Study of multinational currency co-movement and exchange rate stability base on network game

•The co-movement of global exchange rate fluctuations is a small-world network.•Multi-countries exchange rate co-movement gradually shapes an stabilize exchange rate co-movement region.•The more random the currency co-movement relationship among multi-currency countries is, the easier it is to stabilize exchange rate co-movement relationships.•The higher the proportion of investment income to total income is, the easier it is to shape a multi-currency co-movement exchange rate stability relationship.