Game Development Reference
In-Depth Information
The issue of complexity of finding a Nash equilibrium has been a long
standing open problem, clarified only recently, see Daskalakis et al. [2009]
for an account of these developments. Iterated elimination of strictly domi-
nated strategies and of weakly dominated strategies was introduced by Gale
[1953] and Luce and Raiffa [1957]. The corresponding results summarised in
Theorems 1.3, 1.7, 1.16 and 1.19 are folklore results.
Apt [2004] provides uniform proofs of various order independence results,
including the Order Independence Theorems 1.5 and 1.18. The computational
complexity of iterated elimination of strategies has been studied starting with
Knuth et al. [1988], and with Brandt et al. [2009] as a recent contribution.
There is a lot of work on formal aspects of common knowledge and of its
consequences for game theory. see, e.g., Aumann [1999] and Battigalli and
Bonanno [1999].
1.9.2 Suggestions for further reading
Strategic games form a large research area and we have barely scratched its
surface. There are several other equilibria notions and various other types of
games.
Many topics provide introductions to various areas of game theory, in-
cluding strategic games. Most of them are written from the perspective of
applications to Economics. In the 1990s the leading textbooks were Myer-
son [1991], Binmore [1991], Fudenberg and Tirole [1991] and Osborne and
Rubinstein [1994].
Moving to the next decade, Osborne [2005] is an excellent, broad in its
scope, undergraduate level textbook, while Peters [2008] is probably the best
topic on the market on the graduate level. Undeservedly less known is the
short and lucid Tijs [2003]. An elementary, short introduction, focusing on
the concepts, is Shoham and Leyton-Brown [2008]. In turn, Ritzberger [2001]
is a comprehensive topic on strategic games that also extensively discusses
extensive games , i.e., games in which the players choose actions in turn.
Finally, Binmore [2007] is a thoroughly revised version of Binmore [1991].
Several textbooks on microeconomics include introductory chapters on
game theory, including strategic games. Two good examples are Mas-Collel
et al. [1995] and Jehle and Reny [2000]. Finally, Nisan et al. [2007] is a
recent collection of surveys and introductions to the computational aspects
of game theory, with a number of articles concerned with strategic games
and mechanism design.
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