How and how much to invest for fighting cheaters: from an ODE to a Cellular Automata model

Abstract In this paper, we present a study which is the completion of the problem left open in the appendix of the paper Nuño et al. (Eur J Appl Math 21:459–478, 2010). The goal of the paper is to offer a deeper analysis of the type of the ODE system featured in the paper above concerning the evolution of the total wealth and cheater population and, mainly, the purpose is to generalize this one to a Cellular Automata model introducing spatial and local effects. The work presented shows the original interaction between an Ordinary Differential Equations model and a Cellular Automata model.