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

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

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 $e^{ixn}\ (n\in N)$

Closure theorems with applications to entire functions with gaps

In this paper we consider questions of completeness for spaces of continuous functions on a half line which satisfy appropriate growth conditions. The results obtained have consequences in the theory of entire functions with gap power series. In particular we show that, under an appropriate gap hypothesis, the rate of growth of an entire function in the whole plane is determined by its rate of growth along any given ray

A note on the strong law of large numbers

identically distributed (i.i.d.) random variables. Let Sn-t^Xk (fl » 1, 2, • • •)• J f e- 1 A long standing problem in probability theory has been to find neces

Stochastic Approximation to Understand Simple Simulation Models

This paper illustrates how a deterministic approximation of a stochastic process can be usefully applied to analyse the dynamics of many simple simulation models. To demonstrate the type of results that can be obtained using this approximation, we present two illustrative examples which are meant to serve as methodological references for researchers exploring this area. Finally, we prove some convergence results for simulations of a family of evolutionary games, namely, intra-population imitation models in n-player games with arbitrary payoffs.Ministerio de Educación (JC2009- 00263), Ministerio de Ciencia e Innovación (CONSOLIDER-INGENIO 2010: CSD2010-00034, DPI2010-16920

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.