A theory of network games is an adequate and promising mathematical approach for interaction investigation between actors in network structures. Network games in modern sense are not "network formation games” with networks linking players only, but “network based games” with fixed network structures where performance of players and their winnings depend on their actions. In the paper, a multi-agent network “center – agent – market” is investigated on the basic concepts and essentials of the theory of network games. The network is focused on the advancement in the competitive market of homogeneous goods (services). A set of center problems aimed at improvement of network operation efficiency in equilibrium of Cournot-Nash and Stackelberg is studied. The set of problems includes problems of agent number optimization, creation of links, information and strategic reflection, motivational and institutional management of agents. The interaction between “network formation games” and “network based games” is demonstrated while solving the problem of multi-agent “center-agent-market” network management for franchise systems.