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In this paper we present nonlinear 3 player game model for joint routing, network coding, and scheduling problem. To define such a game model, first routing and network coding are modeled by using a new approach based on compressed topology matrix that takes into account the inherent multicast gain of the network. Topology matrix includes the set of all possible paths, including network coded paths, from sources to their corresponding sinks. These paths are identified and compressed, and then by switching between some of them with appropriate usage rates (frequencies), achievable throughput is optimized. The scheduling is optimized by a new approach called network graph soft coloring. Soft graph coloring is designed by switching between different components of a wireless network graph, which we refer to as graph fractals, with appropriate usage rates. Therefore each link can be painted with more than one different colors selected with appropriate probabilities. In the proposed game which is a nonlinear cubic game, the strategy sets of the players are links, path, and network components. The outputs of this game model are mixed strategy vectors of the second and the third players at equilibrium. Strategy vector of the second player specifies optimum multi-path routing and network coding solution while mixed strategy vector of the third players indicates optimum switching rate among different network components or membership probabilities for optimal soft scheduling approach. Optimum throughput is the value of the proposed nonlinear cubic game at equilibrium. The proposed nonlinear cubic game is solved by extending fictitious playing method. Numerical and simulation results prove the superior performance of the proposed techniques compared to other conventional schemes.