Game Theory for Secure Critical Interdependent Gas-Power-Water Infrastructure

A city's critical infrastructure such as gas, water, and power systems, are largely interdependent since they share energy, computing, and communication resources. This, in turn, makes it challenging to endow them with fool-proof security solutions. In this paper, a unified model for interdependent gas-power-water infrastructure is presented and the security of this model is studied using a novel game-theoretic framework. In particular, a zero-sum noncooperative game is formulated between a malicious attacker who seeks to simultaneously alter the states of the gas-power-water critical infrastructure to increase the power generation cost and a defender who allocates communication resources over its attack detection filters in local areas to monitor the infrastructure. At the mixed strategy Nash equilibrium of this game, numerical results show that the expected power generation cost deviation is 35\% lower than the one resulting from an equal allocation of resources over the local filters. The results also show that, at equilibrium, the interdependence of the power system on the natural gas and water systems can motivate the attacker to target the states of the water and natural gas systems to change the operational states of the power grid. Conversely, the defender allocates a portion of its resources to the water and natural gas states of the interdependent system to protect the grid from state deviations.Comment: 7 pages, in proceedings of Resilience Week 201

Smoothed Efficient Algorithms and Reductions for Network Coordination Games

Worst-case hardness results for most equilibrium computation problems have raised the need for beyond-worst-case analysis. To this end, we study the smoothed complexity of finding pure Nash equilibria in Network Coordination Games, a PLS-complete problem in the worst case. This is a potential game where the sequential-better-response algorithm is known to converge to a pure NE, albeit in exponential time. First, we prove polynomial (resp. quasi-polynomial) smoothed complexity when the underlying game graph is a complete (resp. arbitrary) graph, and every player has constantly many strategies. We note that the complete graph case is reminiscent of perturbing all parameters, a common assumption in most known smoothed analysis results. Second, we define a notion of smoothness-preserving reduction among search problems, and obtain reductions from $2$-strategy network coordination games to local-max-cut, and from $k$-strategy games (with arbitrary $k$) to local-max-cut up to two flips. The former together with the recent result of [BCC18] gives an alternate $O(n^8)$-time smoothed algorithm for the $2$-strategy case. This notion of reduction allows for the extension of smoothed efficient algorithms from one problem to another. For the first set of results, we develop techniques to bound the probability that an (adversarial) better-response sequence makes slow improvements on the potential. Our approach combines and generalizes the local-max-cut approaches of [ER14,ABPW17] to handle the multi-strategy case: it requires a careful definition of the matrix which captures the increase in potential, a tighter union bound on adversarial sequences, and balancing it with good enough rank bounds. We believe that the approach and notions developed herein could be of interest in addressing the smoothed complexity of other potential and/or congestion games

Game theoretic control of multi-agent systems: from centralised to distributed control

Differential game theory provides a framework to study the dynamic strategic interactions between multiple decisors, or players, each with an individual criterion to optimise. Noting the analogy between the concepts of "players'' and "agents'', it seems apparent that this framework is well-suited for control of multi-agent systems (MAS). Most of the existing results in the field of differential games assume that players have access to the full state of the system. This assumption, while holding reasonable in certain scenarios, does not apply in contexts where decisions are to be made by each individual agent based only on available local information. This poses a significant challenge in terms of the control design: distributed control laws, which take into account what information is available, are required. In the present work concepts borrowed from differential game theory and graph theory are exploited to formulate systematic frameworks for control of MAS, in a quest to shift the paradigm from centralised to distributed control. We introduce some preliminaries on differential game theory and graph theory, the latter for modeling communication constraints between the agents. Motivated by the difficulties associated with obtaining exact Nash equilibrium solutions for nonzero-sum differential games, we consider three approximate Nash equilibrium concepts and provide different characterisations of these in terms a class of static optimisation problems often encountered in control theory. Considering the multi-agent collision avoidance problem, we present a game theoretic approach, based on a (centralised) hybrid controller implementation of the control strategies, capable of ensuring collision-free trajectories and global convergence of the error system. We make a first step towards distributed control by introducing differential games with partial information, a framework for distributed control of MAS subject to local communication constraints, in which we assume that the agents share their control strategies with their neighbours. This assumption which, in the case of non-acyclic communication graphs, translates into the requirement of shared reasoning between groups of agents, is then relaxed through the introduction of a framework based on the concept of distributed differential games, i.e. a collection of multiple (fictitious) local differential games played by each individual agent in the MAS. Finally, we revisit the multi-agent collision avoidance problem in a distributed setting: considering time-varying communication graph topologies, which enable to model proximity-based communication constraints, we design differential games characterised by a Nash equilibrium solution which yields collision-free trajectories guaranteeing that all the agents reach their goal, provided no deadlocks occur. The efficacy of the game theoretic frameworks introduced in this thesis is demonstrated on several case studies of practical importance, related to robotic coordination and control of microgrids.Open Acces