Massively Parallel Model of Extended Memory Use in Evolutionary Game Dynamics

Amanda Peters Randles,Greg Morrisett,Jayanta Sircar,David G Rand,Hanspeter Pfister,Martin A Nowak,Christopher Lee

doi:10.1109/ipdps.2013.102

Abstract

To study the emergence of cooperative behavior, we have developed a scalable parallel framework for evolutionary game dynamics. This is a critical computational tool enabling large-scale agent simulation research. An important aspect is the amount of history, or memory steps, that each agent can keep. When six memory steps are taken into account, the strategy space spans 24096 potential strategies, requiring large populations of agents. We introduce a multi-level decomposition method that allows us to exploit both multi-node and thread-level parallel scaling while minimizing communication overhead. We present the results of a production run modeling up to six memory steps for populations consisting of up to 1018 agents, making this study one of the largest yet undertaken. The high rate of mutation within the population results in a non-trivial parallel implementation. The strong and weak scaling studies provide insight into parallel scalability and programmability trade-offs for large-scale simulations, while exhibiting near perfect weak and strong scaling on 16,384 tasks on Blue Gene/Q. We further show 99% weak scaling up to 294,912 processors 82% strong scaling efficiency up to 262,144 processors of Blue Gene/P. Our framework marks an important step in the study of game dynamics with potential applications in fields ranging from biology to economics and sociology.

Highlights

Game theory is commonly employed and exploited to describe and predict the interactions between agents in a multi-agent system
It is possible to measure the emergence of altruistic behaviors that can be of benefit to both interacting parties
We have further demonstrated the ability to perform at larger scale by demonstrating 99% efficient weak scaling up to 262,144 processors on the IBM Blue Gene/P supercomputer and 82% strong scaling parallel efficiency up to 262,144 processors

Summary

INTRODUCTION

Game theory is commonly employed and exploited to describe and predict the interactions between agents in a multi-agent system. It is important to both reduce the overall time to solution for these population models as well as enable the simulation of much larger pools of strategies To this end, we define our metric of success to be both the strong and weak scaling efficiency of the code. The abstraction of Strategy Sets enables a hybrid implementation to exploit two levels of parallelism: the subset of agents divided by groups of strategies, and concurrent game play of agents within each strategy group through a flat MPI/OpenMP model. This structure enables optimized communication patterns and memory usage by handling individual data locally and population changes globally. We have further demonstrated the ability to perform at larger scale by demonstrating 99% efficient weak scaling up to 262,144 processors on the IBM Blue Gene/P supercomputer and 82% strong scaling parallel efficiency up to 262,144 processors

RELATED WORK

Prisoner’s Dilemma

Iterated Prisoner’s Dilemma

Population Model

Strategy Types

Strategy Space Size

Errors

ALGORITHM

Game Dynamics

Population Dynamics

Agents

Nature Agent