1,919 research outputs found
Welfare guarantees for proportional allocations
According to the proportional allocation mechanism from the network
optimization literature, users compete for a divisible resource -- such as
bandwidth -- by submitting bids. The mechanism allocates to each user a
fraction of the resource that is proportional to her bid and collects an amount
equal to her bid as payment. Since users act as utility-maximizers, this
naturally defines a proportional allocation game. Recently, Syrgkanis and
Tardos (STOC 2013) quantified the inefficiency of equilibria in this game with
respect to the social welfare and presented a lower bound of 26.8% on the price
of anarchy over coarse-correlated and Bayes-Nash equilibria in the full and
incomplete information settings, respectively. In this paper, we improve this
bound to 50% over both equilibrium concepts. Our analysis is simpler and,
furthermore, we argue that it cannot be improved by arguments that do not take
the equilibrium structure into account. We also extend it to settings with
budget constraints where we show the first constant bound (between 36% and 50%)
on the price of anarchy of the corresponding game with respect to an effective
welfare benchmark that takes budgets into account.Comment: 15 page
On the Efficiency of the Proportional Allocation Mechanism for Divisible Resources
We study the efficiency of the proportional allocation mechanism, that is
widely used to allocate divisible resources. Each agent submits a bid for each
divisible resource and receives a fraction proportional to her bids. We
quantify the inefficiency of Nash equilibria by studying the Price of Anarchy
(PoA) of the induced game under complete and incomplete information. When
agents' valuations are concave, we show that the Bayesian Nash equilibria can
be arbitrarily inefficient, in contrast to the well-known 4/3 bound for pure
equilibria. Next, we upper bound the PoA over Bayesian equilibria by 2 when
agents' valuations are subadditive, generalizing and strengthening previous
bounds on lattice submodular valuations. Furthermore, we show that this bound
is tight and cannot be improved by any simple or scale-free mechanism. Then we
switch to settings with budget constraints, and we show an improved upper bound
on the PoA over coarse-correlated equilibria. Finally, we prove that the PoA is
exactly 2 for pure equilibria in the polyhedral environment.Comment: To appear in SAGT 201
Budget-restricted utility games with ordered strategic decisions
We introduce the concept of budget games. Players choose a set of tasks and
each task has a certain demand on every resource in the game. Each resource has
a budget. If the budget is not enough to satisfy the sum of all demands, it has
to be shared between the tasks. We study strategic budget games, where the
budget is shared proportionally. We also consider a variant in which the order
of the strategic decisions influences the distribution of the budgets. The
complexity of the optimal solution as well as existence, complexity and quality
of equilibria are analyzed. Finally, we show that the time an ordered budget
game needs to convergence towards an equilibrium may be exponential
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
Welfare Guarantees for Proportional Allocations
According to the proportional allocation mechanism from the network optimization literature, users compete for a divisible resource – such as bandwidth – by submitting bids. The mechanism allocates to each user a fraction of the resource that is proportional to her bid and collects an amount equal to her bid as payment. Since users act as utility-maximizers, this naturally defines a proportional allocation game. Syrgkanis and Tardos (STOC 2013) quantified the inefficiency of equilibria in this game with respect to the social welfare and presented a lower bound of 26.8 % on the price of anarchy over coarse-correlated and Bayes-Nash equilibria in the full and incomplete information settings, respectively. In this paper, we improve this bound to 50 % over both equilibrium concepts. Our analysis is simpler and, furthermore, we argue that it cannot be improved by arguments that do not take the equilibrium structure into account. We also extend it to settings with budget constraints where we show the first constant bound (between 36 and 50 %) on the price of anarchy of the corresponding game with respect to an effective welfare benchmark that takes budgets into account
Game Efficiency Through Linear Programming Duality
The efficiency of a game is typically quantified by the price of anarchy (PoA), defined as the worst ratio of the value of an equilibrium - solution of the game - and that of an optimal outcome. Given the tremendous impact of tools from mathematical programming in the design of algorithms and the similarity of the price of anarchy and different measures such as the approximation and competitive ratios, it is intriguing to develop a duality-based method to characterize the efficiency of games.
In the paper, we present an approach based on linear programming duality to study the efficiency of games. We show that the approach provides a general recipe to analyze the efficiency of games and also to derive concepts leading to improvements. The approach is particularly appropriate to bound the PoA. Specifically, in our approach the dual programs naturally lead to competitive PoA bounds that are (almost) optimal for several classes of games. The approach indeed captures the smoothness framework and also some current non-smooth techniques/concepts. We show the applicability to the wide variety of games and environments, from congestion games to Bayesian welfare, from full-information settings to incomplete-information ones
Visibility of Contributions and Cost of Information: An Experiment on Public Goods
We experimentally investigate the impact of visibility of information about contributors on contributions in the public goods game. We systematically consider several treatments that are similar to a wide range of situations in practice. First, we vary the cost of viewing identifiable information about contributors. Second, we vary recognizing all, top or bottom contributors. We find that recognizing all contributors significantly increases contributions relative to the baseline. Recognizing only the top contributors is not significantly different from not recognizing contributors, but recognizing only the bottom contributors is as effective as recognizing all contributors. When viewing information about contributors is costly, there is no significant difference in contributions as compared to the case where all contributors are displayed by default. This effect holds even though the identities of contributors are viewed less than ten percent of the time.public-goods, information, competition
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