  Prisoner's Dilemma (PD) is a widely studied game that plays an important role
in Game Theory. This paper aims at extending PD Tournaments to the case of
infinite, finite or infinitesimal payoffs using Sergeyev's Infinity Computing
(IC). By exploiting IC, we are able to show the limits of the classical
approach to PD Tournaments analysis of the classical theory, extending both the
sets of the feasible and numerically computable tournaments. In particular we
provide a numerical computation of the exact outcome of a simple PD Tournament
where one player meets every other an infinite number of times, for both its
deterministic and stochastic formulations.
