Multi-agent discrete-time graphical games: interactive Nash equilibrium and value iteration solution
- 1 June 2013
- conference paper
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 4189-4195
- https://doi.org/10.1109/acc.2013.6580483
Abstract
This paper introduces a new class of multi-agent discrete-time dynamical games known as dynamic graphical games, where the interactions between agents are prescribed by a communication graph structure. The graphical game results from multi-agent dynamical systems, where pinning control is used to make all the agents synchronize to the state of a command generator or target agent. The relation of dynamic graphical games and standard multi-player games is shown. A new notion of Interactive Nash equilibrium is introduced which holds if the agents are all in Nash equilibrium and the graph is strongly connected. The paper brings together discrete Hamiltonian mechanics, distributed multi-agent control, optimal control theory, and game theory to formulate and solve these multi-agent graphical games. The relationships between the discrete-time Hamilton Jacobi equation and discrete-time Bellman equation are used to formulate a discrete-time Hamilton Jacobi Bellman equation for dynamic graphical games. Proofs of Nash, stability, and convergence are given. A reinforcement learning value iteration algorithm is given to solve the dynamic graphical games.Keywords
This publication has 15 references indexed in Scilit:
- Multi-agent differential graphical games: Online adaptive learning solution for synchronization with optimalityAutomatica, 2012
- Optimal ControlPublished by Wiley ,2012
- Coalition-proof equilibria in a voluntary participation gameInternational Journal of Game Theory, 2010
- Robust Finite-Time Consensus Tracking Algorithm for Multirobot SystemsIEEE/ASME Transactions on Mechatronics, 2009
- Multiagent SystemsPublished by Cambridge University Press (CUP) ,2008
- A Comprehensive Survey of Multiagent Reinforcement LearningIEEE Transactions on Systems, Man and Cybernetics, Part C (Applications and Reviews), 2008
- Discrete variational Hamiltonian mechanicsJournal of Physics A: General Physics, 2006
- Coordinated collective motion in a motile particle group with a leaderPhysica A: Statistical Mechanics and its Applications, 2005
- Pinning a Complex Dynamical Network to Its EquilibriumIEEE Transactions on Circuits and Systems I: Regular Papers, 2004
- Consensus Problems in Networks of Agents With Switching Topology and Time-DelaysIEEE Transactions on Automatic Control, 2004