# Статьи

**Всего статей в данном разделе :**74

Опубликовано на портале: 25-11-2004

*Hal R. Varian*,

*James Andreoni*Wisconsin Madison - Social Systems Working papers. 1999. No. 18.

We consider a modified Prisoners’ Dilemma game in which each agent can offer
to pay the other agent to cooperate. The subgame perfect equilibrium of this two-stage
game is Pareto efficient. We examine experimentally whether subjects actually manage
to achieve this efficient outcome. We find an encouraging level of support for the
mechanism, but also find some evidence that subjects’ tastes for cooperation
and equity may have significant interactions with the incentives provided by the
mechanism.

Опубликовано на портале: 22-01-2007

*Paul Robert Milgrom*,

*Donald John Roberts*Journal of Political Economy. 1986. Vol. 94. No. 4. P. 796-821.

We present a signaling model, based on ideas of Phillip Nelson, in which both the
introductory price and the level of directly "uninformative" advertising or other
dissipative marketing expenditures are choice variables and may be used as signals
for the initially unobservable quality of a newly introduced experience good. Repeat
purchases play a crucial role in our model. A second focus of the paper is on illustrating
an approach to refining the set of equilibria in signaling games with multiple potential
signals.

Опубликовано на портале: 28-04-2005

*John Donald Roberts*,

*Paul R. Milgrom*Econometrica. 1990. Vol. 58. No. 6. P. 1255-1277.

We study a class of non-cooperative games that includes many standard oligopoly games,macro
economic coordination games, network and production externality games, and others.
Forthese games, the sets of rationalizable strategies, pure Nash equilibrium strategies,
and correlated equilibrium strategies are non-empty and have identical upper and
lower bounds. Also,a large class of dynamic learning processes - including both best-response
dynamics and Bayesian learning - lead eventually to behavior that lies between these
same bounds. General comparative static and welfare theorems are provided. We study
the class of (non-cooperative) supermodular games introduced by Topkis (1979) and
further studied by Vives (1988). These are games in which each player's strategy
set is partially ordered, the marginal returns to increasing one's strategy rise
with increases in the competitors' strategies and, if a player's strategies are multidimensional,
the marginal returns to any one component of the player's strategy increase with
increases in the other components. The simplest examples of such games arise in oligopoly
theory. These include the Cournot duopoly game with a wide range of demand specifications
and arbitrary continuous cost functions, Bertrand oligopoly games, R&D racing games,
and oligopoly games with endogenous choice of production technologies. Additional
applications drawn from industrial organization include the Hendricks-Kovenock (1988)
drilling game (in which oil firms decide whether to drill exploratory wells when
the information obtained is a public good), network externality games, and certain
oligopoly games that arise in connection with the Milgrom-Roberts (1988) model of
manufacturing. Other examples include games used to model

**Rationalizable Strategic Behavior**[статья]

Опубликовано на портале: 30-01-2007

*B. Douglas Bernheim*Econometrica. 2006. Vol. 52. No. 4. P. 1007-1028.

This paper examines the nature of rational choice in strategic games. Although there
are many reasons why an agent might select a Nash equilibrium strategy in a particular
game, rationality alone does not require him to do so. A natural extension of widely
accepted axioms for rational choice under uncertainty to strategic environments generates
an alternative class of strategies, labelled "rationalizable." It is argued that
no rationalizable strategy can be discarded on the basis of rationality alone, and
that all rationally justifiable strategies are members of the rationalizable set.
The properties of rationalizable strategies are studied, and refinements are considered.

Опубликовано на портале: 22-01-2007

*Ehud Lehrer*,

*Ehud Kalai*Econometrica. 1993. Vol. 61. No. 5. P. 1019-1045.

Subjective utility maximizers, in an infinitely repeated game, will learn to predict
opponents' future strategies and will converge to play according to a Nash equilibrium
of the repeated game. Players' initial uncertainty is placed directly on opponents'
strategies and the above result is obtained under the assumption that the individual
beliefs are compatible with the chosen strategies. An immediate corollary is that,
when playing a Harsanyi-Nash equilibrium of a repeated game of incomplete information
about opponents' payoff matrices, players will eventually play a Nash equilibrium
of the real game, as if they had complete information.

Опубликовано на портале: 24-01-2007

*Roger B. Myerson*International Journal of Game Theory. 1978. Vol. 7. No. 2. P. 73-80.

Selten's concept of perfect equilibrium for normal form games is reviewed, and a
new concept of proper equilibrium is defined. It is shown that the proper equilibria
form a nonempty subset of the perfect equilibria, which in turn form a subset of
the Nash equilibria. An example is given to show that these inclusions may be strict.

**Reputation and Imperfect Information**[статья]

Опубликовано на портале: 31-01-2007

*David M. Kreps*,

*Robert B. Wilson*Journal of Economic Theory. 1982. Vol. 27. No. 2. P. 253-279.

A common observation in the informal literature of economics (and elsewhere) is that
is multistage games, players may seek early in the game to acquire
a reputation for being tough or benevolent or something
else. But this phenomenon is not observed in some formal game-theoretic analyses
of finite games, such as Selten's finitely repeated chain-store game or in the finitely
repeated prisoners' dilemma. We reexamine Selten's model, adding to it a small
amount of imperfect (or incomplete) information about players' payoffs, and we find
that this addition is sufficient to give rise to the reputation effect that one intuitively
expects.

**Sequential Equilibria**[статья]

Опубликовано на портале: 31-01-2007

*David M. Kreps*,

*Robert B. Wilson*Econometrica. 1982. Vol. 50. No. 4. P. 863-94.

We propose a new criterion for equilibria of extensive games, in the spirit of Selten's
perfectness criteria. This criterion requires that players' strategies be sequentially
rational: Every decision must be part of an optimal strategy for the remainder of
the game. This entails specification of players' beliefs concerning how the game
has evolved for each information set, including information sets off the equilibrium
path. The properties of sequential equilibria are developed; in particular, we study
the topological structure of the set of sequential equilibria. The connections with
Selten's trembling-hand perfect equilibria are given.

**Sequentially Optimal Auctions**[статья]

Опубликовано на портале: 30-01-2007

*Daniel R. Vincent*,

*R. Preston McAfee*Games and Economic Behavior. 1997. Vol. 18. No. 2.

We examine equlibria in sequential auctions where a seller can post a reserve price
but, if the auction fails to result in a sale, can commit keeping the object off
the market only for an exogenously fixed period of time. We restrict attention to
enviornments where bidders have independent private values and where the support
of the bidder types lies strictly above the valuation of the seller. In the case
where the seller sells by second price auction in each period, there is a unique
perfect Bayesian equilbrium. A form of revenue equivalence is shown. There exists
a perfect Bayesian equilibrium of repeated first price auctions with the feature
that in every period, the seller's expected revenue from the continuation is the
same in either auction mechanism. As the length of time the seller can commit to
keeping the object off the market goes to zero, seller expected revenues converge
to those of a static auction with no reserve price. As the number of bidders becomes
large, the seller expected revenue approaches the revenue from an optimal static
auction. We also characterize a parametrized auction game in which the simple equilibrium
reserve price policy of the seller mirrors a policy commonly used by many auctioneers.

Опубликовано на портале: 31-01-2007

*David M. Kreps*,

*In-Koo Cho*Quarterly Journal of Economics. 1987. Vol. 102. No. 2. P. 179-221.

Games in which one party conveys private information to a second through messages
typically admit large numbers of sequential equilibria, as the second party may entertain
a wealth of beliefs in response to out-of-equilibrium messages. By restricting those
out-of equilibrium beliefs, one can sometimes eliminate many unintuitive equilibria.
We present a number of formal restrictions of this sort, investigate their behavior
in specific examples, and relate these restrictions to Kohlberg and Mertens` notion
of stability.

Опубликовано на портале: 30-01-2007

*Susan Carleton Athey*Econometrica. 2001. Vol. 69. No. 4. P. 861-89.

This paper analyzes a class of games of incomplete information where each agent has
private information about her own type, and the types are drawn from an atomless
joint probability distribution. The main result establishes existence of pure strategy
Nash equilibria (PSNE) under a condition we call the single crossing condition (SCC),
roughly described as follows: whenever each opponent uses a nondecreasing strategy
(in the sense that higher types choose higher actions), a player's best response
strategy is also nondecreasing. When the SCC holds, a PSNE exists in every finite-action
game. Further, for games with continuous payoffs and a continuum of actions, there
exists a sequence of PSNE to finite-action games that converges to a PSNE of the
continuum-action game. These convergence and existence results also extend to some
classes of games with discontinuous payoffs, such as first-price auctions, where
bidders may be heterogeneous and reserve prices are permitted. Finally, the paper
characterizes the SCC based on properties of utility functions and probability distributions
over types. Applications include first-price, multi-unit, and all-pay auctions; pricing
games with incomplete information about costs; and noisy signaling games.

**Strategic Information Transmission**[статья]

Опубликовано на портале: 24-01-2007

*Vincent P. Crawford*,

*Joel Sobel*Econometrica. 1982. Vol. 50. No. 6. P. 1431-1451.

This paper develops a model of strategic communication, in which a better-informed
Sender (S) sends a possibly noisy signal to a Reciever (R), who then takes an action
that determines the welfare of both. We characterize the set of Bayesian Nash equilibria
under standart assumptions, and show that equilibrium signaling always takes a strikingly
simple form, in which S partitions the support of the (scalar) variable that represents
his private information and introduces noise into his signal by reporting, in effect,
only which element of the partition his observation actually lies in. We show under
further assumptions that before S observes his private information, the equilibrium
whose partition has the greatest number of elements is Pareto-superior to all other
equilibria, and that if agents coordinate on this equilibrium, R`s equilibrium expected
utility rises when agents` preferences become more similar. Since R bases his choice
of action on rational expectations, this establishes a sense in which equilibrium
signaling is more informative when agents` preferences are more similar.

**The Bargaining Problem**[статья]

Опубликовано на портале: 08-07-2005

*John Forbes Nash*Econometrica. 1950. Vol. 18. No. 2. P. 155-162.

A new treatment is presented of a classical economic problem, one which occurs in
many forms, as bargaining, bilateral monopoly, etc. It may also be regarded as a
nonzero-sum two-person game. In this treatment a few general assumptions are made
concerning the behavior of a single individual and of a group of two individuals
in certain economic environments. From these, the solution (in the sense of this
paper) of classical problem may be obtained. In the terms of game theory, values
are found for the game.
См. также: Two-person cooperative games, автор - Джо Нэш.

**The Evolution of Walrasian Behavior**[статья]

Опубликовано на портале: 24-01-2007

*Fernando Vega-Redondo*Econometrica. 1997. Vol. 65. No. 2. P. 375-384.

This article describes an evolutionary approach to understanding Walrasian behavior.
It avoids any considerations related to the absence of monopoly power or related
notion of a large enough population. Walrasian behavior may evolve within any quantity-setting
oligopoly producing a homogenous good, provided that the law of demand is satisfied.
Evolutionary models may produce interesting behavior that does not correspond to
a Nash equilibrium.

Опубликовано на портале: 22-01-2007

*Eric S. Maskin*,

*Partha Sarathi Dasgupta*Review of Economic Studies. 1986. Vol. 53. No. 1. P. 1-26.

The article presents information about the existence of equilibrium in discontinuous
economic games. In this paper and its sequel presents study the existence of Nash
equilibrium in games where agents' payoff functions are discontinuous. The enquiry
is motivated by a number of recent studies that have uncovered serious existence
problems in seemingly innocuous economic games. In the sequel to this paper, authors
have explained the utility function in the economic games referred to earlier are
neither continuous nor quasi-concave. However, they demonstrate that the payoff functions
in mildly modified versions of these constructs exhibit two weaker forms of continuity
which, together with the requirement of quasi-concavity, suffice for the existence
of an equilibrium. From this one may conclude that, at least in the modified versions
of these models, discontinuities in the payoff functions are not the real source
of the problem. Rather, it is the failure of the payoff functions to the quasi-concave
which is "responsible" for the non-existence of equilibrium. These observations bear
on the existence of Nash equilibrium in pure strategies.