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The objective of this paper is to provide the initial literature based insights into the game theory specifically with the viewpoint of client - vendor relationships in offshore software outsourcing. Game theory has been used for long in understanding various contexts in economics and other disciplines. Offshore software outsourcing relates to the situation in which client and vendor are operating from different countries. Subsequently, in this paper, the initial understanding of game theory focusing on software engineering community is developed. Particularly risk, rationality, payoffs, and other elements of game theory are explored in terms of how they affect offshore software outsourcing. The paper is structured as follows. Section one provides introduction to game theory concept. Section two explores the history, representation and types of games. Section three compares offshore software outsourcing with types and elements of game theory. Section four discusses one of the most famous game theory examples - 'prisoners-dilemma' and relates it to software outsourcing context. Finally, section five concludes this paper with the intended future work.