@ARTICLE{19000094_2001,
author = {Athey, Susan Carleton},
keywords = {auction theory, incomplete information, Nash equilibrium, аукцион, игры с неполной информацией, математическое моделирование, равновесие по Нэшу, теория аукционов, экономическое поведение},
title = {Single Crossing Properties and the Existence of Pure Strategy
Equilibria in Games of Incomplete Information },
journal = {Econometrica},
year = {2001},
month = {},
volume = {69},
number = {4},
pages = {861-89},
url = {http://ecsocman.hse.ru/text/19000094/},
publisher = {},
language = {ru},
abstract = {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. },
annote = {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. }
}