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.

中文翻译：

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使用谢尔盖耶夫无限计算的博弈论数值渐近结果

囚徒困境 (PD) 是一种被广泛研究的博弈，在博弈论中扮演着重要角色。本文旨在使用 Sergeyev 的无限计算 (IC) 将 PD 锦标赛扩展到无限、有限或无限小回报的情况。通过利用 IC，我们能够展示经典理论对 PD 锦标赛分析的经典方法的局限性，扩展了可行和可数值计算的锦标赛的集合。特别是，我们提供了一个简单的 PD 锦标赛的确切结果的数值计算，其中一个玩家无限次地碰面，对于它的确定性和随机公式。