Cooperative business firms are prevalent in agribusiness, yet no concise generalized model exists to demonstrate how and why cooperative firms differ from, and may be selected over, the more common investor owned business firm. It is shown within a generic transaction game that cooperatives fill both producer and consumer roles as an aggregated player that is expected to maximize aggregate producer and consumer payoffs rather than maximizing either payoff separately, which contrasts with investor owned firms as essentially two player games between separate and competing producers and consumers where each player seeks to maximize their separate payoff individually. A cardinally valued game theoretic matrix is used to demonstrate the expected differences between these one-player versus two-player games, which clearly demonstrates that cooperatives are expected to achieve greater total payoffs and social welfare relative to investor owned firms, because investor owned firms generate dead weight loss when maximizing producer surpluses as expected under prevailing microeconomic theory. The use of cardinal payoff values rather than ordinal is important because it permits aggregation of payoffs within the model, and because it directly reflects the cardinal payoffs actually used in agribusiness decisions, such as revenue, expense and profit measures. The results may indicate the reason that cooperative firms are selected and have been successful in agribusiness. However, weaknesses of the cooperative model are also discussed, conjecturing that cooperatives may be preferable to investor owned businesses under limited circumstances but because these circumstances occur frequently in agribusiness the cooperative model is observed more frequently there.