Casting Light on the Hidden Bilevel Combinatorial Structure of the Capacitated Vertex Separator Problem

2021 ◽  
Author(s):  
Furini Fabio ◽  
Ljubić Ivana ◽  
Malaguti Enrico ◽  
Paronuzzi Paolo
Keyword(s):  
Stackelberg Game ◽  
Bilevel Optimization ◽  
Optimization Techniques ◽  
Combinatorial Structure ◽  
Stackelberg Games ◽  
Edge Deletion ◽  
Vertex Separator ◽  
Bounded Number ◽  
Critical Nodes ◽  
Partitioning Problems

Exploiting Bilevel Optimization Techniques to Disconnect Graphs into Small Components In order to limit the spread of possible viral attacks in a communication or social network, it is necessary to identify critical nodes, the protection of which disconnects the remaining unprotected graph into a bounded number of shores (subsets of vertices) of limited cardinality. In the article “'Casting Light on the Hidden Bilevel Combinatorial Structure of the Capacitated Vertex Separator Problem”, Furini, Ljubic, Malaguti, and Paronuzzi provide a new bilevel interpretation of the associated capacitated vertex separator problem and model it as a two-player Stackelberg game in which the leader interdicts (protects) the vertices, and the follower solves a combinatorial optimization problem on the resulting graph. Thanks to this bilevel interpretation, the authors derive different families of strengthening inequalities and show that they can be separated in polynomial time. The ideas exploited in their framework can also be extended to other vertex/edge deletion/insertion problems or graph partitioning problems by modeling them as two-player Stackelberg games to be solved through bilevel optimization.

The Stackelberg Games of Water Extraction with Myopic Agents

2021 ◽  
Author(s):  
Alain Jean-Marie ◽  
Mabel Tidball ◽  
Víctor Bucarey López
Keyword(s):  
Stackelberg Game ◽  
Infinite Horizon ◽  
Dynamic Game ◽  
Water Extraction ◽  
Discount Factor ◽  
Stackelberg Games ◽  
Groundwater Extraction ◽  
Strategic Interactions ◽  
Water Users ◽  
Threshold Policies

We consider a discrete-time, infinite-horizon dynamic game of groundwater extraction. A Water Agency charges an extraction cost to water users and controls the marginal extraction cost so that it depends not only on the level of groundwater but also on total water extraction (through a parameter [Formula: see text] that represents the degree of strategic interactions between water users) and on rainfall (through parameter [Formula: see text]). The water users are selfish and myopic, and the goal of the agency is to give them incentives so as to improve their total discounted welfare. We look at this problem in several situations. In the first situation, the parameters [Formula: see text] and [Formula: see text] are considered to be fixed over time. The first result shows that when the Water Agency is patient (the discount factor tends to 1), the optimal marginal extraction cost asks for strategic interactions between agents. The contrary holds for a discount factor near 0. In a second situation, we look at the dynamic Stackelberg game where the Agency decides at each time what cost parameter they must announce. We study theoretically and numerically the solution to this problem. Simulations illustrate the possibility that threshold policies are good candidates for optimal policies.

Game Theoretic Study of Cooperative Spectrum Leasing in Cognitive Radio Networks

2014 ◽  
Vol 5 (2) ◽  
pp. 61-74 ◽  
Author(s):  
Fatemeh Afghah ◽  
Abolfazl Razi
Keyword(s):  
Cognitive Radio ◽  
Cognitive Radio Networks ◽  
Stackelberg Game ◽  
Cooperative Behavior ◽  
Search Space ◽  
Radio Networks ◽  
Cooperative Relaying ◽  
Stackelberg Games ◽  
Secondary Users ◽  
Spectrum Leasing

In this paper, a novel property-right spectrum leasing solution based on Stackelberg game is proposed for Cognitive Radio Networks (CRN), where part of the secondary users present probabilistic dishonest behavior. In this model, the Primary User (PU) as the spectrum owner allows the Secondary User (SU) to access the shared spectrum for a fraction of time in exchange for providing cooperative relaying service by the SU. A reputation based mechanism is proposed that enables the PU to monitor the cooperative behavior of the SUs and restrict its search space at each time slot to the secondary users that do not present dishonest behavior in the proceeding time slots. The proposed reputation-based solution outperforms the classical Stackelberg games from both primary and reliable secondary users' perspectives. This novel method of filtering out unreliable users increases the PU's expected utility over consecutive time slots and also encourages the SUs to follow the game rule.

Integrating Prospect Theory and Stackelberg Games to Model Strategic Dyad Behavior of Information Providers and Travelers

2005 ◽  
Vol 1926 (1) ◽  
pp. 181-188 ◽  
Author(s):  
Qi Han ◽  
Benedict G. C. Dellaert ◽  
W. Fred Van Raaij ◽  
Harry J. P. Timmermans
Keyword(s):  
Prospect Theory ◽  
Stackelberg Game ◽  
Specific Activity ◽  
Face Validity ◽  
Stackelberg Games ◽  
Start Time ◽  
Policy Objective ◽  
Optimal Guidance ◽  
Activity Schedule ◽  
The Face

Existing policy models of optimal guidance strategies are typically concerned with single-objective optimization based on reliable forecasts in terms of the consistency between predicted and observed aggregate activity–travel patterns. The interaction and interdependencies between policy objective and individuals have not received much attention. This paper considers how one specific activity schedule choice–-namely, the start time of an activity chosen by individual travelers under guidance information–-aggregates to form an equilibrium distribution, which in turn influences guidance generation and determines the best possible achievement of the policy objective. These choices are formalized as the outcomes of a Stackelberg game in which a traveler's behavior model is integrated with prospect theory. The properties of the model are examined by using numerical computer simulations. The results of the simulations support the face validity of the formulated model.

scholarly journals Using Game Theory for Los Angeles Airport Security

AI Magazine ◽  
2009 ◽  
Vol 30 (1) ◽  
pp. 43 ◽  
Author(s):  
James Pita ◽  
Manish Jain ◽  
Fernando Ordóñez ◽  
Christopher Portway ◽  
Milind Tambe ◽  
...  
Keyword(s):  
Los Angeles ◽  
Stackelberg Game ◽  
Information Design ◽  
Airport Security ◽  
Stackelberg Games ◽  
Mixed Strategies ◽  
Costs And Benefits ◽  
Multi Agent ◽  
Mixed Initiative ◽  
Airport Terminals

Security at major locations of economic or political importance is a key concern around the world, particularly given the threat of terrorism. Limited security resources prevent full security coverage at all times, which allows adversaries to observe and exploit patterns in selective patrolling or monitoring, e.g. they can plan an attack avoiding existing patrols. Hence, randomized patrolling or monitoring is important, but randomization must provide distinct weights to different actions based on their complex costs and benefits. To this end, this paper describes a promising transition of the latest in multi-agent algorithms into a deployed application. In particular, it describes a software assistant agent called ARMOR (Assistant for Randomized Monitoring over Routes) that casts this patrolling/monitoring problem as a Bayesian Stackelberg game, allowing the agent to appropriately weigh the different actions in randomization, as well as uncertainty over adversary types. ARMOR combines two key features: (i) It uses the fastest known solver for Bayesian Stackelberg games called DOBSS, where the dominant mixed strategies enable randomization; (ii) Its mixed-initiative based interface allows users to occasionally adjust or override the automated schedule based on their local constraints. ARMOR has been successfully deployed since August 2007 at the Los Angeles International Airport (LAX) to randomize checkpoints on the roadways entering the airport and canine patrol routes within the airport terminals. This paper examines the information, design choices, challenges, and evaluation that went into designing ARMOR.

scholarly journals Stochastic Bilevel Program for Optimal Coordinated Energy Trading of an EV Aggregator

Energies ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3813 ◽  
Author(s):  
Yelena Vardanyan ◽  
Henrik Madsen
Keyword(s):  
Large Scale ◽  
Stackelberg Game ◽  
Strong Duality ◽  
Bilevel Optimization ◽  
Transport Sector ◽  
Global Optimality ◽  
Complementary Slackness ◽  
Bilevel Program ◽  
Ev Charging ◽  
Stochastic Bilevel Program

Gradually replacing fossil-fueled vehicles in the transport sector with Electric Vehicles (EVs) may help ensure a sustainable future. With regard to the charging electric load of EVs, optimal scheduling of EV batteries, controlled by an aggregating agent, may provide flexibility and increase system efficiency. This work proposes a stochastic bilevel optimization problem based on the Stackelberg game to create price incentives that generate optimal trading plans for an EV aggregator in day-ahead, intra-day and real-time markets. The upper level represents the profit maximizer EV aggregator who participates in three sequential markets and is called a Stackelberg leader, while the second level represents the EV owner who aims at minimizing the EV charging cost, and who is called a Stackelberg follower. This formulation determines endogenously the profit-maximizing price levels constraint by cost-minimizing EV charging plans. To solve the proposed stochastic bilevel program, the second level is replaced by its optimality conditions. The strong duality theorem is deployed to substitute the complementary slackness condition. The final model is a stochastic convex problem which can be solved efficiently to determine the global optimality. Illustrative results are reported based on a small case with two vehicles. The numerical results rely on applying the proposed methodology to a large scale fleet of 100, 500, 1000 vehicles, which provides insights into the computational tractability of the current formulation.

scholarly journals Differential Privacy for Stackelberg Games

2020 ◽  
Author(s):  
Ferdinando Fioretto ◽  
Lesia Mitridati ◽  
Pascal Van Hentenryck
Keyword(s):  
Electricity Market ◽  
Original Problem ◽  
Differential Privacy ◽  
Stackelberg Game ◽  
Privacy Preserving ◽  
Coordination Mechanism ◽  
Stackelberg Games ◽  
Sensitive Information ◽  
Near Optimality

This paper introduces a differentially private (DP) mechanism to protect the information exchanged during the coordination of sequential and interdependent markets. This coordination represents a classic Stackelberg game and relies on the exchange of sensitive information between the system agents. The paper is motivated by the observation that the perturbation introduced by traditional DP mechanisms fundamentally changes the underlying optimization problem and even leads to unsatisfiable instances. To remedy such limitation, the paper introduces the Privacy-Preserving Stackelberg Mechanism (PPSM), a framework that enforces the notions of feasibility and fidelity (i.e. near-optimality) of the privacy-preserving information to the original problem objective. PPSM complies with the notion of differential privacy and ensures that the outcomes of the privacy-preserving coordination mechanism are close-to-optimality for each agent. Experimental results on several gas and electricity market benchmarks based on a real case study demonstrate the effectiveness of the proposed approach. A full version of this paper [Fioretto et al., 2020b] contains complete proofs and additional discussion on the motivating application.

scholarly journals Stackelberg vs. Nash in Security Games: An Extended Investigation of Interchangeability, Equivalence, and Uniqueness

2011 ◽  
Vol 41 ◽  
pp. 297-327 ◽  
Author(s):  
D. Korzhyk ◽  
Z. Yin ◽  
C. Kiekintveld ◽  
V. Conitzer ◽  
M. Tambe
Keyword(s):  
Nash Equilibrium ◽  
Stackelberg Game ◽  
Stackelberg Games ◽  
Equilibrium Strategy ◽  
Future Research ◽  
Game Model ◽  
Multiple Targets ◽  
Stackelberg Strategy ◽  
Nash Equilibrium Strategy ◽  
Security Games

There has been significant recent interest in game-theoretic approaches to security, with much of the recent research focused on utilizing the leader-follower Stackelberg game model. Among the major applications are the ARMOR program deployed at LAX Airport and the IRIS program in use by the US Federal Air Marshals (FAMS). The foundational assumption for using Stackelberg games is that security forces (leaders), acting first, commit to a randomized strategy; while their adversaries (followers) choose their best response after surveillance of this randomized strategy. Yet, in many situations, a leader may face uncertainty about the follower’s surveillance capability. Previous work fails to address how a leader should compute her strategy given such uncertainty. We provide five contributions in the context of a general class of security games. First, we show that the Nash equilibria in security games are interchangeable, thus alleviating the equilibrium selection problem. Second, under a natural restriction on security games, any Stackelberg strategy is also a Nash equilibrium strategy; and furthermore, the solution is unique in a class of security games of which ARMOR is a key exemplar. Third, when faced with a follower that can attack multiple targets, many of these properties no longer hold. Fourth, we show experimentally that in most (but not all) games where the restriction does not hold, the Stackelberg strategy is still a Nash equilibrium strategy, but this is no longer true when the attacker can attack multiple targets. Finally, as a possible direction for future research, we propose an extensive-form game model that makes the defender’s uncertainty about the attacker’s ability to observe explicit.

Parametric Deformations and Model Optimality in Concurrent Design

1993 ◽  
Author(s):  
J. R. Jagannatha Rao ◽  
Bala Chidambaram
Keyword(s):  
Engineering Design ◽  
Design Research ◽  
Stackelberg Game ◽  
Stackelberg Games ◽  
Concurrent Design ◽  
Design Problems ◽  
Pareto Model ◽  
Engineering Design Problems ◽  
Analysis And Synthesis ◽  
Potential Benefits

Abstract Concurrent modeling, as an emerging theme in engineering design research, also offers interesting new challenges in applied optimization. However, it is not always clear how best to construct mathematical models that represent such concurrent decision-making. In this paper, a class of engineering design problems, comprising analysis and synthesis tasks, is shown to be a two-player Stackelberg game with synthesis as the leader and analysis as the follower. Situations arising from a reversal of roles of the two tasks are studied and a Pareto model of a Design versus Analysis game is also investigated. Stackelberg games are then viewed in the larger context of concurrent design with design and manufacturing as two players. The potential benefits of such an approach are illustrated in the concurrent design of a stiffened plate structure.

Bilevel Optimization of Taxing Strategies for Carbon Emissions Using Fuzzy Random Matrix Generators

2022 ◽  
pp. 210-234
Author(s):  
Timothy Ganesan ◽  
Irraivan Elamvazuthi
Keyword(s):  
Power Generation ◽  
Carbon Emissions ◽  
Random Matrix ◽  
Matrix Theory ◽  
Stackelberg Game ◽  
Cuckoo Search ◽  
Bilevel Optimization ◽  
Tax Rates ◽  
The Novel ◽  
Fuzzy Random

Bilevel (BL) optimization of taxing strategies in consideration of carbon emissions was carried out in this work. The BL optimization problem was considered with two primary targets: (1) designing an optimal taxing strategy (imposed on power generation companies) and (2) developing optimal economic dispatch (ED) schema (by power generation companies) in response to tax rates. The resulting interaction was represented using Stackelberg game theory – where the novel fuzzy random matrix generators were used in tandem with the cuckoo search (CS) technique. Fuzzy random matrices were developed by modifying certain aspects of the original random matrix theory. The novel methodology was tailored for tackling complex optimization systems with intermediate complexity such as the application problem tackled in this work. Detailed performance and comparative analysis are also presented in this chapter.

scholarly journals A Stackelberg Game Approach for Price Response Coordination of Thermostatically Controlled Loads

2018 ◽  
Vol 8 (8) ◽  
pp. 1370 ◽  
Author(s):  
Peng Wang ◽  
Suli Zou ◽  
Xiaojuan Wang ◽  
Zhongjing Ma
Keyword(s):  
Electricity Market ◽  
Energy Demand ◽  
Stackelberg Game ◽  
Electric Energy ◽  
Stackelberg Games ◽  
Control Center ◽  
Point Temperature ◽  
Set Point ◽  
Price Response ◽  
Thermostatically Controlled Loads

In this paper, we study the demand response of the thermostatically controlled loads (TCLs) to control their set-point temperatures by considering the tradeoff between the electricity payment and TCL user’s comfort preference. Based upon the dynamics of the TCLs, we set up the relationship between the set-point temperature and the energy demand. Then, we define a discomfort function with respect to the associated energy demand which represents the discomfort level of the set-point temperature. More specifically, the system is equipped with a coordinator named electric energy control center (EECC) which can buy energy resources from the electricity market and sell them to TCL users. Due to the interaction between EECC and TCL users, we formulate the specific energy trading process as a one-leader multiple-follower Stackelberg game. As the main contributions of this work, we show the existence and uniqueness of the equilibrium for the underlying Stackelberg games, and develop a DR algorithm based on the so-called Backward Induction to achieve the equilibrium. Several numerical simulations are presented to verify the developed results in this work.

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