Learning in multilevel games with incomplete information. II

Multilevel games are abstractions of situations where decision makers are distributed in a network environment. In Part I of this paper, the authors present several of the challenging problems that arise in the analysis of multilevel games. In this paper a specific set up is considered where the two games being played are zero-sum games and where the decision makers use the linear reward-inaction algorithm of stochastic learning automata. It is shown that the effective game matrix is decided by the willingness and the ability to cooperate and is a convex combination of two zero-sum game matrices. Analysis of the properties of this effective game matrix and the convergence of the decision process shows that players tend toward noncooperation in these specific environments. Simulation results illustrate this noncooperative behavior.

[1]  V. V. Phansalkar,et al.  Decentralized Learning of Nash Equilibria in Multi-Person Stochastic Games With Incomplete Information , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[2]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[3]  Tad Hogg,et al.  Controlling chaos in distributed systems , 1991, IEEE Trans. Syst. Man Cybern..

[4]  S. Lakshmivarahan,et al.  Learning in multilevel games with incomplete information. I , 1999, IEEE Trans. Syst. Man Cybern. Part B.

[5]  Kumpati S. Narendra,et al.  Learning automata approach to hierarchical multiobjective analysis , 1991, IEEE Trans. Syst. Man Cybern..

[6]  M. Norman.  On the linear model with two absorbing barriers , 1968 .

[7]  H. Young,et al.  Learning dynamics in games with stochastic perturbations , 1995 .

[8]  Kumpati S. Narendra,et al.  Learning Models for Decentralized Decision Making , 1985, 1985 American Control Conference.

[9]  Edward A. Billard,et al.  Stability of adaptive search in multi-level games under delayed information , 1996, IEEE Trans. Syst. Man Cybern. Part A.

[10]  E. A. Billard.  Instabilities in learning automata playing games with delayed information , 1994, Proceedings of IEEE International Conference on Systems, Man and Cybernetics.

[11]  Radu Theodorescu.  Review: M. Frank Norman, Markov Processes and Learning Models , 1974 .

[12]  Kumpati S. Narendra,et al.  Learning automata - an introduction , 1989 .

[13]  S. K. Polumienko.  Extensions of coalition games , 1992 .

[14]  K. Narendra,et al.  Learning Algorithms for Two-Person Zero-Sum Stochastic Games with Incomplete Information: A Unified Approach , 1982 .

[15]  S. Lakshmivarahan,et al.  Simulation of period-doubling behavior in distributed learning automata , 1998, SAC '98.

[16]  E. A. Billard.  Chaotic behavior of learning automata in multi-level games under delayed information , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[17]  Eckmann,et al.  Liapunov exponents from time series. , 1986, Physical review. A, General physics.

[18]  Edward A. Billard.  Stabilizing distributed queuing systems using feedback based on diversity , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[19]  Joseph Pasquale,et al.  Coadaptive behaviour in a simple distributed job scheduling system , 1993, IEEE Trans. Syst. Man Cybern..

[20]  Richard Bellman,et al.  Differential-Difference Equations , 1967 .

[21]  S. Lakshmivarahan,et al.  Learning Algorithms for Two-Person Zero-Sum Stochastic Games with Incomplete Information , 1981, Math. Oper. Res..

[22]  S. Lakshmivarahan,et al.  Learning Algorithms Theory and Applications , 1981 .