Sequential Stackelberg equilibria in two-person games

Breton, Michèle; Alj, Abdelkamel; Haurie, Alain

doi:10.1007/bf00939867

Cited by 157 publications

(73 citation statements)

References 10 publications

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“…al. [3]. The strong form assumes that the follower will always choose the optimal strategy for the leader in cases of indifference, while the weak form assumes that the follower will choose the worst strategy for the leader.…”

Section: Stackelberg Equilibriummentioning

confidence: 99%

“…s l } is a subset of the power set of the targets, with restrictions on this set representing scheduling constraints. We define the relationship between targets and schedules with the function M : S × T → {0, 1}, which evaluates to 1 if and only if t is covered in s. 3 The defender's strategy is an assignment of resources to schedules, rather than targets. A second extension introduces resource types, Ω = {ω1, .…”

Section: Scheduling and Resource Con-straintsmentioning

confidence: 99%

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Computing Optimal Randomized Resource Allocations for Massive Security Games

Kiekintveld¹,

Jain²,

Tsai³

et al. 2011

Security and Game Theory

140

247

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Predictable allocations of security resources such as police officers, canine units, or checkpoints are vulnerable to exploitation by attackers. Recent work has applied game-theoretic methods to find optimal randomized security policies, including a fielded application at the Los Angeles International Airport (LAX). This approach has promising applications in many similar domains, including police patrolling for subway and bus systems, randomized baggage screening, and scheduling for the Federal Air Marshal Service (FAMS) on commercial flights. However, the existing methods scale poorly when the security policy requires coordination of many resources, which is central to many of these potential applications.We develop new models and algorithms that scale to much more complex instances of security games. The key idea is to use a compact model of security games, which allows exponential improvements in both memory and runtime relative to the best known algorithms for solving general Stackelberg games. We develop even faster algorithms for security games under payoff restrictions that are natural in many security domains. Finally, introduce additional realistic scheduling constraints while retaining comparable performance improvements. The empirical evaluation comprises both random data and realistic instances of the FAMS and LAX problems. Our new methods scale to problems several orders of magnitude larger than the fastest known algorithm.

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Section: Stackelberg Equilibriummentioning

confidence: 99%

Section: Scheduling and Resource Con-straintsmentioning

confidence: 99%

Computing Optimal Randomized Resource Allocations for Massive Security Games

Kiekintveld¹,

Jain²,

Tsai³

et al. 2011

Security and Game Theory

140

247

View full text Add to dashboard Cite

show abstract

“…Constraints (5) and (12) force each adversary to select a pure strategy attacking a single target. The coverage vector C is constrained by the number of available resources through (8) and the coverage in each target to be in the range [0, 1] by (13).…”

Section: Solution Methodsmentioning

confidence: 99%

“…al. [12]. The strong form assumes that the follower will always choose the optimal strategy for the leader in cases of indifference, while the weak form assumes that the follower will choose the worst strategy for the leader.…”

Section: Stackelberg Equilibriummentioning

confidence: 99%

Deployed Security Games for Patrol Planning

Ordóñez

Tambe

Jara

et al. 2012

International Series in Operations Research &Amp; Management Science

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Nations and organizations need to secure locations of economic, military, or political importance from groups or individuals that can cause harm. The fact that there are limited security resources prevents complete security coverage, which allows adversaries to observe and exploit patterns in patrolling or monitoring, and enables them to plan attacks that avoid existing patrols. The use of randomized security policies that are more difficult for adversaries to predict and exploit can counter their surveillance capabilities and improve security. In this chapter we describe the recent development of models to assist security forces in randomizing their patrols and their deployment in real applications. The systems deployed are based on fast algorithms for solving large instances of Bayesian Stackelberg games that capture the interaction between security forces and adversaries. Here we describe a generic mathematical formulation of these models, present some of the results that have allowed these systems to be deployed in practice, and outline remaining future challenges. We discuss the deployment of these systems in two real-world security applications: 1) The police at the Los Angeles International Airport uses these models to randomize the placement of checkpoints on roads entering the airport and the routes of canine unit patrols within the airport terminals.2) The Federal Air Marshal Service uses these models to randomize the schedules of air marshals on international flights.

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“…In the case of multiple followers' responses, the max-selection corresponds (for M = 1) to the so-called strong Stackelberg-Nash solution or optimistic Stackelberg-Nash solution (see [32][33][34][35]). …”

Section: A More General Case In An Optimistic Viewmentioning

confidence: 99%

Multi-Leader Multi-Follower Model with Aggregative Uncertainty

Mallozzi

Messalli

2017

Games

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Abstract:We study a non-cooperative game with aggregative structure, namely when the payoffs depend on the strategies of the opponent players through an aggregator function. We assume that a subset of players behave as leaders in a Stackelberg model. The leaders, as well the followers, act non-cooperatively between themselves and solve a Nash equilibrium problem. We assume an exogenous uncertainty affecting the aggregator and we obtain existence results for the stochastic resulting game. Some examples are illustrated.

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Sequential Stackelberg equilibria in two-person games

Cited by 157 publications

References 10 publications

Computing Optimal Randomized Resource Allocations for Massive Security Games

Computing Optimal Randomized Resource Allocations for Massive Security Games

Deployed Security Games for Patrol Planning

Multi-Leader Multi-Follower Model with Aggregative Uncertainty

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