Nonlinear dynamics in a public good game

Abstract

The present work aims to study the problem of individual voluntary anonymous contributions to the financing of public goods in a dynamic setting. To do this, the article departs from a textbook model à la Naimzada and Tramontana (2010) augmented with public goods. The article studies how bounded rationality and dependence on agents’ past decisions combine with the problem of voluntary contributions. This favours the emergence of nonlinear dynamics in individual behaviour as well as in the aggregate contribution to the financing of a public good project. The Nash equilibrium can be destabilised through a flip bifurcation when the agent reactivity increases. In addition, some Neimark–Sacker bifurcations can also occur although not around the steady-state equilibrium. A sufficiently high agent reactivity level can also lead to chaotic dynamics with possible multiple attractors. When the chaotic regime prevails, synchronisation phenomena in agent behaviour may occur but are rare. Thus, usually, even if agents are homogeneous, they behave as if they were heterogeneous by making non-synchronised decisions. The work also explicitly deepens the case of a heterogeneous economy in terms of both consumer preferences and income.