Differential Games For Multi-agent Systems Under Distributed Information

In this dissertation, we consider differential games for multi-agent systems under distributed information where every agent is only able to acquire information about the others according to a directed information graph of local communication/sensor networks. Such games arise naturally from many applications including mobile robot coordination, power system optimization, multiplayer pursuit-evasion games, etc. Since the admissible strategy of each agent has to conform to the information graph constraint, the conventional game strategy design approaches based upon Riccati equation(s) are not applicable because all the agents are required to have the information of the entire system. Accordingly, the game strategy design under distributed information is commonly known to be challenging. Toward this end, we propose novel open-loop and feedback game strategy design approaches for Nash equilibrium and noninferior solutions with a focus on linear quadratic differential games. For the open-loop design, approximate Nash/noninferior game strategies are proposed by integrating distributed state estimation into the open-loop global-information Nash/noninferior strategies such that, without global information, the distributed game strategies can be made arbitrarily close to and asymptotically converge over time to the global-information strategies. For the feedback design, we propose the best achievable performance indices based approach under which the distributed strategies form a Nash equilibrium or noninferior solution with respect to a set of performance indices that are the closest to the original indices. This approach overcomes two issues in the classical optimal output feedback approach: the simultaneous optimization and initial state dependence. The proposed open-loop and feedback design approaches are applied to an unmanned aerial vehicle formation control problem and a multi-pursuer single-evader differential game problem, respectively. Simulation results of several scenarios are presented for illustration

A differential game approach to urban drainage systems control

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Urban drainage systems (UDSs) are complex large-scale systems that carry stormwater and wastewater throughout urban areas. During heavy rain scenarios, UDSs are not able to handle the amount of extra water that enters the network and flooding occurs. Usually, this might happen because the network is not being used efficiently, i.e., some structures remain underused while many others are overused. This paper proposes a control methology based on differential game theory that aims to efficiently use the existing network elements in order to minimize overflows and properly manage the water resource. The proposed controller is tested on a typical UDS and is compared with a centralized MPC achieving similar results in terms of flooding minimization and network usage, but only using local information on distributed controllers.Peer ReviewedPostprint (author's final draft

Difference games and policy evaluation: A conceptual framework

Economics

Sharing Rules and Stability in Coalition Games with Externalities

This paper examines cooperative sharing rules in fisheries coalition games and develops a new sharing rule that takes into account the stability of cooperation when externalities are present. We contribute to existing knowledge by introducing a connection between cooperative games (sharing rules) and non-cooperative games (stability). As an illustrative example, we describe a discrete-time, deterministic, coalition game model of the major agents who exploit the cod stock in the Baltic Sea.Baltic Sea cod, characteristic function, coalition game, cooperation, fisheries, nucleolus, Shapley value, sharing rules, stability of cooperation, Environmental Economics and Policy, C62, C70, Q22, Q28,

Dynamic Price Competition with Price Adjustment Costs and Product Differentiation

We study a discrete time dynamic game of price competition with spatially differentiated products and price adjustment costs. We characterise the Markov perfect and the open-loop equilibrium of our game. We find that in the steady state Markov perfect equilibrium, given the presence of adjustment costs, equilibrium prices are always higher than prices at the repeated static Nash solution, even though, adjustment costs are not paid in steady state. This is due to intertemporal strategic complementarity in the strategies of the firms and from the fact that the cost of adjusting prices adds credibility to high price equilibrium strategies. On the other hand, the stationary open-loop equilibrium coincides always with the static solution. Furthermore, in contrast to continuous time games, we show that the stationary Markov perfect equilibrium converges to the static Nash equilibrium when adjustment costs tend to zero. Moreover, we obtain the same convergence result when adjustment costs tend to infinity.Price adjustment costs, Difference game, Markov perfect equilibrium, Open-loop equilibrium

A Game-Theoretic Approach to Energy-Efficient Resource Allocation in Device-to-Device Underlay Communications

Despite the numerous benefits brought by Device-to-Device (D2D) communications, the introduction of D2D into cellular networks poses many new challenges in the resource allocation design due to the co-channel interference caused by spectrum reuse and limited battery life of User Equipments (UEs). Most of the previous studies mainly focus on how to maximize the Spectral Efficiency (SE) and ignore the energy consumption of UEs. In this paper, we study how to maximize each UE's Energy Efficiency (EE) in an interference-limited environment subject to its specific Quality of Service (QoS) and maximum transmission power constraints. We model the resource allocation problem as a noncooperative game, in which each player is self-interested and wants to maximize its own EE. A distributed interference-aware energy-efficient resource allocation algorithm is proposed by exploiting the properties of the nonlinear fractional programming. We prove that the optimum solution obtained by the proposed algorithm is the Nash equilibrium of the noncooperative game. We also analyze the tradeoff between EE and SE and derive closed-form expressions for EE and SE gaps.Comment: submitted to IET Communications. arXiv admin note: substantial text overlap with arXiv:1405.1963, arXiv:1407.155