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There can be no doubt that mathematical models has made a huge contribution to the natural sciences. This thesis, as well as game theory in general, grows from a belief that mathematical modelling can be equally beneficial in the social sciences. That the great questions about human behavior can not be solved without rigorous modelling and that right now there is no language more appropriate for these models then mathematics. There are several problems that needs to be thoroughly dealt with before the game theoretical project can be a success. In this thesis the focus is on one of them, how to model people's behavior when they have very restricted information.