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Using Brandenburger and Nalebuff's 1995 co‐opetition model as a reference, the purpose of this paper is to seek to develop a tool that, based on the tenets of classical game theory, would enable scholars and managers to identify which games may be played in response to the different conflict of interest situations faced by companies in their business environments.

The literature on game theory and business strategy are reviewed and a conceptual model, the strategic games matrix (SGM), is developed. Two novel games are described and modeled.

The co‐opetition model is not sufficient to realistically represent most of the conflict of interest situations faced by companies. It seeks to address this problem through development of the SGM, which expands upon Brandenburger and Nalebuff's model by providing a broader perspective, through incorporation of an additional dimension (power ratio between players) and three novel, respectively, (rival, individualistic, and associative).

This proposed model, based on the concepts of game theory, should be used to train decision‐ and policy‐makers to better understand, interpret and formulate conflict management strategies.

A practical and original tool to use game models in conflict of interest situations is generated. Basic classical games, such as Nash, Stackelberg, Pareto, and Minimax, are mapped on the SGM to suggest in which situations they could be useful. Two innovative games are described to fit four different types of conflict situations that so far have no corresponding game in the literature. A test application of the SGM to a classic Intel Corporation strategic management case, in the complex personal computer industry, shows that the proposed method is able to describe, to interpret, to analyze, and to prescribe optimal competitive and/or cooperative strategies for each conflict of interest situation.