# Статьи

**Всего статей в данном разделе :**69

**Learning to Play Bayesian Games**[статья]

Опубликовано на портале: 14-02-2005

*Eddie Dekel*,

*Drew Fudenberg*,

*David Knudsen Levine*Games and Economic Behavior. 2004. Vol. 46. No. 2. P. 282-303.

This paper discusses the implications of learning theory for the analysis of games
with a move by Nature. One goal is to illuminate the issues that arise when modeling
situations where players are learning about the distribution of Nature's move as
well as learning about the opponents' strategies. A second goal is to argue that
quite restrictive assumptions are necessary to justify the concept of Nash equilibrium
without a common prior as a steady state of a learning process.

Опубликовано на портале: 31-01-2007

*Jeremy I. Bulow*,

*John Geanakoplos*,

*Paul Klemperer*Journal of Political Economy. 1985. Vol. 3. No. 93. P. 488-511.

A firm's actions in one market can change competitors' strategies in a second market
by affecting its own marginal costs in that other market. Whether the action provides
costs or benefits in the second market depends on (a) whether it increases or decreases
marginal costs in the second market and (b) whether competitors' products are strategic
substitutes or strategic complements. The latter distinction is determined by whether
more "aggressive" play (e.g., lower price or higher quantity) by one firm in a market
lowers or raises competing firms' marginal profitabilities in that market. Many recent
results in oligopoly theory can be most easily understood in terms of strategic substitutes
and complements.

Опубликовано на портале: 24-01-2007

*Eric S. Maskin*Review of Economic Studies. 1999. Vol. 66. No. 1. P. 23-38.

If is a set of social alternatives, a social choice rule (SCR) assigns a subset of
A to each potential profile of individuals' preferences over A, where the subset
is interpreted as the set of 'welfare optima.' A game form (or 'mechanism') implements
the social choice rule if, for any potential profile of preferences, (1) any welfare
optimum can arise as a Nash equilibrium of the game form (implying, in particular,
that a Nash equilibrium exists) and, (2) all Nash equilibria are welfare optimal.
The main result of this paper establishes that any SCR that satisfies two properties
- monotonicity and no veto power--can be implemented by a game form if there are
three or more individuals. The proof is constructive.

Опубликовано на портале: 22-01-2007

*Edward Green*,

*Robert H. Porter*Econometrica. 1984. Vol. 52. No. 1. P. 87-100.

Recent work in game theory has shown that, in principle, it may be possible for firms
in an industry to form a self-policing cartel to maximize their joint profits. This
paper examines the nature of cartel self-enforcement in the presence of demand uncertainty.
A model of a noncooperatively supported cartel is presented, and the aspects of industry
structure which would make such a cartel viable are discussed.

Опубликовано на портале: 22-01-2007

*Hugo F. Sonnenschein*,

*Faruk Gul*Econometrica. 1988. Vol. 56. No. 3. P. 601-611.

Recently, attention has been given to a model of two-person bargaining in which the
parties alternate making offers and there is uncertainty about the valuation of one
party. The purpose of the analysis has been to identify delay to agreement with a
screening process, where agents with relatively lower valuations distinguish themselves
by waiting longer to settle. We point out a fundamental difficulty with this program
by demonstrating that the assumptions used in the literature allow for delay only
in so far as the time between offers is significant.

Опубликовано на портале: 24-01-2007

*John Hillas*Econometrica. 1990. Vol. 58. No. 6. P. 1365-1390.

A new definition of strategic stability is shown to satisfy all of the requirements
given by Elon Kohlberg and Jean-Francois Mertens (1986). The definition follows the
general form of the original definition of Kohlberg and Mertens, but, rather than
working with perturbations of the payoffs or strategy space, works directly with
perturbations to the best reply correspondence. With the appropriate topology on
this space of perturbations, the resulting definition does satisfy all of the requirements
given by Kohlberg and Mertens. It is shown that one does not have much freedom in
the topology one uses.

Опубликовано на портале: 24-01-2007

*Jean-François Mertens*,

*Elon Kohlberg*Econometrica. 1986. Vol. 54. No. 5. P. 1003-1037.

A basic problem in the theory of noncooperative games is the following: which Nash
equilibria are strategically stable, i.e. self-enforcing, and does every game have
a strategically stable equilibrium? We list three conditions which seem necessary
for strategic stability - backwards induction, iterated dominance, and invariance
- and define a set-valued equilibrium concept that satisfies all three of them. We
prove that every game has at least one such equilibrium set. Also, we show that the
departure from the usual notion of single-valued equilibrium is relatively minor,
because the sets reduce to points in all generic games.

**Optimal Auction Design**[статья]

Опубликовано на портале: 22-01-2007

*Roger B. Myerson*Mathematics of Operations Research. 1978. Vol. 6. No. 1. P. 58-73.

This paper considers the problem faced by a seller who has a single object to sell
to one of several possible buyers, when the seller has imperfect information about
how much the buyers might be willing to pay for the object. The seller's problem
is to design an auction game which has a Nash equilibrium giving him the highest
possible expected utility. Optimal auctions are derived in this paper for a wide
class of auction design problems.

Опубликовано на портале: 22-03-2007

*Kyle Bagwell*,

*Susan Carleton Athey*RAND Journal of Economics. 2001. Vol. 32. No. 3. P. 428-465.

We analyze collusion in an infinitely repeated Bertrand game, where prices are publicly
observed and each firm receives a privately observed, i.i.d. cost shock in each period.
Productive efficiency is possible only if high-cost firms relinquish market share.
In the most profitable collusive schemes, firms implement productive efficiency,
and high-cost firms are favored with higher expected market share in future periods.
If types are discrete, there exists a discount factor strictly less than one above
which first-best profits can be attained using history-dependent reallocation of
market share between equally efficient firms. We also analyze the role of communication
and side-payments.

Опубликовано на портале: 30-01-2007

*Ehud Kalai*,

*Meir Smorodinsky*Econometrica. 1975. Vol. 43. No. 3. P. 513-518.

A two-person bargaining model is considered. It is shown that under four axioms that
describe the behavior of players there is a unique solution for such a problem. The
axioms and the solution presented are different from those suggested by Nash. Also,
families of solutions which are continuous are discussed.

Опубликовано на портале: 30-01-2007

*Drew Fudenberg*,

*Jean Tirole*Journal of Economic Theory. 1991. Vol. 53. No. 2. P. 236-260.

We introduce a formal definition of perfect Bayesian equilibrium (PBE) for multi-period
games with observed actions. In a PBE, (P) the strategies form a Bayesian equilibrium
for each continuation game, given the specified beliefs, and (B) beliefs are updated
from period to period in accordance with Bayes rule whenever possible, and satisfy
a “no-signaling-what-you-don't-know” condition. PBE is equivalent to
sequential equilibrium if each player has only two types, or there are only two periods,
but differs otherwise. Equivalence is restored by requiring that (B) apply to the
relative probabilities of types with posterior probability zero.

**Power to the People**[статья]

Опубликовано на портале: 27-02-2004

*Vernon L. Smith*Wall Street Journal. 2002. No. 16. P. 20-.

Conduct the following mental experiment in the airline and hotel examples: Imagine that a flat average cost price is charged independent of day of week, holidays and season. Presto, there would be a shortage of airplane seats and accommodation rooms at all peak demand times, more airplanes and more hotels would have to be built and this extra capacity would be idle at all other times. All customers able and willing to consume more off-peak, if they could save money, would be forced to help pay for the idle capacity caused by the peak users…

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.