Rational versus presumptive decisions in a decentralized co-production system: Solutions and applications

Recent research has examined the decentralized decisions of two independent parties when the system output is co-produced, i.e., the output depends on the efforts exerted by both parties. In this paper, we present a general modeling framework to reexamine the robustness of the results obtained from this stream of research. To model the decision-making process in a decentralized co-production system, we use the Constant Elasticity of Substitution (CES) function to model the output co-produced from the two parties and consider both simultaneous-move and sequential-move games. We also compare the equilibrium efforts exerted by rational firms and the optimal efforts exerted by presumptive firms. Here, each rational firm makes decisions by anticipating the other firm’s rational decision, whereas each presumptive firm makes decisions based on a prior belief about the other firm’s decision. We show that both simultaneous-move and sequential-move games yield similar structural results. First, the effort exerted by each rational (or presumptive) firm increases with the firm’s “returns on effort investment”. Second, while the efforts exerted by presumptive firms are not in equilibrium, we find that these off-equilibrium efforts can result in higher payoffs than the efforts exerted by rational firms when the prior beliefs are sufficiently high and effort cost factors are sufficiently low. We also apply these results to reexamine some key findings obtained in the recent literature whose co-production model can be viewed as special cases of the CES output function. We find that the existing results based on the special case may not hold under the general CES functions. Hence, our general model and results provide new insights. Finally, we demonstrate how our general model can be applied to examine other settings arising from product development and capacity planning decisions involving two independent parties with self-interests.