Game-theoretic learning and allocations in robust dynamic coalitional games

M. Smyrnakis, D. Bauso, Tembine Hamidou

Research output: Contribution to journalArticle

Abstract

The problem of allocation in coalitional games with noisy observations and dynamic environments is considered. The evolution of the excess is modeled by a stochastic differential inclusion involving both deterministic and stochastic uncertainties. The main contribution is a set of linear matrix inequality conditions which guarantee that the distance of any solution of the stochastic differential inclusions from a predefined target set is second-moment bounded. As a direct consequence of the above result we derive stronger conditions still in the form of linear matrix inequalities to hold in the entire state space, which guarantee second-moment boundedness. Another consequence of the main result is conditions for convergence almost surely to the target set, when the Brownian motion vanishes in proximity of the set. As a further result we prove convergence conditions to the target set of any solution to the stochastic differential equation if the stochastic disturbance has bounded support. We illustrate the results on a simulated intelligent mobility scenario involving a transport network.

Original languageEnglish (US)
Pages (from-to)2902-2923
Number of pages22
JournalSIAM Journal on Control and Optimization
Volume57
Issue number4
DOIs
StatePublished - Jan 1 2019

Fingerprint

Coalitional Games
Dynamic Games
Linear matrix inequalities
Game
Brownian movement
Differential Inclusions
Differential equations
Target
Matrix Inequality
Linear Inequalities
Almost Convergence
Moment
Convergence Condition
Dynamic Environment
Proximity
Stochastic Equations
Excess
Brownian motion
Boundedness
Vanish

Keywords

  • Differential inclusions
  • Intelligent mobility network
  • Robust dynamic coalitional games
  • Second-moment stability
  • Stable core

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

Cite this

Game-theoretic learning and allocations in robust dynamic coalitional games. / Smyrnakis, M.; Bauso, D.; Hamidou, Tembine.

In: SIAM Journal on Control and Optimization, Vol. 57, No. 4, 01.01.2019, p. 2902-2923.

Research output: Contribution to journalArticle

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