Noncooperative Games

Hespanha, João P.

doi:10.23943/princeton/9780691175218.003.0001

Cited by 6 publications

(4 citation statements)

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“…Next, this work may be extended to some other application scenarios such as malware containment [23–28], rumor restraint [29, 30, 49, 50], and cyber defense [31–33, 51]. Finally, a viral marketing campaign is essentially a game between the merchant and the customers, where the merchant goes after the maximum possible net profit, and the customers wish to buy the desired items at the lowest possible costs [52]. Therefore, it is expected that we can gain a deep insight into viral marketing through game-theoretic approach [33, 53–56].…”

Section: Discussionmentioning

confidence: 99%

A dynamic discount pricing strategy for viral marketing

et al. 2018

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Viral marketing has been one of the main marketing modes. However, theoretical study of viral marketing is still lacking. This paper focuses on the problem of developing a cost-effective dynamic discount pricing strategy for a viral marketing campaign. First, based on a novel word-of-mouth propagation model, we model the original problem as an optimal control problem. Second, we show that the optimal control problem admits an optimal control and present the optimality system for solving the optimal control problem. Next, we solve some optimal control models to get their respective optimal dynamic discount pricing strategies. Finally, we examine the effect of some factors on the maximum marketing profit. These results contribute to gaining insight into viral marketing.

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Section: Discussionmentioning

confidence: 99%

A dynamic discount pricing strategy for viral marketing

et al. 2018

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“…The mathematical model for the collaborating agents assignment problem (hereinafter referred to as the "assignment problem," is given by equations (1) - (5). The problem data that must be computed prior to solving this assignment problem is the reward matrix, r ∈ R N×2 M −1 , where r jk is the reward of assigning interceptor group I k to threat T j .…”

Section: Assignment Problem Formulationmentioning

confidence: 99%

“…We use the set of constraints in (4) to limit each individual interceptor to participate in no more than one interceptor group. Finally, constraint (5) ensures that the elements of the matrix z are binary. Note that by introducing a slack variable and transforming the optimization program into epigraph form, we can formulate the stated assignment problem as a mixedinteger linear program to be solved by off-the-shelf solvers.…”

Section: Assignment Problem Formulationmentioning

confidence: 99%

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Optimal assignment of collaborating agents in multi-body asset-guarding games

Sin

Arcak

Packard

et al. 2020

Preprint

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We study a multi-body asset-guarding game in missile defense where teams of interceptor missiles collaborate to defend a non-manuevering asset against a group of threat missiles. We approach the problem in two steps. We first formulate an assignment problem where we optimally assign subsets of collaborating interceptors to each threat so that all threats are intercepted as far away from the asset as possible. We assume that each interceptor is controlled by a collaborative guidance law derived from linear quadratic dynamic games. Our results include a 6-DOF simulation of a 5-interceptor versus 3-threat missile engagement where each agent is modeled as a missile airframe controlled by an autopilot. Despite the assumption of linear dynamics in our collaborative guidance law and the unmodeled dynamics in the simulation environment (e.g., varying density and gravity), we show that the simulated trajectories match well with those predicted by our approach. Furthermore, we show that a more agile threat, with greater speed and acceleration, can be intercepted by inferior interceptors when they collaborate. We believe the concepts introduced in this paper may be applied in asymmetric missile defense scenarios, including defense against advanced cruise missiles and hypersonic vehicles.

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Formal Synthesis

Lin

Antsaklis

2021

Advanced Textbooks in Control and Signal Processing

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Formal SynthesisSo far, we have presented and discussed basic results for the modeling, verification, stability, and optimal control of hybrid systems. These results have been introduced by both the computer science and control engineering communities. The computer science community has been primarily interested in verifying the correctness of embedded codes in the face of real-time constraints and interactions with the physical world; while the control engineering community has been mainly focusing on the effects of discontinuities (such as switching of dynamics and jumping of states) caused by the use of digital processors and communication networks that are increasingly becoming ubiquitous.The past decade has witnessed efforts to merge these two schools of thought, and a noticeable trend in the recent hybrid system literature is the emphasis on the synthesis of hybrid controllers for continuous or hybrid dynamical systems to satisfy complicated temporal logic specifications. This approach is known as symbolic control or hybrid supervisory control. The basic idea is first to obtain equivalent or approximating finite abstractions of the hybrid or continuous systems to be controlled. Then the design is carried out in the discrete domain using model checking [1], game-theoretic approaches [2], or discrete event supervisory control theory [3]. The final step is to convert the designed discrete supervisor back to a hybrid controller (since the controller usually contains both discrete transitions and continuous flows) so that it can be used to control the original hybrid or continuous system. The effectiveness of the abstraction-based method depends on whether or not there exists a finite state discrete abstracted model for the original hybrid or continuous system. Significant research efforts have been devoted to developing abstraction methods based on reachability analysis; see, e.g., [4,5]. However, the number of abstracted states could grow exponentially with respect to the dimension of the physical dynamics. We, therefore, introduce symbolic approaches to formal synthesis as well, which can be seen as extensions of symbolic model checking methods to the formal synthesis problems. Symbolic approaches have shown great promise in tackling the state explosion problem.

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Noncooperative Games

Cited by 6 publications

References 0 publications

A dynamic discount pricing strategy for viral marketing

A dynamic discount pricing strategy for viral marketing

Optimal assignment of collaborating agents in multi-body asset-guarding games

Formal Synthesis

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