection rate where the positive curvature of the endemic stationary state attains its maximum value. Hence, the maximum curvature reinfection threshold can be interpreted as the moment when the graph of the stationary state of infected attains the maximum change in its direction. When the temporary immunity transition rate tends to zero, the limiting point of the maximum curvature reinfection threshold coincides with the Gomes' reinfection threshold and the curvature blows up to infinity.

Abstract

Abstract

Abstract