The Cost of Uncoordinated Decisions in Early-Stage Architectural Design: A Game-Theoretic Proof of Concept

Source abstract

Early-stage architectural design distributes decisions across parties who control different variables but share the same performance consequences. Envelope geometry is settled largely on the architectural side, while glazing specification and system efficiency are settled largely on the engineering side, and the two sets of decisions determine thermal comfort, daylight, energy use, and cost jointly. Multi-objective optimization identifies which design states are attainable under a coordinated formulation, and multi-criteria methods rank alternatives under stated preferences, but neither represents what happens when coupled variables are held under separate utility functions. The objective of this paper is to test, as a proof of concept, whether modeling that division as a two-player non-cooperative game yields information that Pareto analysis of the same problem does not. A worked 3 × 3 game, built on constructed values consistent with documented physical relationships for a single-zone office, yields a unique pure strategy Nash equilibrium in which neither player holds a dominant strategy. All nine design states are Pareto-efficient in the four-objective performance space, but once the four indicators are aggregated into the two player utilities, the equilibrium is strictly Pareto-dominated in the two-player utility space: a different design state raises the first player’s utility by 15.6 percent and the second player’s utility by 22.0 percent simultaneously, a loss of 15.6 percent in the summed normalized utility of the two players relative to the best available joint state. This figure is a model-specific utility measure, not a share of energy, comfort, daylight, or cost performance. A sensitivity analysis across 169 weighting combinations shows the equilibrium migrating across eight distinct design states and falling outside the utility Pareto set in 54 of the 188 resulting equilibrium instances (29 percent), a descriptive frequency rather than a probability; 52 of the 169 combinations admit at least one such equilibrium. When the performance values and the preference weights are both perturbed at random, at least one inefficient equilibrium appears in 20 to 30 percent of draws, and a sequential Stackelberg version of the game reaches an inefficient state whichever player moves first. The results show that, within the specified utility representation, the stable state implied by decentralized decision-making can be inefficient and that, within a given model, the size of that gap can be estimated before the design is fixed. They do not show how large the gap is in real projects. The numerical demonstration uses constructed performance measures rather than simulation output and establishes the analytical behavior of the framework rather than the performance of any building. Applying the framework to simulated and, where possible, calibrated models is left to future work, and the framework is intended to inform design judgment, not to replace it.