In problem solving, there is a search for the appropriate solution. A state space is a problem domain consisting of the start state, the goal state and the operations that will necessitate the various moves from the start state to the goal state. Each move operation takes one away from the start state and closer to the goal state. In this work we have attempted implementing this concept in adversarial problem solving, which is a more complex problem space. We noted that real world adversarial problems vary in their types and complexities, and therefore solving an adversarial problem would depend on the nature of the adversarial problem itself. Specifically, we examined a real world case, "the prisoner's dilemma" which is a critical, mutually independent, decision making adversarial problem. We combined the idea of the Thagard's Theory of Explanatory Coherence (TEC) with Bayes' theorem of conditional probability to construct the model of an opponent that includes the opponent's model of the agent. A further conversion of the model into a series of state space structures led us into the use of breadth-first search strategy to arrive at our decision goal.