Abstarct: Generally probability is one of the substantive properties of quantum mechanics, which could not be separated from the quantum mechanics. There have been lots of studies considering removing concept of probability from quantum mechanics. Yet not successfully resolving the issue. One of such studies is done by Deutsch. He claims to drive the "probabilistic predictions of quantum theory" from the "non-probabilistic axioms of quantum theory" and the "non-probabilistic part of classical decision theory." In this thesis we explain the details of Deutsch's discussion. In addition, considering the fact that game theory is a type of decision theory which is considerably on the basis of probability, there is a great tendency to generalize game theory to the domain of quantum probability. There are lots of games in game theory which have many aspect involving quantum teleportation, cryptography and quantum key distribution. Some of such games like PQ penny flip have like oracle problem for known quantum algorithm, eg simon's algorithm and Grover 's algorithm. Here games such as PQ penny flip and prisoner's dilemma game are studied regarding classical and quantum theory, and it has been observed that games moves desirable results when played by adopting quantum strategies. Moreover PQ penny flip when applied in quantum Grover search algorithm is studied. In this study we have establish a model through generalized 2 dimensional strategy space in to 3 dimensional also generalizing each game with qubit state in to qutrit state. Mean while we have compared each game in qubit and qutrit states. In a way that in PQ penny flip game in quantum system, we calculate Hadmard operator for a qutrit system, and with the help of such operator.we estimate game in qutrit system. An while, in prisoner's dilemma, we obtain the equation by which plaxyer's payoff is determined and the value of each strategy's payoff will be estimated.