A double-sided jamming game with resource constraints

Sourabh Bhattacharya, Ali Khanafer, M Tamer Basar

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this article, we study the problem of power allocation in teams of mobile agents in a conflict situation. Each team consists of two agents who try to split their available power between the tasks of communication and jamming the nodes of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function is the difference between the rates of erroneously transmitted bits of each team. We present a 2-level game formulation: At the higher level, the agents solve a continuous-kernel power allocation game at each instant. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a Pure Strategy Nash Equilibrium for the continuous-kernel power allocation game. At the lower level, we have a zero-sum differential game between the two teams and use Isaacs’ approach to obtain necessary conditions for the optimal trajectories. The optimal power allocation scheme obtained at the upper level is used to solve the lower level differential game. This gives rise to a games-in-games scenario which is one of the first such phenomena documented in the literature.

Original languageEnglish (US)
Title of host publicationAnnals of the International Society of Dynamic Games
PublisherBirkhauser
Pages209-227
Number of pages19
DOIs
StatePublished - Jan 1 2016

Publication series

NameAnnals of the International Society of Dynamic Games
Volume14
ISSN (Print)2474-0179
ISSN (Electronic)2474-0187

Fingerprint

Resource Constraints
Jamming
Power Allocation
Game
Mobile agents
Communication
Cost functions
Differential Games
Trajectories
kernel
Zero sum game
Optimal Trajectory
Mobile Agent
Optimal Allocation
Nash Equilibrium
Instant
Instantaneous
Cost Function
Resource constraints
Necessary Conditions

Keywords

  • Games-in-games
  • Jamming
  • Multi-level games
  • Nash equilibrium
  • Pursuit-evasion games

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability
  • Applied Mathematics

Cite this

Bhattacharya, S., Khanafer, A., & Basar, M. T. (2016). A double-sided jamming game with resource constraints. In Annals of the International Society of Dynamic Games (pp. 209-227). (Annals of the International Society of Dynamic Games; Vol. 14). Birkhauser. https://doi.org/10.1007/978-3-319-28014-1_10

A double-sided jamming game with resource constraints. / Bhattacharya, Sourabh; Khanafer, Ali; Basar, M Tamer.

Annals of the International Society of Dynamic Games. Birkhauser, 2016. p. 209-227 (Annals of the International Society of Dynamic Games; Vol. 14).

Research output: Chapter in Book/Report/Conference proceedingChapter

Bhattacharya, S, Khanafer, A & Basar, MT 2016, A double-sided jamming game with resource constraints. in Annals of the International Society of Dynamic Games. Annals of the International Society of Dynamic Games, vol. 14, Birkhauser, pp. 209-227. https://doi.org/10.1007/978-3-319-28014-1_10
Bhattacharya S, Khanafer A, Basar MT. A double-sided jamming game with resource constraints. In Annals of the International Society of Dynamic Games. Birkhauser. 2016. p. 209-227. (Annals of the International Society of Dynamic Games). https://doi.org/10.1007/978-3-319-28014-1_10
Bhattacharya, Sourabh ; Khanafer, Ali ; Basar, M Tamer. / A double-sided jamming game with resource constraints. Annals of the International Society of Dynamic Games. Birkhauser, 2016. pp. 209-227 (Annals of the International Society of Dynamic Games).
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