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1. A Quantitative Analysis of Rational Decisions Under Uncertainty in Engineering Systems Design

   https://doi.org/10.1017/pds.2025.10039  

   Mutlu, Kaan; Javadpour, Nikoo; Sha, Zhenghui; Bayrak, Alparslan Emrah (August 2025, Proceedings of the Design Society)

   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. 

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2. Singularities of local models

   https://doi.org/10.1007/s00208-024-03036-y  

   Fakhruddin, Najmuddin; Haines, Thomas; Lourenço, João; Richarz, Timo (April 2025, Mathematische Annalen)

   Abstract We construct local models of Shimura varieties and investigate their singularities, with special emphasis on wildly ramified cases. More precisely, with the exception of odd unitary groups in residue characteristic 2 we construct local models, show reducedness of their special fiber, Cohen–Macaulayness and in equicharacteristic also (pseudo-)rationality. In mixed characteristic we conjecture their pseudo-rationality. This is based on the construction of parahoric group schemes over two dimensional bases for wildly ramified groups and an analysis of singularities of the attached Schubert varieties in positive characteristic using perfect geometry. 

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3. Measuring higher-order rationality with belief control

   https://doi.org/10.1017/eec.2025.5  

   Chen, Wei James; Fong, Meng-Jhang; Lin, Po-Hsuan (May 2025, Experimental Economics)

   Determining an individual’s strategic reasoning capability based solely on choice data is a complex task. This complexity arises because sophisticated players might have non-equilibrium beliefs about others, leading to non-equilibrium actions. In our study, we pair human participants with computer players known to be fully rational. This use of robot players allows us to disentangle limited reasoning capacity from belief formation and social biases. Our results show that, when paired with robots, subjects consistently demonstrate higher levels of rationality, compared to when paired with human players. Furthermore, players’ rationality levels are relatively stable across games when paired with robot players, even though those with intermediate rationality levels exhibit inconsistency across games. Leveraging our experimental design, we identify and document potential causes of this inconsistency. 

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4. Bounded-Rational Pursuit-Evasion Games

   https://doi.org/10.23919/ACC50511.2021.9483152  

   Guan, Yue; Maity, Dipankar; Kroninger, Christopher M.; Tsiotras, Panagiotis (May 2021, American Control Conference)

   We present a framework that incorporates the principle of bounded rationality into dynamic stochastic pursuit-evasion games. The solution of a stochastic game is generally characterized by its (Nash) equilibria in feedback form, whose calculation may require extensive computational resources. In this paper, the agents are modeled as bounded rational entities with limited computational capabilities. We illustrate the proposed framework by applying it to a pursuit-evasion game between two aerial vehicles in a stochastic wind field. We show how such a game may be discretized and properly analyzed by casting it as an iterative sequence of finite-state Markov Decision Processes (MDPs). Leveraging tools and algorithms from the cognitive hierarchy theory (“level-k thinking”) we compute the solution of the ensuing discrete game, while taking into consideration the rationality level of each agent. We also present an online algorithm for each agent to infer its opponent's rationality level. 

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5. Rationality of forms of M¯0,n$$\overline{{\mathcal {M}}}_{0,n}$$

   https://doi.org/10.1112/jlms.70097  

   Hassett, Brendan; Tschinkel, Yuri; Zhang, Zhijia (February 2025, Journal of the London Mathematical Society)

   Abstract We study equivariant geometry and rationality of moduli spaces of points on the projective line, for twists associated with permutations of the points. 

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