Numerical Asymptotic Results in Game Theory Using Sergeyev's Infinity Computing

TL;DR

This paper extends Prisoner's Dilemma tournaments to infinite and infinitesimal payoffs using Sergeyev's Infinity Computing, enabling new numerical analyses of classical game theory scenarios with infinite interactions.

Contribution

It introduces a novel application of Infinity Computing to analyze PD Tournaments with infinite or infinitesimal payoffs, expanding the scope of classical game theory analysis.

Findings

Numerical computation of PD tournament outcomes with infinite interactions.

Extension of feasible tournament sets using Infinity Computing.

Analysis of deterministic and stochastic PD tournaments with infinite repetitions.

Abstract

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.