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Register a new userA numbers-on-foreheads game
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Added by
Sune K. Jakobsen
Publication date
2015
fields
Informatics Engineering
and research's language is
English
Authors
Sune K. Jakobsen
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Is there a joint distribution of $n$ random variables over the natural numbers, such that they always form an increasing sequence and whenever you take two subsets of the set of random variables of the same cardinality, their distribution is almost the same? We show that the answer is yes, but that the random variables will have to take values as large as $2^{2^{dots ^{2^{Thetaleft(frac{1}{epsilon}right)}}}}$, where $epsilonleq epsilon_n$ measures how different the two distributions can be, the tower contains $n-2$ $2$s and the constants in the $Theta$ notation are allowed to depend on $n$. This result has an important consequence in game theory: It shows that even though you can define extensive form games that cannot be implemented on players who can tell the time, you can have implementations that approximate the game arbitrarily well.
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We consider a game in which players are the vertices of a directed graph. Initially, Nature chooses one player according to some fixed distribution and gives her a buck, which represents the request to perform a chore. After completing the task, the player passes the buck to one of her out-neighbors in the graph. The procedure is repeated indefinitely and each players cost is the asymptotic expected frequency of times that she receives the buck. We consider a deterministic and a stochastic version of the game depending on how players select the neighbor to pass the buck. In both cases we prove the existence of pure equilibria that do not depend on the initial distribution; this is achieved by showing the existence of a generalized ordinal potential. We then use the price of anarchy and price of stability to measure fairness of these equilibria. We also study a buck-holding variant of the game in which players want to maximize the frequency of times they hold the buck, which includes the PageRank game as a special case.
We present the first game characterization of contrasimilarity, the weakest form of bisimilarity. The game is finite for finite-state processes and can thus be used for contrasimulation equivalence checking, of which no tool has been capable to date. A machine-checked Isabelle/HOL formalization backs our work and enables further use of contrasimilarity in verification contexts.
We want to introduce another smoothing approach by treating each geometric element as a player in a game: a quest for the best element quality. In other words, each player has the goal of becoming as regular as possible. The set of strategies for each element is given by all translations of its vertices. Ideally, he would like to quantify this regularity using a quality measure which corresponds to the utility function in game theory. Each player is aware of the other players utility functions as well as their set of strategies, which is analogous to his own utility function and strategies. In the simplest case, the utility functions only depend on the regularity. In more complicated cases this utility function depends on the element size, the curvature, or even the solution to a differential equation. This article is a sketch of a possible game-theoretical approach to mesh smoothing and still on-going research.
Designing an incentive compatible auction that maximizes expected revenue is a central problem in Auction Design. While theoretical approaches to the problem have hit some limits, a recent research direction initiated by Duetting et al. (2019) consists in building neural network architectures to find optimal auctions. We propose two conceptual deviations from their approach which result in enhanced performance. First, we use recent results in theoretical auction design (Rubinstein and Weinberg, 2018) to introduce a time-independent Lagrangian. This not only circumvents the need for an expensive hyper-parameter search (as in prior work), but also provides a principled metric to compare the performance of two auctions (absent from prior work). Second, the optimization procedure in previous work uses an inner maximization loop to compute optimal misreports. We amortize this process through the introduction of an additional neural network. We demonstrate the effectiveness of our approach by learning competitive or strictly improved auctions compared to prior work. Both results together further imply a novel formulation of Auction Design as a two-player game with stationary utility functions.
In this paper, a multi-user cooperative computing framework is applied to enable mobile users to utilize available computing resources from other neighboring users via direct communication links. An incentive scheme based on Bertrand game is proposed for the user to determine textit{who} and textit{how} to cooperate. We model the resource demand users as textit{buyers} who aim to use minimal payments to maximize energy savings, whereas resource supply users as textit{sellers} who aim to earn payments for their computing resource provision. A Bertrand game against textit{buyers market} is formulated. When the users have textit{complete information} of their opponents, the Nash equilibrium (NE) of the game is obtained in closed form, while in the case of textit{incomplete information}, a distributed iterative algorithm is proposed to find the NE. The simulation results verify the effectiveness of the proposed scheme.
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