E. Corchado et al. (Eds.): IDEAL 2006, LNCS 4224, pp. 172 – 182, 2006. © Springer-Verlag Berlin Heidelberg 2006 On the Structural Robustness of Evolutionary Models of Cooperation Segismundo S. Izquierdo 1 and Luis R. Izquierdo 2 1 Social Systems Engineering Centre (INSISOC), University of Valladolid, 47011, Spain 2 The Macaulay Institute, Craigiebuckler, AB15 8QH, Aberdeen, UK segis@eis.uva.es, l.izquierdo@macaulay.ac.uk Abstract. This paper studies the structural robustness of evolutionary models of cooperation, i.e. their sensitivity to small structural changes. To do this, we fo- cus on the Prisoner’s Dilemma game and on the set of stochastic strategies that are conditioned on the last action of the player’s opponent. Strategies such as Tit-For-Tat (TFT) and Always-Defect (ALLD) are particular and classical cases within this framework; here we study their potential appearance and their evolu- tionary robustness, as well as the impact of small changes in the model parame- ters on their evolutionary dynamics. Our results show that the type of strategies that are likely to emerge and be sustained in evolutionary contexts is strongly dependent on assumptions that traditionally have been thought to be unimpor- tant or secondary (number of players, mutation-rate, population structure…). We find that ALLD-like strategies tend to be the most successful in most envi- ronments, and we also discuss the conditions that favor the appearance of TFT- like strategies and cooperation. Keywords: Evolution of Cooperation; Evolutionary Game Theory; Iterated Prisoner's Dilemma; Tit for Tat; Agent-based Modeling. 1 Introduction The evolutionary emergence and stability of cooperation is a problem of fundamental importance that has been studied for decades in a wide range of disciplines. The value of understanding such a question is clear: in the social and biological sciences, the emergence of cooperation is at the heart of subjects as diverse as the first appearance of life, the ecological functioning of countless environmental interactions, the effi- cient use of natural resources, the development of modern societies, and the sustain- able stewardship of our planet. From an engineering point of view, the problem of understanding how cooperation can emerge and be promoted is crucial for the design of efficient decentralized systems where collective action can lead to a common bene- fit but individual units may (purposely or not) undermine the collective good for their own advantage. At the most elementary level, the problem of cooperation can be formalized using the symmetric Prisoner’s Dilemma (PD), a two-person game where each player can either cooperate or defect. The payoff that players gain when they both cooperate (R)