Emergence of coordination among individual agents in a complex system, where there is no central authority controlling their actions, requires information transfer between them and the ability to respond appropriately. Often, the interactions between these agents recur and the information generated from these interactions collectively, takes the form of some global cues available to all agents of the complex system. Agents respond to such information by altering their behavior accordingly, which results in adaptive dynamics in the system. Thus the amount and quality of the information available to the interacting agents plays an important role in the level of coordination they can achieve while competing for limited resources. Collecting and processing such information is a resource consuming task and therefore agents may resort to coarse-graining the data to suitable levels. Alternatively, the conditions maybe such that only coarse-grained data are available to agents.
In general, information can be of different types - qualitatively as well as quantitatively. Also there are different levels to which information may be coarse-grained. While in some cases detailed information may appear to be extremely useful, e.g., when one is playing against other agents in a financial market, in other situations, such as when choosing between alternative routes in one’s daily commute, it may suffice to know which option was chosen by the larger fraction of one’s peers.
Between these two extremes several intermediate levels of coarse-graining of past information may be defined. In this work, we address the question of how such coarse-graining can affect the emergent coordination of agents in a complex adaptive system. One might anticipate that a group of agents having finely resolved data would be better off and would be able to coordinate better compared to a group of agents who have less resolved data. In this work we show that this is not the case and in fact there could be an optimum level of coarse-graining which will result in better global outcomes in terms of coordination. To address the issue of the effect of information coarse-graining on the emergent coordination, we use a paradigmatic complex adaptive system in which one can study these issues in a precise way. In particular we use the well-known minority rewarding scenario to address this problem. We show that too little as well as too much information reduces the payoff of the agents. For each level of coarse-graining we determine the memory (i.e., the number of previous rounds of interactions that agents retain information about) that leads to the best collective outcome. We show that the optimal value for the memory exhibits a crossover behavior, being constant at high 1resolution but having logarithmic scaling with system size at lower resolutions.