Inspired by a military context, we study a Stackelberg production game where a country's government, the leader, wants to maximize the production of military assets. The leader does so by allocating his resources among a set of production facilities. His opponent, the follower, observes this allocation and tries to destroy the associated production as much as possible by allocating his destructive resources, for example bombs, among these facilities. In this paper, we identify a follower's optimal strategy. For the leader, we show that an optimal production strategy can be found in the class of so-called seried-balanced strategies. We present a linear time algorithm that finds an optimal strategy in this class.
The multilevel reverse Stackelberg game is considered. In this game, the leader controls the outcome by announcing a strategy as a function of decision variables of the followers to his/her own decision space. Corresponding to the leader's strategy, the player in the next level presents his/her strategy as a function of decision variables of the remaining players. This procedure is repeated until it is the turn of the bottom level player in the hierarchy, who reacts by determining his/her optimal decision variables. The structure of this game can be adopted in decentralized multilevel decision…
In this paper we establish hierarchic control for the linear heat equation in $\re^N$ with potentials. Our strategy is inspired by the techniques developed by J.I. Díaz and J.-L. Lions \cite{DL}; however many new difficulties arise due to lack of compactness of Sobolev embeddings. We manage these adversities by employing similarity variables and weighted Sobolev spaces.
This paper studies a stochastic robotic surveillance problem where a mobile robot moves randomly on a graph to capture a potential intruder that strategically attacks a location on the graph. The intruder is assumed to be omniscient: it knows the current location of the mobile agent and can learn the surveillance strategy. The goal for the mobile robot is to design a stochastic strategy so as to maximize the probability of capturing the intruder. We model the strategic interactions between the surveillance robot and the intruder as a Stackelberg game, and optimal and suboptimal Markov chain ba…
China School of Banking and Finance, University of International Business and Economics（对外经济贸易大学中国银行业与金融学院）；School of Mathematics and Statistics, University of Sydney（悉尼大学数学与统计学院）
Mean Field Stackelberg Game for Production and Carbon Emission Reduction with State Reflections
School of Mathematics and Statistics, Xidian University（西安电子科技大学数学与统计学院）；The Chinese University of Hong Kong（香港中文大学）；University of Science and Technology of China（中国科学技术大学）
In this paper, we consider a discrete-time stochastic Stackelberg game with a single leader and multiple followers. Both the followers and the leader together have conditionally independent private types, conditioned on action and previous state, that evolve as controlled Markov processes. The objective is to compute the stochastic Stackelberg equilibrium of the game where the leader commits to a dynamic strategy. Each follower's strategy is the best response to the leader's strategies and other followers' strategies while the each leader's strategy is optimum given the followers play the best…
Two major problems in modern cities are air contamination and road congestion. They are closely related and present a similar origin: traffic flow. To face these problems, local governments impose traffic restrictions to prevent the entry of vehicles into sensitive areas, with the final aim of dropping down air pollution levels. However, these restrictions force drivers to look for alternative routes that usually generate congestions, implying both longer travel times and higher levels of air pollution. In this work, combining optimal control of partial differential equations and computational…
Following the solution to the One-Round Voronoi Game in arXiv:2011.13275, we naturally may want to consider similar games based upon the competitive locating of points and subsequent dividing of territories. In order to appease the tears of White (the first player) after they have potentially been tricked into going first in a game of point-placement, an alternative game (or rather, an extension of the Voronoi game) is the Stackelberg game where all is not lost if Black (the second player) gains over half of the contested area. It turns out that plenty of results can be transferred from One-Ro…
Linear-quadratic mixed Stackelberg-zero-sum game for mean-field regime switching system
Shandong University of Finance and Economics（山东财经大学）；Dalian University of Technology（大连理工大学）；The Hong Kong Polytechnic University（香港理工大学）；Imperial College（帝国理工学院）
Two-player mean-payoff Stackelberg games are nonzero-sum infinite duration games played on a bi-weighted graph by Leader (Player 0) and Follower (Player 1). Such games are played sequentially: first, Leader announces her strategy, second, Follower chooses his best-response. If we cannot impose which best-response is chosen by Follower, we say that Follower, though strategic, is adversarial towards Leader. The maximal value that Leader can get in this nonzero-sum game is called the adversarial Stackelberg value (ASV) of the game. We study the robustness of strategies for Leader in these games a…
A linear-quadratic partially observed Stackelberg stochastic differential game with multiple followers and its application to multi-agent formation control
East China University of Science and Technology（华东理工大学）；University of Alberta（阿尔伯塔大学）；Shandong University（山东大学）；Fudan University（复旦大学）
We present a resource-planning game for cyber-security of networked control systems (NCS). The NCS is assumed to be operating in closed-loop using a linear state-feedback $\mathcal{H}_2$ controller. A zero-sum, two-player Stackelberg game (SG) is developed between an attacker and a defender for this NCS. The attacker aims to disable communication of selected nodes and thereby render the feedback gain matrix to be sparse, leading to degradation of closed-loop performance, while the defender aims to prevent this loss by investing in the protection of targeted nodes. Both players trade their $\ma…
The paper deals with a class of parametrized equilibrium problems, where the objectives of the players do possess nonsmooth terms. The respective Nash equilibria can be characterized via a parameter-dependent variational inequality of the second kind, whose Lipschitzian stability is thoroughly investigated. This theory is then applied to evolution of a oligopolistic market in which the firms adopt their production strategies to changing input costs, while each change of the production is associated with some "costs of change". We examine both the Cournot-Nash equilibria as well as the two-leve…
This paper investigates a Stackelberg game between an insurer and a reinsurer under the $α$-maxmin mean-variance criterion. The insurer can purchase per-loss reinsurance from the reinsurer. With the insurer's feedback reinsurance strategy, the reinsurer optimizes the reinsurance premium in the Stackelberg game. The financial market consists of cash and stock with Heston's stochastic volatility. Both the insurer and reinsurer maximize their respective $α$-maxmin mean-variance preferences in the market. The criterion is time-inconsistent and we derive the equilibrium strategies by the extended H…
We consider a two-player game of war of attrition under complete information. It is well-known that this class of games admits equilibria in pure, as well as mixed strategies, and much of the literature has focused on the latter. We show that if the players' payoffs whilst in "war" vary stochastically and their exit payoffs are heterogeneous, then the game admits Markov Perfect equilibria in pure strategies only. This is true irrespective of the degree of randomness and heterogeneity, thus highlighting the fragility of mixed-strategy equilibria to a natural perturbation of the canonical model.…
In this paper, the problem of distributed detection in tree networks in the presence of Byzantines is considered. Closed form expressions for optimal attacking strategies that minimize the miss detection error exponent at the fusion center (FC) are obtained. We also look at the problem from the network designer's (FC's) perspective. We study the problem of designing optimal distributed detection parameters in a tree network in the presence of Byzantines. Next, we model the strategic interaction between the FC and the attacker as a Leader-Follower (Stackelberg) game. This formulation provides a…
