PRELIMINARY VERSION. As a motivating example we consider a population, say of birds or fish, whose members are moving in IR 3. It has been observed that under some initial conditions, for example on their positions and velocities, the state of the flock converges to one

A common situation occurring in a number of disciplines is that in which a number of autonomous agents reach a consensus without a central direction. An example of this is the emergence of a common belief in a price system when activity takes place in a given market. Another example is the emergence of common languages in primitive societies, or the dawn of vowel systems. Yet a third example is the way in which populations of animals move together (referred as “schooling”, “flocking”, or “herding ” depending on the considered animals). As a motivating example in this introduction we consider a population, say of birds, whose members are moving in IE = IR 3. This situation has been recently studied in [6] and in what follows we freely draw from this paper. It has been observed that under some initial conditions, for example on the positions and velocities of the birds, the state of the flock converges to one in which all birds fly with the same velocity. A way to justify this observation is to postulate a model for the evolution of the flock and exhibit conditions on the initial state under which a convergence as above is established. In case these conditions are not satisfied, dispersion of the flock may occur. ∗ For the Japanese Journal of Mathematics. † Partially supported by an NSF grant.

Over the past years, several computational models have been introduced to study the coordination of communication between distributed agents. Although these models have given valuable insights into the mechanisms required for letting agents develop a successful communication system, few theoretical results have been obtained which substantiate these findings. In this paper we introduce a theoretical framework which allows us to analyze and compare different existing models in a uniform way. Therefore we only look at the observable behavior of an agent and not at the internal mechanisms that cause that behavior. In particular, we define an agent’s response function and argue that a stability analysis of its fixed points reveals crucial information about the convergence properties of the dynamical system of interacting agents. 1

We review some of the main theories about how language emerged. We suggest that including the study of the emergence of artificial languages, in simulation settings, allows us to ask a more general question, namely, what are the minimal initial conditions for the emergence of language? This is a very important question from a technological viewpoint, because it is very closely tied to questions of intelligence and autonomy. We identify anticipation as being a key underlying computational principle in the emergence of language. We suggest that this is in fact present implicitly in many of the theories in contention today. Focused simulations that address precise questions are necessary to isolate the roles of the minimal initial conditions for the emergence of language. 1 What is the problem of language emergence? It is very hard to imagine what life would be like without language. Before some point in our evolutionary history, however, our ancestors did not have language.

We study the role of the interaction network in a collaborative learning model known as the classification game. This involves a population of agents collaboratively learning to solve a classification task. We have previously shown that interaction while learning allows the agents to converge upon a simpler solution, which in turns guarantees better generalization. This clearly shows the benefits of social learning over individual learning. Here we show that by varying the interaction topology during the learning process, convergence can be achieved very rapidly, at the expense of only a small decrease in the quality of the solution. The interaction topology is evolved using Noisy Preferential Attachment (NPA) algorithm, which is a variant of preferential attachment that unifies the network dynamics with evolutionary dynamics. In the classification game, NPA can be viewed as a recommendation mechanism. We also compare convergence times for several fixed topologies, and show that convergence using NPA is the fastest. 1

Multi-Agent Agreement problems (MAP)- the ability of a population of agents to search out and converge on a common state- are central issues in many multi-agent settings, from distributed sensor networks, to meeting scheduling, to development of norms, conventions, and language. While much work has been done on particular agreement problems, no unifying framework exists for comparing MAPs that vary in, e.g., strategy space complexity, inter-agent accessibility, and solution type, and understanding their relative complexities. We present such a unification, the Distributed Optimal Agreement Framework, and show how it captures a wide variety of agreement problems. To demonstrate DOA and its power, we apply it to two well-known MAPs: convention evolution and language convergence. We demonstrate the insights DOA provides toward improving known approaches to these problems. Using a careful comparative analysis of a range of MAPs and solution approaches via the DOA framework, we identify a single critical differentiating factor: how accurately an agent can discern other agent’s states. To demonstrate how variance in this factor influences solution tractability and complexity we show its effect on the convergence time and quality of Particle Swarm Optimization approach to a generalized MAP.

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This dissertation studies multiagent agreement problems – problems in which a population of agents must agree on some quantity or behavior in a distributed manner. Agreement problems are central in many areas, from the study of magnetism (Ising model), to understanding the diffusion of innovations (such as the diffusion of hybrid corn planting in Illinois), to modeling linguistic change. The thesis of this dissertation is that the ability for agents to optimally allocate resources towards 1) gaining information from which to infer the agreeing population’s global agreement state (“information gathering”) and 2) effectively using that information to make convergence decisions that move towards agreement (“information use”), are the fundamental factors that explain the performance of a distributed agreement-seeking collective, and that variations on these processes capture all prevalent styles of agreement problems. In this dissertation we develop a taxonomic framework that organizes a wide range of agreement problems according to constraints on information gathering and information use. We explore two specific instances of agreement problems in more depth; the first modulates information gathering by constraining the ability of agents to communicate; the second modulates information use by constraining the ability of agents to

We investigate the emergent behavior of four types of generic dynamical systems under random environmental perturbations. Sufficient conditions for nearly-emergence in various scenarios are presented. Recent fundamental works of F. Cucker and S. Smale on the construction and analysis of flocking models directly inspired our present work. Keywords: emergence; Cucker-Smale model; dynamical system; flocking; multiagent system; consensus problems; random noise; linguistic evolution.