with Economic Applications

Editors: Robert J. Aumann and Sergiu Hart

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Robert J. Aumann and Sergiu Hart

This is the third and last volume of the

We follow the rough division into "noncooperative,"
"cooperative," and
"general" adopted in the previous volumes. Chapters 41 through 52
are
mainly noncooperative; 53 through 58, cooperative; 59 through 62,
general.
This division should not be taken too seriously; chapters may well
contain
aspects of both approaches. Indeed, we hope that the
*Handbook* will
help demonstrate that noncooperative and cooperative game theory
are two
sides of the same coin, which complement each other well.

The noncooperative part of the volume starts with three chapters on the basic concepts of the noncooperative approach. Chapter 41 discusses strategic equilibrium -- "Nash," its refinements, and its extensions -- without doubt the most used solution of game theory. The conceptual foundations and significance of these notions are by no means straightforward; Chapter 42 delves into these matters from various perspectives. The following chapter, 43, deals with incomplete information in multi-person interactive contexts, with special reference to "Bayesian" games.

Chapters 44 through 48 survey three important classes of games. The case of two players is of particular significance: A two-person interaction is the simplest and most basic there is; there are no non-trivial group structures. The theoretical and computational implications of this in the general (non-zero-sum) case are studied in Chapters 44 and 45 (two-person zero-sum games are covered in Chapter 20 in Volume 2). The other extreme -- when there are many individually insignificant players (a continuum or "ocean" -- is the subject of Chapter 46. The next two chapters are devoted to stochastic games: multi-stage games in which current actions physically affect future opportunities (unlike repeated games, surveyed in Volume 1, which reflect mainly the informational side of ongoing interactions). Chapter 47 covers the period up to 1995; Chapter 48, the period since then.

Considerable attention is paid in this *Handbook* to
applications,
economic and otherwise; in this volume, chapters 49 through 52 and
57
through 61. Among the "hottest" applications is Industrial
Organization,
studied in Chapter 49, which discusses matters like collusion,
entry and
entry deterrence, predation, price wars, subsidies, strategic
international
trade, and "clearance" sales. The next chapter, 50, continues the
discussion of noncooperative models of bargaining (Chapter 7 in
Volume 1),
with special reference to the implications of incomplete
information about
the other player (his reservation prices, red lines, true
preferences, and
so on). Here, the participants must credibly convey their position;
a
special section is devoted to empirical data from strikes.
Inspection games
-- which may be viewed as statistical inference when data can be
strategically manipulated -- are covered in Chapter 51. This area
became
popular in the mid-sixties, at the height of the "cold war," when
arms
control and disarmament treaties were being negotiated; more
recently, these
techniques have been applied to auditing, environmental control,
material
accountancy, and so on. The last "noncooperative" chapter, 52,
shows how
the area of economic history benefits from the discipline of game
theory.

The cooperative part of this volume centers on the Shapley value, its extensions and applications. Perhaps the most "successful" cooperative solution concept, the value is universally applicable (unlike the core), and leads to significant insights in widely varying contexts. The basic definitions and results are presented in Chapter 53. Relaxing and generalizing the axioms defining the value leads to the extensions discussed in Chapter 54. The previous two chapters study the basic model with transferable utility; in many contexts (especially economic ones) non-transferable utilities, covered in Chapter 55, are more realistic. Chapter 56 treats values of games with many individually insignificant players (a continuum or "ocean" Inter alia, this case is basic to understanding perfectly competitive economies, whose value theory is reviewed in Chapter 57. Other applications of the value in continuum games -- taxation, public goods and fixed prices -- are dealt with in Chapter 58.

The *Handbook* closes with four "mixed" chapters, each
combining
cooperative and noncooperative tools and approaches in four very
different
areas of application. Chapter 59 treats political systems from the
"micro," strategic viewpoint (sophisticated voting equilibria,
manipulation of agendas and voting rules, and so on). This is to be
distinguished from the more "macro"oriented power considerations
discussed in Chapter 32 in Volume 2. Chapter 60 treats a
relatively new
area of game-theoretic application: Law. It has to do both with the
"game"
implicit in a given legal system, and with the design of
"optimal" legal
systems. This brings us to the general mechanism design problem, or
"implementation," the subject of Chapter 61: how to design the
"rules of
the game" to achieve certain desired results (as in auctions,
matching
markets, and final offer arbitration). The last chapter, 62,
discusses some
of the interplay between theory and experiments in games, and also
the role
that game theory plays in the design of interactive simulations (as
in
business games and war games).

This concludes our summary of the contents of the
*Handbook*.
Unfortunately, certain topics that we planned to cover were in the
end
omitted for one reason or another. They include adaptive dynamic
learning,
social psychology, macroeconomics, and the history of game theory.
Needless
to say, game theory is constantly expanding its horizons and
increasing its
depth (as attested to by the large and varied participation in the
First
Congress of the Game Theory Society in 2000 in Bilbao). Thus, any
coverage
in a *Handbook* is necessarily incomplete.

We would like to thank heartily all the many people who were involved in this project: the contributors, referees, series editors, and all those who helped us with their advice and support. Finally, we are grateful to our editorial assistant Mike Borns, without whom this volume would never have been completed.

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