Nau R. Arbitrage and Rational Decisions 2025

Textbook in PDF format

This unique book offers a new approach to the modeling of rational decision-making under conditions of uncertainty and strategic and competition interactions among agents. It presents a unified theory in which the most basic axiom of rationality is the principle of no-arbitrage, namely that neither an individual decision maker nor a small group of strategic competitors nor a large group of market participants should behave in such a way as to provide a riskless profit opportunity to an outside observer.
Both those who work in the finance area and those who work in decision theory more broadly will be interested to find that basic tools from finance (arbitrage pricing and risk-neutral probabilities) have broader applications, including the modeling of subjective probability and expected utility, incomplete preferences, inseparable probabilities and utilities, nonexpected utility, ambiguity, noncooperative games, and social choice. Key results in all these areas can be derived from a single principle and essentially the same mathematics.
A number of insights emerge from this approach. One is that the presence of money (or not) is hugely important for modeling decision behavior in quantitative terms and for dealing with issues of common knowledge of numerical parameters of a situation. Another is that beliefs (probabilities) do not need to be uniquely separated from tastes (utilities) for the modeling of phenomena such as aversion to uncertainty and ambiguity. Another over-arching issue is that probabilities and utilities are always to some extent indeterminate, but this does not create problems for the arbitrage-based theories.
One of the book’s key contributions is to show how noncooperative game theory can be directly unified with Bayesian decision theory and financial market theory without introducing separate assumptions about strategic rationality. This leads to the conclusion that correlated equilibrium rather than Nash equilibrium is the fundamental solution concept.
The book is written to be accessible to advanced undergraduates and graduate students, researchers in the field, and professionals