1. Department of Non-linear Dynamics, Keldysh Institute of Applied Mathematics of RAS, Moscow 125047, Russia
2. Department of Ecology and Evolutionary Biology, University of Connecticut, Storrs, Connecticut 06269-3042, USA

Correspondence to: Mikhail Burtsev¹ Correspondence and requests for materials should be addressed to M.B. (Email: mbur@narod.ru).

One of the greatest challenges in the modern biological and social sciences is to understand the evolution of cooperative behaviour. General outlines of the answer to this puzzle are currently emerging as a result of developments in the theories of kin selection^{1, 2, 3, 4, 5, 6, 7}, reciprocity^{8, 9, 10}, multilevel selection^{11, 12, 13, 14, 15} and cultural group selection^{16, 17}. The main conceptual tool used in probing the logical coherence of proposed explanations has been game theory, including both analytical models and agent-based simulations^{6, 7, 9, 18, 19, 20, 21, 22, 23, 24}. The game-theoretic approach yields clear-cut results but assumes, as a rule, a simple structure of payoffs and a small set of possible strategies. Here we propose a more stringent test of the theory by developing a computer model with a considerably extended spectrum of possible strategies. In our model, agents are endowed with a limited set of receptors, a set of elementary actions and a neural net in between. Behavioural strategies are not predetermined; instead, the process of evolution constructs and reconstructs them from elementary actions. Two new strategies of cooperative attack and defence emerge in simulations, as well as the well-known dove, hawk and bourgeois strategies. Our results indicate that cooperative strategies can evolve even under such minimalist assumptions, provided that agents are capable of perceiving heritable external markers of other agents.

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