Network Games : A Model where One Player Controls Multiple Nodes

This paper proposes a Network Game model where one agent controls multiple nodes, and studies how equilibrium changes when a game is transformed from a one-agent-controls-one-node setting to a one-agent-controls-multiple-nodes setting. The model discusses how equilibrium might continue to exist or completely change given different forms of players’ utilities. It also discusses how the structure of a network and the structure of a player’s controlling nodes (holding connected or independent nodes) can influence equilibria. Moreover, using this model, the author explains several real-world businesses or policy cases related to games and spatial competition, such as why monopolies develop relatively fast in smaller markets/nations, and why disability supporting policies carried by governments are often futile