On the Stackelberg knapsack game

Pferschy, Ulrich; Nicosia, Gaia; Pacifici, Andrea; Schauer, Joachim

doi:10.1016/j.ejor.2020.09.007

Cited by 16 publications

(4 citation statements)

References 28 publications

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“…. , 13; i ∈ V; t ∈ W (25) in which, for all i ∈ V, c i = 1 t t∈W b i t is a base-step capacity 4 (corresponding to the number of average per day arrival for vaccine i) and (1 + α…”

Section: ) VI Experiments and Resultsmentioning

confidence: 99%

“…Another important topic to be considered in future extended models for mass vaccination is the design of inducement policies to encourage the largest possible fraction of the population to uptake the vaccine. From a methodological point of view, Stackelberg game approaches (see, e.g., [25], [26]) appear as a natural direction to deal with these issues. Of course, from a different perspective, also communication strategies play a crucial role, as discussed in [27] in which the effectiveness of different health communication frames is assessed.…”

Section: Discussionmentioning

confidence: 99%

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Mass Vaccine Administration under Uncertain Supply Scenarios

Foderaro

Naldi

Nicosia

et al. 2021

Annals of Computer Science and Information Systems

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The insurgence of COVID-19 requires fast mass vaccination, hampered by scarce availability and uncertain supply of vaccine doses and a tight schedule for boosters. In this paper, we analyze planning strategies for the vaccination campaign to vaccinate as many people as possible while meeting the booster schedule. We compare a conservative strategy and q-days-ahead strategies against the clairvoyant strategy. The conservative strategy achieves the best trade-off between utilization and compliance with the booster schedule. Q-days-ahead strategies with q < 7 provide a larger utilization but run out of stock in over 30% of days.

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“…. , 13; i ∈ V; t ∈ W (25) in which, for all i ∈ V, c i = 1 t t∈W b i t is a base-step capacity 4 (corresponding to the number of average per day arrival for vaccine i) and (1 + α…”

Section: ) VI Experiments and Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Mass Vaccine Administration under Uncertain Supply Scenarios

Foderaro

Naldi

Nicosia

et al. 2021

Annals of Computer Science and Information Systems

Self Cite

View full text Add to dashboard Cite

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“…The leader's payoff is the total weight of the items he controls and selected by the follower. Very recently, Pferschy et al [31] tackled a "symmetrical" problem in which the leader can control the profits instead of item weights. In addition to these works, a matrix interdiction problem was studied by Kasiviswanathan and Pan [24].…”

Section: Related Workmentioning

confidence: 99%

Approximation Algorithms for Interdiction Problem with Packing Constraints

Chen¹,

Wang²,

Zhang³

2022

Preprint

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We study a bilevel optimization problem which is a zero-sum Stackelberg game. In this problem, there are two players, a leader and a follower, who pick items from a common set. Both the leader and the follower have their own (multi-dimensional) budgets, respectively. Each item is associated with a profit, which is the same to the leader and the follower, and will consume the leader's (follower's) budget if it is selected by the leader (follower). The leader and the follower will select items in a sequential way: First, the leader selects items within the leader's budget. Then the follower selects items from the remaining items within the follower's budget. The goal of the leader is to minimize the maximum profit that the follower can obtain. Let s A and s B be the dimension of the leader's and follower's budget, respectively. A special case of our problem is the bilevel knapsack problem studied by Caprara et al. [SIAM Journal on Optimization, 2014], where s A = s B = 1. We consider the general problem and obtain an (s B + ε)-approximation algorithm when s A and s B are both constant. In particular, if s B = 1, our algorithm implies a PTAS for the bilevel knapsack problem, which is the first O(1)approximation algorithm. We also complement our result by showing that there does not exist any (4/3 − ε)-approximation algorithm even if s A = 1 and s B = 2. We also consider a variant of our problem with resource augmentation when s A and s B are both part of the input. We obtain an O(1)-approximation algorithm with O(1)-resource augmentation, that is, we give an algorithm that returns a solution which exceeds the given leader's budget by O(1) times, and the objective value achieved by the solution is O(1) times the optimal objective value that respects the leader's budget.

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“…Traditional knapsack algorithms used for analyzing game theoretical models are often employed for this purpose (Pferschy, Nicosia, Pacifici, & Schauer, 2021; Wang & Bier, 2011). However, some features of our problem may create challenges to traditional approaches, such as the recursive knapsack algorithm (Lin, 1998; Salkin & De Kluyver, 1975).…”

Section: Tackling Scalability In the Stackelberg Gamementioning

confidence: 99%

Deterrence against Terrorist Attacks in Sports‐Mega Events: A Method to Identify the Optimal Portfolio of Defensive Countermeasures

et al. 2021

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Sports mega‐events, such as the Olympic Games or the Super Bowl, are attractive targets for terrorist organizations, due to their visibility, size, and number of people involved. Two characteristics of sports mega‐events, however, make them distinctive in comparison with other well‐studied target protection problems in counterterrorism analysis (such as transportation hubs or infrastructure facilities). First, defensive measures are often publicly known. Second, their finite horizon means that deterrence against any attack must be prioritized. In this article we thus propose a method that identifies the best portfolio of defensive measures the defense may adopt, given a fixed budget, to minimize the chances of suffering a terrorist attack during a sports mega‐event. The method makes some relevant contributions to adversarial risk analysis: (i) it represents attackers that can choose among multiple attack scenarios and the no‐attack scenario; (ii) it measures the deterrence effect caused by synergic portfolios of defensive measures; and (iii) it proposes an algorithm that identifies dominated portfolios and may, thus, overcome the scalability problems inherent to this portfolio optimization. We apply this method to a real‐world defense problem, revisiting the defensive countermeasure planning for the 2016 Brazilian Olympic Games in Rio de Janeiro, Brazil. In the case study, we find a nonlinear relationship between budget expenditure and deterrence, as well as a decreasing marginal effectiveness use of resources after a given budget threshold, which would support a more efficient allocation of investments in the Games defense.

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On the Stackelberg knapsack game

Cited by 16 publications

References 28 publications

Mass Vaccine Administration under Uncertain Supply Scenarios

Mass Vaccine Administration under Uncertain Supply Scenarios

Approximation Algorithms for Interdiction Problem with Packing Constraints

Deterrence against Terrorist Attacks in Sports‐Mega Events: A Method to Identify the Optimal Portfolio of Defensive Countermeasures

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