The assumption is that the players are rational, utility-maximizing agents and from that assumption, and the design of the game, springs the outcomes of the game. You could make alternative assumptions (which people do) and come up with different outcomes, but the fact remains that game theory was developed to answer economic questions (i.e., how utility-maximizing individuals make decisions within constraints, whether those constraints are budgetary, resource, or the actions of other players).

The theory was formalized into mathematical logic as a means to maintain the rigor. Math is a tool, not the source of game theory.