28,062 research outputs found
Multiple equilibria as a difficulty in understanding correlated distributions
We view achieving a particular correlated equilibrium distribution for a normal form game as an implementation problem. We show, using a parametric version of the two-person Chicken game and a wide class of correlated equilibrium distributions, that a social choice function that chooses a particular correlated equilibrium distribution from this class does not satisfy the Maskin monotonicity condition and therefore can not be fully implemented in Nash equilibriu
MULTIPLE EQUILIBRIA AS A DIFFICULTY IN UNDERSTANDING CORRELATED DISTRIBUTIONS
We view achieving a particular correlated equilibrium distribution for a normal form game as an implementation problem. We show, using a parametric version of the two-person Chicken game and a wide class of correlated equilibrium distributions, that a social choice function that chooses a particular correlated equilibrium distribution from this class does not satisfy the Maskin monotonicity condition and therefore can not be fully implemented in Nash equilibrium
Multiple equilibria as a difficulty in understanding correlated distributions.
We view achieving a particular correlated equilibrium distribution for a normal form game as an implementation problem. We show, using a parametric version of the two-person Chicken game and a wide class of correlated equilibrium distributions, that a social choice function that chooses a particular correlated equilibrium distribution from this class does not satisfy the Maskin monotonicity condition and therefore can not be fully implemented in Nash equilibrium
Implementability of Correlated and Communication Equilibrium Outcomes in Incomplete Information Games
In a correlated equilibrium, the players’ choice of actions is affected by random, correlated messages that they receive from an outside source, or mechanism. This allows for more equilibrium outcomes than without such messages (pure-strategy equilibrium) or with statistically independent ones (mixed-strategy equilibrium). In an incomplete information game, the messages may also convey information about the types of the other players, either because they reflect extraneous events that affect the types (correlated equilibrium) or because the players themselves report their types to the mechanism (communication equilibrium). Thus, mechanisms can be classified by the connections between the messages that the players receive and their own and the other players’ types, the dependence or independence of the messages, and whether randomness is involved. These properties may affect the achievable equilibrium outcomes, i.e., the payoffs and joint distributions of type and action profiles. Whereas for complete information games there are only three classes of equilibrium outcomes, with incomplete information the number is 14–15 for correlated equilibria and 15–17 for communication equilibria. Each class is characterized by the properties of the mechanisms that implement its members. The majority of these classes have not been described before.Correlated equilibrium, Communication equilibrium, Incomplete information, Bayesian games, Mechanism, Correlation device, Implementation
Draft Auctions
We introduce draft auctions, which is a sequential auction format where at
each iteration players bid for the right to buy items at a fixed price. We show
that draft auctions offer an exponential improvement in social welfare at
equilibrium over sequential item auctions where predetermined items are
auctioned at each time step. Specifically, we show that for any subadditive
valuation the social welfare at equilibrium is an -approximation
to the optimal social welfare, where is the number of items. We also
provide tighter approximation results for several subclasses. Our welfare
guarantees hold for Bayes-Nash equilibria and for no-regret learning outcomes,
via the smooth-mechanism framework. Of independent interest, our techniques
show that in a combinatorial auction setting, efficiency guarantees of a
mechanism via smoothness for a very restricted class of cardinality valuations,
extend with a small degradation, to subadditive valuations, the largest
complement-free class of valuations. Variants of draft auctions have been used
in practice and have been experimentally shown to outperform other auctions.
Our results provide a theoretical justification
Belief-Invariant and Quantum Equilibria in Games of Incomplete Information
Drawing on ideas from game theory and quantum physics, we investigate
nonlocal correlations from the point of view of equilibria in games of
incomplete information. These equilibria can be classified in decreasing power
as general communication equilibria, belief-invariant equilibria and correlated
equilibria, all of which contain the familiar Nash equilibria. The notion of
belief-invariant equilibrium has appeared in game theory before, in the 1990s.
However, the class of non-signalling correlations associated to
belief-invariance arose naturally already in the 1980s in the foundations of
quantum mechanics.
Here, we explain and unify these two origins of the idea and study the above
classes of equilibria, and furthermore quantum correlated equilibria, using
tools from quantum information but the language of game theory. We present a
general framework of belief-invariant communication equilibria, which contains
(quantum) correlated equilibria as special cases. It also contains the theory
of Bell inequalities, a question of intense interest in quantum mechanics, and
quantum games where players have conflicting interests, a recent topic in
physics.
We then use our framework to show new results related to social welfare.
Namely, we exhibit a game where belief-invariance is socially better than
correlated equilibria, and one where all non-belief-invariant equilibria are
socially suboptimal. Then, we show that in some cases optimal social welfare is
achieved by quantum correlations, which do not need an informed mediator to be
implemented. Furthermore, we illustrate potential practical applications: for
instance, situations where competing companies can correlate without exposing
their trade secrets, or where privacy-preserving advice reduces congestion in a
network. Along the way, we highlight open questions on the interplay between
quantum information, cryptography, and game theory
Complexity Theory, Game Theory, and Economics: The Barbados Lectures
This document collects the lecture notes from my mini-course "Complexity
Theory, Game Theory, and Economics," taught at the Bellairs Research Institute
of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th
McGill Invitational Workshop on Computational Complexity.
The goal of this mini-course is twofold: (i) to explain how complexity theory
has helped illuminate several barriers in economics and game theory; and (ii)
to illustrate how game-theoretic questions have led to new and interesting
complexity theory, including recent several breakthroughs. It consists of two
five-lecture sequences: the Solar Lectures, focusing on the communication and
computational complexity of computing equilibria; and the Lunar Lectures,
focusing on applications of complexity theory in game theory and economics. No
background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some
recent citations to v1 Revised v3 corrects a few typos in v
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