Rational decision-making is crucial in the later stages of engineering system design to allocate resources efficiently and minimize costs. However, human rationality is bounded by cognitive biases and limitations. Understanding how humans deviate from rationality is critical for guiding designers toward better design outcomes. In this paper, we quantify designer rationality in competitive scenarios based on utility theory. Using an experiment inspired by crowd-sourced contests, we show that designers employ varied search strategies. Some participants approximate a Bayesian agent that aimed to maximize its expected utility. Those with higher rationality reduce uncertainty more effectively. Furthermore, rationality correlates with both the proximity to optimal design and design iteration costs, with winning participants exhibiting greater rationality than losing participants.