Generalizing Pure and Impure Iterated Prisoner’s Dilemmas to the Case of Infinite and Infinitesimal Quantities

In this work, a generalization of both Pure and Impure iterated Prisoner’s Dilemmas is presented. More precisely, the generalization concerns the use of non-Archimedean quantities, i.e., payoffs that can be infinite, finite or infinitesimal and probabilities that can be finite or infinitesimal. This new approach allows to model situations that cannot be adequately addressed using iterated games with purely finite quantities. This novel class of models contains, as a special case, the classical known ones. This is an important feature of the proposed methodology, which assures that we are proposing a generalization of the already known games. The properties of the generalized models have also been validated numerically, by using a Matlab simulator of Sergeyev’s Infinity Computer.