1 Learning and innovation expand cooperative network topologies Shijun Wang *# , Mate S. Szalay ‡ , Changshui Zhang * , and Peter Csermely ‡† * Department of Automation, FIT Building, Tsinghua University, 100084 Beijing, China; and ‡ Department of Medical Chemistry, Semmelweis University, Puskin str. 9, H-1088 Budapest, Hungary Cooperation plays a key role in the evolution of complex systems. However, the level of cooperation extensively varies with the topology of agent networks in the widely used models of repeated games. Here we show that cooperation remains rather stable by applying long-term learning + innovative strategy adoption rules on a variety of random, regular, small-word, scale-free and modular networks in repeated, multi-agent games. Furthermore, we found that while long-term learning promotes cooperation, innovation makes the level of cooperation less dependent on the actual network topology. Our results demonstrate that long-term learning and innovation, when acting together, extend the range of network topologies enabling the development of cooperation at a wider range of costs and temptations. Learning and innovation help to preserve cooperation during network re-organization, and may be key mechanisms promoting the evolution of self-organizing, complex systems. altruism │Hawk-Dove game│ network evolution │network topology │Prisoner’s Dilemma game │social dilemmas Cooperation is necessary for the emergence of complex, hierarchical systems (1–6). Why is cooperation maintained, when there is a conflict between self-interest and the common good? A set of answers emphasized agent similarity, in terms of kin- or group-selection and compact network communities, which is helped by learning of successful strategies (1–3, 5, 7). On the other hand, agent diversity in terms of innovation, noise, variation of behavior and strategies (5, 8), as well as the changing environment of the agent-community (9) all promoted cooperation in different games and settings. Small-world, scale-free or modular networks, which all give a chance to develop the complexity of similar, yet diverse agent-neighborhoods, provide a good starting environment for the study of cooperative behavior (10–19). However, the actual level of cooperation in various games, such as the Prisoner’s Dilemma or Hawk-Dove games is very sensitive to the topology of the agent network [16–21, supporting information (SI) Table 1]. Author contributions: S.W., C.Z., and P.C. designed research; S.W., and M.S.S. performed research; S.W., and P.C. analyzed data; P.C. wrote the paper. The authors declare no conflict of interest. † To whom correspondence should be addressed. E-mail: csermely@puskin.sote.hu # Present address: Diagnostic Radiology Department, Clinical Center, National Institutes of Health, 10 Center Dr, MSC 1182, Bldg 10, Room B2S-231, Bethesda, MD 20892-1182 USA. This article contains supporting information.