Altruists and Egoists: A Local Interaction Model of Imitation in Social Graphs

Open Access
Author:
Wray, Kyle Hollins
Graduate Program:
Mathematics
Degree:
Master of Arts
Document Type:
Master Thesis
Date of Defense:
July 10, 2013
Committee Members:
  • Eli Christopher C Byrne, Thesis Advisor
Keywords:
  • imitation dynamics
  • prisoner's dilemma on graphs
Abstract:
The imitation dynamics within large societies of agents are a growing topic of interest to game theorists and multiagent researchers. These models attempt to provide an explanation for the causes of widespread changes in behavior, e.g., reasons for war or peace. Knowing the effects that particular structures have on an agent society enable us to predict the long-term behavior of the system and even induce desired behavior within the society. This thesis extends the popular altruist and egoist local interaction model, originally proposed by Eshel et al., by expanding the problem's scope to include geodesic domes as well as arbitrary graphs. We present a formal mathematical model for the problem domain, as well as demonstrate that it extends the original problem. We show numerical bounds on the social cost for altruism based on the graph structure. We define the concept of power players, who are altruist or egoist players that are supported by communities of altruists. These power players can greatly influence others as a result of their high utilities. We state the exact bounds of their stability as a function of their "power level" and the cost of playing altruism. With both mathematical rigor and experimentation, we demonstrate that there are specific configurations of agents within a society that can induce either altruistic or egotistical strategies in others, and therefore define stability regions for which altruism can successfully survive iteration.