Symmetric Coordination of Heterogeneous Agents Saori Iwanaga (Nonmember) & Akira Namatame (Member) Dept. of Computer Science, National Defense Academy, Yokosuka, 239-8686, JAPAN, E-mail: {g38042, nama}@nda.ac.jp Abstract Large-scale effects of locally interacting agents are called emergent properties of the system. Emergent properties are often surprising because it can be hard to anticipate the full consequences of even simple forms of interaction. In this paper we address the following questions: how do heterogeneous agents generate emergent coordination, and how do they manage and self-organize macroscopic orders from bottom up without any central authority? These questions will depend crucially on how they interact and adapt their behavior. Agents myopically evolve their behavior based on the threshold rule, which is given as the function of the collective behavior and their idiosyncratic utilities. We obtain the micro-macro dynamics that relate the aggregate behavior with the underlying individual behavior. We show that agents' rational behavior reflecting their micromotives combined with the behavior of others produce stable orders, and sometimes unanticipated cyclic behavior. We consider the roles of particular types of agents, conformists, and nonconformists to manage emergent collective behavior. As a specific example, we address an emergent and evolutionary approach for designing the efficient network management policies. Keywords: heterogeneity, symmetric coordination, asymmetric coordination, emergence, evolutionary dynamics 1 Introduction As many tasks in information processing grow in complexity, the strong growing interests have been given toward heterogeneous agents [1][18]. To take advantage of the growing interests for multi-agents, the methodologies must be explored to process which beyond each agent's capability and knowledge. For instance, the integration of heterogeneous viewpoints becomes important [14]. The design of efficient collective action also becomes crucial. The group can offer something not available in the individuals. In collective activity, two types of activities may be necessary: each agent behaves as a member an organization, while at the same time, it behaves independently by adjusting its view and action. For the individual, it can learn to improve its problem-solving skills based on its own observation and experiences. At the cooperative stage, they can put forward their learnt knowledge for consideration by others. Therefore, cooperative work, if it is by a team of engineers, or by a collection of agents, requires efficient coordination, communication, knowledge sharing. In order to satisfy these requirements, it may need to create dynamic and highly interconnected networks among them [3][20]. In this paper we consider the coordination problems of more loosely connected agents, where they behave to satisfy their own goal, and they may coordinate with others in order to improve it. There are many situations where interacting agents can benefit from coordinating their action. Coordination implies that increased effort by some agents leads the remaining agents to follow suit, which gives rise multiplier effects. We call this type of coordination as symmetric coordination, Coordination is also necessary to ensure that their individual actions are carried out with little conflicts, and we distinguish this type of coordination by referring asymmetric coordination. We illustrate some examples of symmetric and asymmetric coordination. Consider the situation in which two agents must independently decide where to locate or which route to use. They receive the utility if and only if they choose the same location (symmetric coordination). They gain utility if and if only if they choose the different route (asymmetric coordination). For coordinating situations, there are multiple equilibria, and then a coordination failure, resulting in inefficiency, can easily arise. Coordination failures may also result from their independent inductive processes [7]. In this paper, we study the problem of asymmetric coordination and obtain some conditions for emergence of coordination among heterogeneous agents. Our focus is the theoretical basis for coordination problems in strategic situations and the likely outcome. We explore the mechanism in which heterogeneous agents may be stuck at an inefficient equilibrium. While all agents understand the that the outcome is inefficient, each acting independently is power less to manage this collective activity about what to