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arXiv2026

Tractable Estimation of the Money Pump Index: A Comment

The Money Pump Index (MPI) of Echenique et al. (2011) measures the severity of consumer irrationality, but computing the exact mean and median MPI over all revealed preference cycles is NP-hard (Smeulders et al., 2013). Existing solutions rely on heuristic proxies, such as evaluating only shorter cycles or bounding the MPI. By framing revealed preferences as a directed graph, this paper projects choice violations onto fundamental cycle bases, which are minimal sets of linearly independent cycles that span the graph's entire cycle space. This yields computationally tractable estimators for the mean and median MPI that are asymptotically equivalent to the original MPI. Applying this methodology to the scanner dataset analyzed by Echenique et al. (2011) and Smeulders et al., (2013), the proposed estimators compute quickly and with negligible small-sample bias.

econ.EM↗

arXiv2025

The Emergence of Strategic Reasoning of Large Language Models

As large language models (LLMs) have demonstrated strong reasoning abilities in structured tasks (e.g., coding and mathematics), we explore whether these abilities extend to strategic multi-agent environments. We investigate strategic reasoning capabilities -- the process of choosing an optimal course of action by predicting and adapting to others' actions -- of LLMs by analyzing their performance in three classical games from behavioral economics. Using hierarchical models of bounded rationality, we evaluate three standard LLMs (ChatGPT-4, Claude-3.5-Sonnet, Gemini 1.5) and three reasoning LLMs (OpenAI-o1, Claude-4-Sonnet-Thinking, Gemini Flash Thinking 2.0). Our results show that reasoning LLMs exhibit superior strategic reasoning compared to standard LLMs (which do not demonstrate substantial capabilities) and often match or exceed human performance; this represents the first and thus most fundamental transition in strategic reasoning capabilities documented in LLMs. Since strategic reasoning is fundamental to future AI systems (including Agentic AI), our findings demonstrate the importance of dedicated reasoning capabilities in achieving effective strategic reasoning.

econ.GN↗