Generative Grammars and Games of Addition: Comparing Their Mathematical Structures and Applicability to Organizational Decision-Making

Source abstract

<span>This paper examines whether Barberà and Gerber’s framework of games of addition can provide a formal basis for analyzing organizational decision-making and whether it eliminates the need for the distinct mathematical treatment of the internal operations of hierarchical organizations envisaged by Oskar Morgenstern in the RAND Corporation’s RM-734 report, entitled Prolegomena to a Theory of Organization. Building on a generative-grammar formalization of Morgenstern’s proposal, it compares two sources of structure in organizational decision processes: preference-sensitive strategic interaction and the generative effects of delegation, signaling, and resource deployment. Games of addition extend sequential game theory by allowing the identity of the actors initiating subsequent actions and the possible orders of play to emerge endogenously through strategic interaction and equilibrium conditions, making them suitable for organizational processes in which several actors may be able to initiate subsequent actions. However, this game-theoretic framework does not by itself explain how the underlying space of organizational possibilities is generated and constrained through historically constituted competence structures, resource-deployment outcomes, and other contextual conditions. The paper therefore distinguishes strategic choice within a decision structure from the generation or transformation of that structure and proposes a complementary analytical approach in which competence structures generate the space of feasible organizational trajectories while games of addition analyze strategic interaction within that space. The analysis supports the complementary application of both formal frameworks to the analysis of organizational decision-making rather than the substitution of one for the other.</span>