Tuning Rate of Strategy Revision in Population Games

We investigate a multi-agent decision problem in population games where each agent in a population makes a decision on strategy selection and revision to engage in repeated games with others. The strategy revision is subject to time delays which represent the time it takes for an agent revising its strategy needs to spend before it can adopt a new strategy and return back to the game. We discuss the effect of the time delays on long-term behavior of the agents' strategy revision. In particular, when the time delays are large, the strategy revision would exhibit oscillation and the agents spend substantial time in "transitioning" between different strategies, which prevents the agents from attaining the Nash equilibrium of the game. As a main contribution of the paper, we propose an algorithm that tunes the rate of the agents' strategy revision and show such tuning approach ensures convergence to the Nash equilibrium. We validate our analytical results using simulations

Optimal Remote State Estimation for Self-Propelled Particle Models

We investigate the design of a remote state estimation system for a self-propelled particle (SPP). Our framework consists of a sensing unit that accesses the full state of the SPP and an estimator that is remotely located from the sensing unit. The sensing unit must pay a cost when it chooses to transmit information on the state of the SPP to the estimator; and the estimator computes the best estimate of the state of the SPP based on received information. In this paper, we provide methods to design transmission policies and estimation rules for the sensing unit and estimator, respectively, that are optimal for a given cost functional that combines state estimation distortion and communication costs. We consider two notions of optimality: joint optimality and person-by-person optimality. Our main results show the existence of a jointly optimal solution and describe an iterative procedure to find a person-by-person optimal solution. In addition, we explain how the remote estimation scheme can be applied to tracking of animal movements over a costly communication link. We also provide experimental results to show the effectiveness of the scheme.Comment: a part of the article was submitted to IEEE Conference on Decision and Control 201

Payoff Mechanism Design for Coordination in Multi-Agent Task Allocation Games

We investigate a multi-agent decision-making problem where a large population of agents are responsible for carrying out a set of assigned tasks. The amount of jobs in each task varies over time governed by a dynamical system model. Each agent needs to select one of available strategies to take on one or more tasks. Since each strategy allows an agent to perform multiple tasks at a time, possibly at distinct rates, the strategy selection of the agents need to be coordinated. The main objective of this work is to design a decentralized decision-making model that coordinates the agents in selecting strategies and allows them to asymptotically adopt the optimal strategies, e.g., the strategies that minimize remaining jobs in all assigned tasks. We formulate the problem using the population game formalism and refer to it as the task allocation game. We discuss the design of a decision-making model that incentivizes the agents to coordinate in the strategy selection process. As key contributions, we propose a method to find a payoff-driven decision-making model, and discuss how the model allows the strategy selection of the agents to be responsive to the amount of remaining jobs in each task while asymptotically attaining the optimal strategies. Leveraging analytical tools from feedback control theory, we derive technical conditions that the model needs to satisfy, which are used to construct a numerical approach to compute the model. We validate our solution through simulations to highlight how the proposed approach coordinates the agents in task allocation games

DISTRIBUTED ESTIMATION AND STABILITY OF EVOLUTIONARY GAME DYNAMICS WITH APPLICATIONS TO STUDY OF ANIMAL MOTION

In this dissertation, we consider three problems: in the first we investigate distributed state estimation of linear time-invariant (LTI) plants; in the second we study optimal remote state estimation of Markov processes; while in the third we examine stability of evolutionary game dynamics in large populations. Problem 1: Consider that an autonomous LTI plant is given and that each member of a network of LTI observers accesses a portion of the output of the plant. The dissemination of information within the network is dictated by a pre-specified directed graph in which each vertex represents an observer. This work proposes a distributed estimation scheme that is a natural generalization of consensus in which each observer computes its own state estimate using only the portion of the output vector accessible to it and the state estimates of other observers that are available to it, according to the graph. Unlike straightforward high-order solutions in which each observer broadcasts its measurements throughout the network, the average size of the state of each observer in the proposed scheme does not exceed the order of the plant plus one. We determine necessary and sufficient conditions for the existence of a parameter choice for which the proposed scheme attains asymptotic omniscience of the state of the plant at all observers. The conditions reduce to certain detectability requirements that imply that if omniscience is not possible under the proposed scheme then it is not viable under any other scheme -- including higher order LTI, nonlinear, and time-varying ones -- subject to the same graph. We apply the proposed scheme to distributed tracking of a group of water buffaloes. Problem 2: Consider a two-block remote estimation framework in which a sensing unit accesses the full state of a Markov process and decides whether to transmit information about the state to a remotely located estimator given that each transmission incurs a communication cost. The estimator finds the best state estimate of the process using the information received from the sensing unit. The main purpose of this work is to design transmission policies and estimation rules that dictate decision making of the sensing unit and estimator, respectively, and that are optimal for a cost functional which combines the expectation of squared estimation error and communication costs. Our main results establish the existence of transmission policies and estimation rules that are jointly optimal, and propose an iterative procedure to find ones. Our convergence analysis shows that the sequence of sub-optimal solutions generated by the proposed procedure has a convergent subsequence, and the limit of any convergent subsequence is a person-by-person optimal solution. We apply the proposed scheme to remote estimation of location of a water buffalo. Problem 3: We investigate an energy conservation and dissipation (passivity) aspect of evolutionary dynamics in evolutionary game theory. We define a notion of passivity for evolutionary dynamics, and describe conditions under which dynamics exhibit passivity. For dynamics that are defined on a finite-dimensional state space, we show that the conditions can be characterized in connection with state-space realizations of the dynamics. In addition, we establish stability of passive dynamics in terms of dissipation of stored energy defined by passivity, and present stability results in population games. We provide implications of stability for various passive dynamics both analytically and by means of numerical simulations

Proactive Opinion-Driven Robot Navigation around Human Movers

We propose, analyze, and experimentally verify a new proactive approach for robot social navigation driven by the robot's "opinion" for which way and by how much to pass human movers crossing its path. The robot forms an opinion over time according to nonlinear dynamics that depend on the robot's observations of human movers and its level of attention to these social cues. For these dynamics, it is guaranteed that when the robot's attention is greater than a critical value, deadlock in decision making is broken, and the robot rapidly forms a strong opinion, passing each human mover even if the robot has no bias nor evidence for which way to pass. We enable proactive rapid and reliable social navigation by having the robot grow its attention across the critical value when a human mover approaches. With human-robot experiments we demonstrate the flexibility of our approach and validate our analytical results on deadlock-breaking. We also show that a single design parameter can tune the trade-off between efficiency and reliability in human-robot passing. The new approach has the additional advantage that it does not rely on a predictive model of human behavior.Comment: 8 pages, 7 figure

Analysis and control of agreement and disagreement opinion cascades

We introduce and analyze a continuous time and state-space model of opinion cascades on networks of large numbers of agents that form opinions about two or more options. By leveraging our recent results on the emergence of agreement and disagreement states, we introduce novel tools to analyze and control agreement and disagreement opinion cascades. New notions of agreement and disagreement centrality, which depend only on network structure, are shown to be key to characterizing the nonlinear behavior of agreement and disagreement opinion formation and cascades. Our results are relevant for the analysis and control of opinion cascades in real-world networks, including biological, social and artificial networks, and for the design of opinion-forming behaviors in robotic swarms. We illustrate an application of our model to a multi-robot task-allocation problem and discuss extensions and future directions opened by our modeling framework