**Всего публикаций в данном разделе:**136

**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.

**Bidding Rings**[статья]

Опубликовано на портале: 31-01-2007

*John McMillan*,

*R. Preston McAfee*American Economic Review. 1992. Vol. 82. No. 3. P. 579-99.

The authors characterize coordinated bidding strategies in two cases: a weak cartel,
in which the bidders cannot make side-payments; and a strong cartel, in which the
cartel members can exclude new entrants and can make transfer payments. The weak
cartel can do no better than have its members submit identical bids. The strong cartel
in effect reauctions the good among the cartel members.

**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.

**Agreeing to Disagree**[статья]

Опубликовано на портале: 31-01-2007

*Robert J. Aumann*Annals of Statistics. 1976. Vol. 4. No. 6. P. 1236-39.

Aumann (1976) put forward a formal definition of common knowledge and used it to prove that two "like minded" individuals cannot "agree to disagree" in the following sense. If they start from a common prior and update the probability of an event E (using Bayes' rule) on the basis of private information, then it cannot be common knowledge between them that individual 1 assigns probability p to E and individual 2 assigns probability q to E with p, which is not equal to q. In other words, if their posteriors of event E are common knowledge then they must coincide. Aumann's Agreement Theorem has given rise to a large literature which review in this paper. The results are classified according to whether they are probabilistic (Bayesian) or qualitative. Particular attention is paid to the issue of how to interpret the notion of Harsanyi consistency as a (local) property of belief hierarchies.

Опубликовано на портале: 31-01-2007

*Motty Perry*,

*Philip John Reny*Econometrica. 1994. Vol. 62. No. 4. P. 795-817.

A noncooperative implementation of the core is provided for games with transferable
utility. The implementation obtained here is meant to reflect the standard motivation
for the core as closely as possible. In the model proposed, time is continuous. This
idealized treatment of time is most amenable for capturing an essential feature of
the core - there is always time to reject a noncore proposal before it is consumated.

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: 31-01-2007

*Debraj Ray*,

*Rakesh V. Vohra*Games and Economic Behavior. 1999. Vol. 26. No. 2. P. 286-336.

Consider an environment with widespread externalities, and suppose that binding agreements
can be written. We study coalition formation in such a setting. Our analysis proceeds
by defining on a partition function an extensive-form bargaining game. We establish
the existence of a stationary subgame perfect equilibrium for such a game. Our main
results are concerned with the characterization of equilibrium coalition structures.
We develop an algorithm that generates (under certain conditions) an equilibrium
coalition structure. Our characterization results are especially sharp for symmetric
partition functions. In particular, we provide a uniqueness theorem and apply our
results to a Cournot oligopoly.

**Contracting with Externalities**[статья]

Опубликовано на портале: 31-01-2007

*Ilya R. Segal*Quarterly Journal of Economics. 1999. Vol. 114. No. 2. P. 337-388.

The paper studies inefficiencies arising in contracting between one principal and
N agents when the utility of each agent depends on all agents' trades with the principal.
When the principal commits to a set of publicly observable bilateral contract offers,
the arising inefficiency is due entirely to the externalities imposed on non-signers.
In contrast, when the principal's offers are privately observed, the distortion is
due to the externalities given agents' equilibrium trades. Comparison of the two
externalities determines the relative efficiency of the two contracting regimes.
In both cases, we show that when N is large, each agent can be treated as non-pivotal,
provided that appropriate continuity assumptions are satisfied. We also study the
case in which the principal can condition each agent's trade on other agents' messages.
We characterize the set of such mechanisms in which each agent's participation is
voluntary. When the principal can commit to any such mechanism, she implements the
first-best outcome, while threatening each deviator with the harshest possible punishment.
However, in the presence of noise that goes to zero slower than N goes to infinity,
in the limit we obtain a (generally inefficient) outcome in which each agent feels
non-pivotal.

Опубликовано на портале: 31-01-2007

*Dilip Abreu*,

*Prajit K. Dutta*,

*Lones Smith*Econometrica. 1994. Vol. 62. No. 4. P. 939-948.

The paper discusses perfect "folk theorems" for infinitely repeated games with complete
information. Folk theorems assert that any feasible and individually rational payoff
vector of the stage game is a subgame perfect equilibrium payoff in the associated
infinitely repeated game with little or no discounting. It is obvious that feasibility
and individual rationality are necessary conditions for a payoff vector to be an
equilibrium payoff. The content of the folk theorems is that these conditions are
also sufficient. Perhaps the first folk theorem type result is due to Friedman (1971)
who showed that any feasible payoff which Pareto dominates a Nash equilibrium payoff
of the stage game will be an equilibrium payoff in the associated repeated game with
sufficiently patient players.

Опубликовано на портале: 30-01-2007

*George J. Mailath*,

*Larry Samuelson*,

*Jeroen M. Swinkels*Econometrica. 1993. Vol. 61. No. 2. P. 273-302.

Different extensive form games with the same reduced normal form can have different
information sets and subgames. This generates a tension between a belief in the strategic
relevance of information sets and subgames and a belief in the sufficiency of the
reduced normal form. We identify a property of extensive form information sets and
subgames which we term strategic independence. Strategic independence is captured
by the reduced normal form, and can be used to define normal form information sets
and subgames. We prove a close relationship between these normal form structures
and their extensive form namesakes. Using these structures, we are able to motivate
and implement solution concepts corresponding to subgame perfection, sequential equilibrium,
and forward induction entirely in the reduced normal form, and show close relations
between their implications in the normal and extensive form.

Опубликовано на портале: 30-01-2007

*Drew Fudenberg*,

*Eric S. Maskin*Econometrica. 1986. Vol. 54. No. 3. P. 533-554.

When either there are only two players or a "full dimensionality" condition holds,
any individually rational payoff vector of a one-shot game of complete information
can arise in a perfect equilibrium of the infinitely-repeated game if players are
sufficiently patient. In contrast to earlier work, mixed strategies are allowed in
determining the individually rational payoffs (even when only realized actions are
observable). Any individually rational payoffs of a one-shot game can be approximated
by sequential equilibrium payoffs of a long but finite game of incomplete information,
where players' payoffs are almost certainly as in the one-shot game.

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.

**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.

**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: 30-01-2007

*Philip John Reny*,

*R. Preston McAfee*Econometrica. 1992. Vol. 60. No. 2. P. 395-421.

In models of asymmetric information, possession of private information leads to rents
for the possessors. This induces mechanism designers to distort away from efficiency.
The authors show that this is an artifact of the presumption that information is
independently distributed. Rent extraction in a large class of mechanism design games
is analyzed, and a necessary and sufficient condition for arbitrarily small rents
to private information is provided. Additionally, the two-person bargaining game
is shown to have an efficient solution under first-order stochastic dominance and
a hazard rate condition. Similar conditions allow full rent extraction in Milgrom-Weber
auctions.

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

*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.

Опубликовано на портале: 30-01-2007

*Lawrence M. Ausubel*American Economic Review. 2004. Vol. 94. No. 5. P. 1452-1475.

When bidders exhibit multi-unit demands, standard auction methods generally yield
inefficient outcomes. This article proposes a new ascending-bid auction for homogeneous
goods, such as Treasury bills or telecommunications spectrum. The auctioneer announces
a price and bidders respond with quantities. Items are awarded at the current price
whenever they are "clinched," and the price is incremented until the market clears.
With private values, this (dynamic) auction yields the same outcome as the (sealed-bid)
Vickrey auction, but has advantages of simplicity and privacy preservation. With
interdependent values, this auction may retain efficiency, whereas the Vickrey auction
suffers from a generalized Winner's Curse.

Опубликовано на портале: 30-01-2007

*Debraj Ray*,

*Kaljan Chatterjee*,

*Kunal Sengupta*,

*Bhaskar Dutta*Review of Economic Studies. 1993. Vol. 60. No. 2. P. 463-77.

The authors explore a sequential offers model of n-person coalitional bargaining
with transferable utility and with time discounting. Their focus is on the efficiency
properties of stationary equilibria of strictly superadditive games when the discount
factor 'delta' is sufficiently large. It is shown that delay and the formation of
inefficient subcoalitions can occur in equilibrium, the latter for some or all orders
of proposer. However, efficient stationary equilibrium payoffs converge to a point
in the core as 'delta' approaches one. Strict convexity is a sufficient condition
for there to exist an efficient stationary equilibrium payoff vector for sufficiently
high 'delta'.

**Auctions versus Negotiations**[статья]

Опубликовано на портале: 30-01-2007

*Paul D. Klemperer*,

*Jeremy I. Bulow*American Economic Review. 1996. Vol. 86. No. 1. P. 180-94.

Which is the more profitable way to sell a company: an auction with no reserve price
or an optimally structured negotiation with one less bidder? The authors show, under
reasonable assumptions, that the auction is always preferable when bidders' signals
are independent. For affiliated signals, the result holds under certain restrictions
on the seller's choice of negotiating mechanism. The result suggests that the value
of negotiating skill is small relative to the value of additional competition. The
paper also shows how the analogies between monopoly theory and auction theory can
help derive new results in auction theory.