Games Theory and Applications [Anglais] [Broché]

Thomas' 274 page, 6"x9" textbook was written explicitly for undergraduates such as those he taught at University of Manchester in England. In way of a mathematics background only a solid grounding in differential and integral calculus is assumed. Nevertheless, because there are many subtle concepts explored in this book I suspect that it might be most appropriate for third year American college students majoring in such math-intensive disciplines as mathematics, physical sciences, and engineering.

I actually sought out this book after seeing the movie A Beautiful Mind starring Russell Crowe and then reading A Beautiful Mind by Sylvia Nasar. John Nash's Nobel-prize winning work is addressed primarily in Chapter 3 "Two person Non-zero-sum Games" that spans pp.53-84. The preceding Chapter addresses "Two person Zero-sum Games". It is noteworthy that Nash's Theorem deals with conflicts and competitions in which the two players might both benefit from certain cooperative strategies.

Thomas helps the reader by "sketching" a proof of Nash's Theorem with the aid of Brouwer's Fixed Point Theorem. Brouwer's contribution is a topological theorem that is akin to the observation that a person is unable to get all the hair on his head to lie flat, for at some point, such as at the cowlick or base of the part, the hair must stand up--a bane to small boys everywhere. It is at this "cowlick" that a function maps a point onto itself (i.e. f(x)=x). It is at this self-mapping point that the two competitors find the most mutually advantageous situation.

This textbook provides many games and situations to illustrate its points, as well as a number of appropriate problems to solve at the end of each chapter. Ten pages of references are also provided for the reader who wants to look up the original journal articles, such as those authored by John Nash.