New book: "Arbitrage and Rational Decisions"
Bob Nau
I’d like to announce the publication of a new book entitled
“Arbitrage and Rational Decisions” which explores the unifying role that the
no-arbitrage standard of rationality plays in various subfields of rational
choice theory. Links to the publisher’s
web page and Amazon’s web page for the book can be found at this link:
https://people.duke.edu/~rnau/book/Arbitrage_and_Rational_Decisions.htm
There you will also find a not-quite-final draft copy of chapters 1, 2 and 10, which provide an introduction and historical survey, a discussion of the key tools of analysis, and a summary of the main concepts and results in the book. A draft copy of the entire book is also available here:
https://people.duke.edu/~rnau/book/Arbitrage_and_Rational_Decisions_draft_RNau.pdf
The book has been in progress for a long time. It is a synthesis and extension of early work of my own, and it deals with some foundational issues that are timeless: incomplete preferences, imprecise probabilities, inseparable beliefs and tastes, unobservable status quo stakes in events, state-dependent utility for outcomes, source-dependent aversion to uncertainty, ambiguity, common knowledge of a game’s rules, common knowledge of strategic rationality, desiderata of equilibria, aggregation of beliefs and risk attitudes in financial markets, etc..
The book’s focus on the modeling of acts with monetary payoffs over (usually) a finite set of states is admittedly restrictive in terms of its range of application and its connection to contemporary work in our field. It is not concerned with explicitly modeling the psychology of the decision-maker nor explaining qualitative patterns of personal behavior that are observed in the laboratory or on the street. Rather, the situations it considers are idealizations of those in which decision-makers really do routinely and deliberately quantify their thoughts in terms of numbers that can be communicated to and commonly understood and acted upon by others, with a degree of precision that is itself quantifiable. These are situations in which rationality is inherently interactive, and in them money plays a key role in quantitative thinking and communicating about uncertainties and values, not merely as a medium of exchange or one among many attributes of consequences. This method of analysis descends from the work of de Finetti and Arrow and Aumann, as opposed to von Neumann and Savage and Nash.
The book is a set of variations on a classic theme, a theme that applies to games and markets in exactly the same way as it applies to individuals. Its results in the area of noncooperative game theory tie everything else together (providing a unification of game theory with subjective probability and asset pricing theory) and they do not assume that you’re an expert on the topic. In fact, it might be better if you are not a devotee of Nash equilibrium.
Best,
Bob