期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 60, 期 9, 页码 2402-2415出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2015.2404471
关键词
Controlled NEG; fundamental evolutionary equation (FEE); networked evolutionary game (NEG); STP; strategy profile dynamics (SPD); strategy updating rule
资金
- National Natural Science Foundation (NNSF) of China [61074114, 61273013, 61333001, 61104065, 61473099]
- National Center for Mathematics and Interdisciplinary Sciences, CAS
Consider a networked evolutionary game (NEG). According to its strategy updating rule, a fundamental evolutionary equation (FEE) for each node is proposed, which is based on local information. Using FEEs, the network strategy profile dynamics (SPD) is expressed as a k-valued (deterministic or probabilistic) logical dynamic system. The SPD is then used to analyze the network dynamic behaviors, such as the fixed points, the cycles, and the basins of attractions, etc. Particularly, when the homogeneous networked games are considered, a necessary and sufficient condition is presented to verify when a stationary stable profile exists. Then the equivalence of two NEGs is investigated. Finally, after a rigorous definition of controlled NEGs, some control problems, including controllability, stabilization, and network consensus, are considered, and some verifiable conditions are presented. Examples with various games are presented to illustrate the theoretical results. The basic tool for this approach is the semi-tensor product (STP) of matrices, which is a generalization of the conventional matrix product.
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