# A maximum entropy model of bounded rational decision-making with prior beliefs and market feedback

arXiv: https://arxiv.org/abs/2102.09180 · HTML: https://mlsanity.com/paper/2102.09180/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 85 references that are in the map.
- First posted on arXiv 18 Feb 2021.

## Builds on (most cited first, 5 of 5)

- [Action and Perception as Divergence Minimization](https://mlsanity.com/paper/2009.01791/) (2020)
- [The Two Kinds of Free Energy and the Bayesian Revolution](https://mlsanity.com/paper/2004.11763/) (2020)
- [Human Decision-Making under Limited Time](https://mlsanity.com/paper/1610.01698/) (2016)
- [The impact of social influence in Australian real-estate: market forecasting with a spatial agent-based model](https://mlsanity.com/paper/2009.06914/) (2020)
- [A Theory of Cheap Control in Embodied Systems](https://mlsanity.com/paper/1407.6836/) (2014)

## Built on by (most cited first, 5 of 5)

- [The Physics of Preference: Unravelling Imprecision of Human Preferences through Magnetisation Dynamics](https://mlsanity.com/paper/2310.00267/) (2023)
- [Entropy, Information, and the Updating of Probabilities](https://mlsanity.com/paper/2107.04529/) (2021)
- [Bounded rationality for relaxing best response and mutual consistency: The Quantal Hierarchy model of decision-making](https://mlsanity.com/paper/2106.15844/) (2021)
- [Learning and Calibrating Heterogeneous Bounded Rational Market Behaviour with Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2402.00787/) (2024)
- [Modelling bounded rational decision-making through Wasserstein constraints](https://mlsanity.com/paper/2504.03743/) (2025)

## Abstract (arXiv)

Bounded rationality is an important consideration stemming from the fact that agents often have limits on their processing abilities, making the assumption of perfect rationality inapplicable to many real tasks. We propose an information-theoretic approach to the inference of agent decisions under Smithian competition. The model explicitly captures the boundedness of agents (limited in their information-processing capacity) as the cost of information acquisition for expanding their prior beliefs. The expansion is measured as the Kullblack-Leibler divergence between posterior decisions and prior beliefs. When information acquisition is free, the homo economicus agent is recovered, while in cases when information acquisition becomes costly, agents instead revert to their prior beliefs. The maximum entropy principle is used to infer least-biased decisions based upon the notion of Smithian competition formalised within the Quantal Response Statistical Equilibrium framework. The incorporation of prior beliefs into such a framework allowed us to systematically explore the effects of prior beliefs on decision-making in the presence of market feedback, as well as importantly adding a temporal interpretation to the framework. We verified the proposed model using Australian housing market data, showing how the incorporation of prior knowledge alters the resulting agent decisions. Specifically, it allowed for the separation of past beliefs and utility maximisation behaviour of the agent as well as the analysis into the evolution of agent beliefs.