Foundations Of Game Theory Research Articles

Changing Types: Information Dynamics for Qualitative Type Spaces

Many different approaches to describing the players’ knowledge and beliefs can be found in the literature on the epistemic foundations of game theory. We focus here on non-probabilistic approaches. The two most prominent are the so-called Kripkeor Aumann- structures and knowledge structures (non-probabilistic variants of Harsanyi type spaces). Much of the recent work on Kripke structures has focused on dynamic extensions and simple ways of incorporating these. We argue that many of these ideas can be applied to knowledge structures as well. Our main result characterizes precisely when one type can be transformed into another type by a specific type of information update. Our work in this paper suggest that it would be interesting to pursue a theory of “information dynamics” for knowledge structures (and eventually Harsanyi type spaces).

An Impossibility Theorem on Beliefs in Games

A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell's Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob's assumption is wrongThis is formalized to show that any belief model of a certain kind must have a “hole.” An interpretation of the result is that if the analyst's tools are available to the players in a game, then there are statements that the players can think about but cannot assume. Connections are made to some questions in the foundations of game theory.

Mathematical and Quantitative Methods: Jane Austen, Game Theorist

Rakesh V. Vohra of University of Pennsylvania reviews, “Jane Austen, Game Theorist” by Michael Suk-Young Chwe. The Econlit abstract of this book begins: “Explores the ways in which the core ideas of game theory appear in Jane Austen's novels. Discusses the argument; game theory in context; folk tales and human rights; game theory in Flossie and the Fox; Austen's six novels; Austen's foundations of game theory; Austen's competing models; Austen on what strategic thinking is not; Austen's innovations; Austen on strategic thinking's disadvantages; Austen's intentions; Austen on cluelessness; and real-world cluelessness. Chwe is Associate Professor of Political Science at the University of California, Los Angeles.”

Harsanyi Type Spaces and Final Coalgebras Constructed from Satisfied Theories

This paper connects coalgebra with a long discussion in the foundations of game theory on the modeling of type spaces. We argue that type spaces are coalgebras, that universal type spaces are final coalgebras, and that the modal logics already proposed in the economic theory literature are closely related to those in recent work in coalgebraic modal logic. In the other direction, the categories of interest in this work are usually measurable spaces or compact (Hausdorff) topological spaces. A coalgebraic version of the construction of the universal type space due to Heifetz and Samet [Journal of Economic Theory 82 (2) (1998) 324–341] is generalized for some functors in those categories. Since the concrete categories of interest have not been explored so deeply in the coalgebra literature, we have some new results. We show that every functor on the category of measurable spaces built from constant functors, products, coproducts, and the probability measure space functor has a final coalgebra. Moreover, we construct this final coalgebra from the relevant version of coalgebraic modal logic. Specifically, we consider the set of theories of points in all coalgebras and endow this set with a measurable and coalgebra structure.

John von Neumann's Contribution to Modern Game Theory

The paper gives a brief account of von Neumann's contribution to the foundation of game theory: definition of abstract games, the minimax theorem for two-person zero-sum games and the stable set solution for cooperative games with side payments. The presentation is self-contained, uses very little mathematical formalism and caters to the nonspecialist. Basic concepts and their implications are in focus. It is also indicated how von Neumann's groundbreaking work initiated further research, and a few unsolved problems are also mentioned.

Decisions in games: why there should be a special exemption from Bayesian rationality

I examine the Bayesian foundations of game theory and advance three main theses: (i) that if Bayesianism is to be used in game theory, then simpler versions of it are methodologically preferable to the more sophisticated ones; (ii) that it is dubious whether the Savage (or Anscombe and Aumann) axiom system can yield an axiomatic justification for Bayesianism in game theory; and (iii) that there exist other foundational frameworks for games which are at least as convincing as the Bayesian one.

Epistemic logic and the foundations of game theory

Epistemic logic and the foundations of game theory

Essays on the Foundations of Game Theory.

The aims and scope of game theory Nash equilibrium information common knowledge and game theory modelling rational payers modeling rational players.

BOOK REVIEWS

BOOK REVIEWS

Essays on the foundations of game theory, by Binmore, K., Basil Blackwell, 1990, ix pages + 239 pages

Essays on the foundations of game theory, by Binmore, K., Basil Blackwell, 1990, ix pages + 239 pages

Essays on the Foundations of Game Theory.

Essays on the Foundations of Game Theory.

A Social Psychological Approach to Coalition Membership: An Expectancy Model of Individual Choice

The study of coalitions is required in order to fully understand behavior in com plex organizations. Central to the study of coalitions is the study of individual participation in them. To date, the study of coalition membership has been dominated by work constructed on the foundation of game theory. The limita tions of this approach in terms of descriptive and predictive utility have been well recognized. It is argued here that future work constructed on a social psychological foundation would overcome many of these problems. First, an expectancy model of coalition membership addressing inducements, contribu tions, and exchange in coalitions is presented. Concepts and considerations both addressed and ignored in past work are shown to be accommodated by the model. Second, a number of practical implications of the model are given by focusing on interventions into client systems.

Nonstandard utilities and the foundation of game theory

In a recent paperFishburn [1972] discussed some consequences which the use of non-Archimedean utilities has on finite two-person zero-sum games. We shall show that the state of affairs with non-Archimedean utilities is not so different from the results undervon Neumann-Morgenstern utilities asFishburn asserts, if we represent the utilities in an appropriate non-Archimedean ordered field (nonstandard model of the real numbers) and admit that the components of the optimal strategies also may assume values in this ordered field. Moreover it is proved that for every utility space (in the sense ofHausner [1954] a nonstandard utility function exists.

On the foundations of game theory: The case of non-Archimedean utilities

Contrary to what appears to have become an accepted part of the folklore of game theory, a finite two-person zero-sum game with non-Archimedean utilities may have no equilibrium-point solution, and either one or both players may have no “minimax” strategy. Even when both players have “minimax” strategies, such a game may lack an equilibrium point.