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This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…

History and Overview · Mathematics 2015-08-24 Jeremy Avigad

We give an interpretation of the Maximum Entropy (MaxEnt) Principle in game-theoretic terms. Based on this interpretation, we make a formal distinction between different ways of {em applying/} Maximum Entropy distributions. MaxEnt has…

Artificial Intelligence · Computer Science 2013-01-18 Peter D. Grunwald

Autonomous software agents operating in dynamic environments need to constantly reason about actions in pursuit of their goals, while taking into consideration norms which might be imposed on those actions. Normative practical reasoning…

Artificial Intelligence · Computer Science 2017-01-31 Zohreh Shams , Marina De Vos , Julian Padget , Wamberto W. Vasconcelos

Money is a technology for promoting economic prosperity. Over history money has become increasingly abstract, it used to be hardware, gold coins and the like, now it is mostly software, data structures located in banks. Here I propose the…

General Finance · Quantitative Finance 2016-08-03 Ross D. King

Two traditional paradigms are often used to describe the behavior of agents in multi-agent complex systems. In the first one, agents are considered to be fully rational and systems are seen as multi-player games. In the second one, agents…

Computer Science and Game Theory · Computer Science 2016-03-17 Mickael Randour

Econometrics is based on the nonempiric notion of utility. Prices, dynamics, and market equilibria are supposed to be derived from utility. Utility is usually treated by economists as a price potential, other times utility rates are treated…

Statistical Mechanics · Physics 2009-10-31 Joseph L. McCauley

We study a class of heterogeneous agent-based models which are based on a basic set of principles, and the most fundamental operations of an economic system: trade and product transformations. A basic guiding principle is scale invariance,…

Trading and Market Microstructure · Quantitative Finance 2009-02-24 Samuel E. Vazquez

Many fairness criteria constrain the policy or choice of predictors, which can have unwanted consequences, in particular, when optimizing the policy under such constraints. Here, we advocate to instead focus on the utility function the…

Machine Learning · Statistics 2025-03-19 Frederik Hytting Jørgensen , Sebastian Weichwald , Jonas Peters

We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed…

Trading and Market Microstructure · Quantitative Finance 2009-11-13 Edward W. Piotrowski , Jan Sladkowski

We consider the problem of designing an expected-revenue maximizing mechanism for allocating multiple non-perishable goods of $k$ varieties to flexible consumers over $T$ time steps. In our model, a random number of goods of each variety…

Computer Science and Game Theory · Computer Science 2020-07-08 Shiva Navabi , Ashutosh Nayyar

When evaluating policies that affect future generations, the most commonly used criterion is the discounted utilitarian rule. However, in terms of intergenerational fairness, it is difficult to justify prioritizing the current generation…

Theoretical Economics · Economics 2025-02-10 Kensei Nakamura

The Principle of Sufficient Reason implies determinism. An explicit indeterministic quantum jump dynamics is constructed, which may be naturally transformed into a deterministic one. A consistent application of the Principle of Sufficient…

Quantum Physics · Physics 2010-12-16 Vladimir S. Mashkevich

The concept of movable evidence masses that flow from supersets to subsets as specified by experts represents a suitable framework for reasoning under uncertainty. The mass flow is controlled by specialization matrices. New evidence is…

Artificial Intelligence · Computer Science 2013-03-26 Rudolf Kruse , Detlef Nauck , Frank Klawonn

In this paper, we make a review on the concepts of rationality across several different fields, namely in economics, psychology and evolutionary biology and behavioural ecology. We review how processes like natural selection can help us…

Artificial Intelligence · Computer Science 2018-12-03 Catarina Moreira

An analyst observes an agent take a sequence of actions. The analyst does not have access to the agent's information and ponders whether the observed actions could be justified through a rational Bayesian model with a known utility…

Theoretical Economics · Economics 2025-04-08 Henrique de Oliveira , Rohit Lamba

Reasoning has long been understood as a pathway between stages of understanding. Proper reasoning leads to understanding of a given subject. This reasoning was conceptualized as a process of understanding in a particular way, i.e.,…

Artificial Intelligence · Computer Science 2026-01-06 Hendrik Kempt , Alon Lavie

Personalized pricing is a business strategy to charge different prices to individual consumers based on their characteristics and behaviors. It has become common practice in many industries nowadays due to the availability of a growing…

Computers and Society · Computer Science 2022-02-22 Renzhe Xu , Xingxuan Zhang , Peng Cui , Bo Li , Zheyan Shen , Jiazheng Xu

The aim of this paper is to reemphasize the money theory of exchange which is centered on the function of exchange medium of money, and make a contribution towards linearization of the quantity equation of exchange. A dynamical quantity…

Economics · Quantitative Finance 2020-04-28 Zhao Jianglin

The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this…

General Finance · Quantitative Finance 2008-12-02 J. Doyne Farmer , John Geanakoplos

Among the remarkable emergent capabilities of large language models (LMs) is free-text rationalization; beyond a certain scale, large LMs are capable of generating seemingly useful rationalizations, which in turn, can dramatically enhance…

Computation and Language · Computer Science 2023-05-15 Brihi Joshi , Ziyi Liu , Sahana Ramnath , Aaron Chan , Zhewei Tong , Shaoliang Nie , Qifan Wang , Yejin Choi , Xiang Ren