On Networked Evolutionary Games Part 1: Formulation

This paper presents a comprehensive modeling technique for networked evolutionary games (NEG). Three kinds of network graphs are considered, which are (i) undirected graph for symmetric games; (ii) directed graph for asymmetric games, and (iii) d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games (FEGs) are discussed, which are (i) two strategies and symmetric (S-2); (ii) two strategies and asymmetric (A-2); and (iii) three strategies and symmetric (S-3). Three strategy updating rules (SUR) are introduced, which are (i) Unconditional Imitation (UI); (ii) Fermi Rule (FR); (iii) Myopic Best Response Adjustment Rule (MBRA). Then we review the fundamental evolutionary equation (FEE), and give the detailed formulation for different models. Finally, the network profile dynamics (NPD) of NEGs are investigated via their FEE.