Stochastic interactions increase cooperation in a spatial Prisoner's Dilemma

This article implements the spatial Prisoner's Dilemma (PD) as an agent‐based model. Many previous models have assumed that agents in a spatial PD interaction exclusively and deterministically within their von Neumann neighborhood. The model presented here introduces stochastic interactions within a subset of the von Neumann neighborhood. This implementation allows a direct comparison of the effect of stochastic interactions relative to deterministic interactions on the level of cooperation that emerges in the system. The results show that when holding the total number of interactions agents participate in each round constant, allowing agents to interact stochastically increases cooperation in the system relative to deterministic interactions. © 2014 Wiley Periodicals, Inc. Complexity 21: 82–92, 2015     

Arithmetical Identities in a 2‐element Model of Tarski's System

All arithmetical identities involving 1, addition, multiplication and exponentiation will be true in a 2‐element model of Tarski's system if a certain sequence of natural numbers is not bounded. That sequence can be bounded only if the set of Fermat's prime numbers is finite.