Can knowledge be justified true belief?

Knowledge was traditionally held to be justified true belief. This paper examines the implications of maintaining this view if justication is interpreted algorithmically. It is argued that if we move sufficiently far from the small worlds to which Bayesian decision theory properly applies, we can steer between the rock of fallibilism and the whirlpool of skepticism only by explicitly building into our framing of the underlying decision problem the possibility that its attempt to describe the world is inadequate

Does game theory work? The bargaining challenge

Book description: This volume brings together all of Ken Binmore's influential experimental papers on bargaining along with newly written commentary in which Binmore discusses the underlying game theory and addresses the criticism leveled at it by behavioral economists. When Binmore began his experimental work in the 1980s, conventional wisdom held that game theory would not work in the laboratory, but Binmore and other pioneers established that game theory can often predict the behavior of experienced players very well in favorable laboratory settings. The case of human bargaining behavior is particularly challenging for game theory. Everyone agrees that human behavior in real-life bargaining situations is governed at least partly by considerations of fairness, but what happens in a laboratory when such fairness considerations supposedly conflict with game-theoretic predictions? Behavioral economists, who emphasize the importance of other-regarding or social preferences, sometimes argue that their findings threaten traditional game theory. Binmore disputes both their interpretations of their findings and their claims about what game theorists think it reasonable to predict. Binmore's findings from two decades of game theory experiments have made a lasting contribution to economics. These papers—some coauthored with other leading economists, including Larry Samuelson, Avner Shaked, and John Sutton—show that game theory does indeed work in favorable laboratory environments, even in the challenging case of bargaining

The origins of fair play

This paper gives a brief overview of an evolutionary theory of fairness. The ideas are fleshed out in Binmore's book 'Natural Justice' (Oxford University Press, New York, 2005.), which is itself a condensed version of his earlier two-volume book 'Game Theory and the Social Contract' (MIT Press, Cambridge, MA, 1994 and 1998)

Economic man – or straw man?

The target article by Henrich et al. describes some economic experiments carried out in fifteen small-scale societies. The results are broadly supportive of an approach to understanding social norms that is commonplace among game theorists. It is therefore perverse that the rhetorical part of the paper should be devoted largely to claiming that “economic man” is an experimental failure that needs to be replaced by an alternative paradigm. This brief commentary contests the paper's caricature of economic theory, and offers a small sample of the enormous volume of experimental data that would need to be overturned before “economic man” could be junked

Do conventions need to be common knowledge?

Do conventions need to be common knowledge? David Lewis builds this requirement into his definition of a convention. This paper explores the extent to which his approach finds support in the game theory literature. The knowledge formalism developed by Robert Aumann and others militates against Lewis’s approach, because it demonstrates that it is almost impossible for something to become common knowledge in a large society. On the other hand, Ariel Rubinstein’s Email Game suggests that coordinated action is equally hard for rational players. But an unnecessary simplifying assumption in the Email Game turns out to be doing all the work, and the paper concludes that common knowledge is better excluded from a definition of the conventions that we use to regulate our daily lives

A density theorem with an application to gap power series

Let N be a set of positive integers and let $F(z)=\Sigma \ A_{n}z^{n}$ be an entire function for which $A_{n}=0\ (n\not\in N)$. It is reasonable to expect that, if D denotes the density of the set N in some sense, then F(z) will behave somewhat similarly in every angle of opening greater than 2πD. For functions of finite order, the appropriate density seems to be the Pólya maximum density P. In this paper we introduce a new density D which is perhaps the appropriate density for the consideration of functions of unrestricted growth. It is shown that, if |I|>2\pi \scr{D}, then ${\rm log}\ M(r)\sim {\rm log}\ M(r,I)$ outside a small exceptional set. Here M(r) denotes the maximum modulus of F(z) on the circle $|z|=r$ and M(r, I) that of $F(re^{i\theta})$ for values of θ in the closed interval I. The method used is closely connected with the question of approximating to functions on an interval by means of linear combinations of the exponentials $e^{ixn}\ (n\in N)$