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We summarize some recent progress in the understanding of the statistical properties of cosmological billiards.

General Relativity and Quantum Cosmology · Physics 2015-05-27 Thibault Damour , Orchidea Maria Lecian

The aim of this work is to put together two novel concepts from the theory of integrable billiards: billiard ordered games and confocal billiard books. Billiard books appeared recently in the work of Fomenko's school, in particular of V.…

Dynamical Systems · Mathematics 2022-04-20 Vladimir Dragovic , Sean Gasiorek , Milena Radnovic

Bidding strategies that help advertisers determine bidding prices are receiving increasing attention as more and more ad impressions are sold through real-time bidding systems. This paper first describes the problem and challenges of…

Computer Science and Game Theory · Computer Science 2022-12-06 Mengjuan Liu , Zhengning Hu , Zhi Lai , Daiwei Zheng , Xuyun Nie

I study symmetric competitions in which each player chooses an arbitrary distribution over a one-dimensional performance index, subject to a convex cost. I establish existence of a symmetric equilibrium, document various properties it must…

Theoretical Economics · Economics 2026-05-07 Mark Whitmeyer

We address the problem of building a decision model for a specific bidding situation in the game of Bridge. We propose the following multi-step methodology i) Build a set of examples for the decision problem and use simulations to associate…

Modern commercial Internet search engines display advertisements along side the search results in response to user queries. Such sponsored search relies on market mechanisms to elicit prices for these advertisements, making use of an…

Computer Science and Game Theory · Computer Science 2008-12-18 Jon Feldman , S. Muthukrishnan

We provide a self-contained introduction to finite extensive games with perfect information. In these games players proceed in turns having, at each stage, finitely many moves to their disposal, each play always ends, and in each play the…

Computer Science and Game Theory · Computer Science 2022-04-20 Krzysztof R. Apt , Sunil Simon

For the most up-to-date version please visit http://www.cis.upenn.edu/~brautbar/ccgame.pdf

Social and Information Networks · Computer Science 2011-07-05 Mickey Brautbar , Michael Kearns

The article describes a model of chess based on information theory. A mathematical model of the partial depth scheme is outlined and a formula for the partial depth added for each ply is calculated from the principles of the model. An…

Artificial Intelligence · Computer Science 2011-12-12 Alexandru Godescu

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas and recent development in quantum game theory. In this…

Quantum Physics · Physics 2007-05-23 E. W. Piotrowski , J. Sladkowski

This paper is intended to help the readers to understand the article: Y. Hirashita, Least-Squares Prices of Games, Preprint (arXiv:math.OC/0703079).

Optimization and Control · Mathematics 2007-05-23 Yukio Hirashita

Two-player zero-sum "graph games" are a central model, which proceeds as follows. A token is placed on a vertex of a graph, and the two players move it to produce an infinite "play", which determines the winner or payoff of the game.…

Computer Science and Game Theory · Computer Science 2022-11-28 Guy Avni , Ismael Jecker , Djordje Zikelic

This paper contributes a new way to evaluate AI. Much as one might evaluate a machine in terms of its performance at chess, this approach involves evaluating a machine in terms of its performance at a game called "MAD Chairs". At the time…

Computers and Society · Computer Science 2025-09-08 Chris Santos-Lang

We study collusion in a second-price auction with two bidders in a dynamic environment. One bidder can make a take-it-or-leave-it collusion proposal, which consists of both an offer and a request of bribes, to the opponent. We show that…

Theoretical Economics · Economics 2021-05-31 Jingfeng Lu , Zongwei Lu , Christian Riis

To reduce the danger of powerful super-intelligent AIs, we might make the first such AIs oracles that can only send and receive messages. This paper proposes a possibly practical means of using machine learning to create two classes of…

Artificial Intelligence · Computer Science 2020-10-07 James D. Miller , Roman Yampolskiy , Olle Haggstrom , Stuart Armstrong

We characterize the statistical properties of a large number of online auctions run on eBay. Both stationary and dynamic properties, like distributions of prices, number of bids etc., as well as relations between these quantities are…

Physics and Society · Physics 2009-11-13 Alireza Namazi , Andreas Schadschneider

Many casinos routinely use mechanical card shuffling machines. We were asked to evaluate a new product, a shelf shuffler. This leads to new probability, new combinatorics and to some practical advice which was adopted by the manufacturer.…

Combinatorics · Mathematics 2013-07-24 Persi Diaconis , Jason Fulman , Susan Holmes

A recurring theme in recent computer science literature is that proper design of signaling schemes is a crucial aspect of effective mechanisms aiming to optimize social welfare or revenue. One of the research endeavors of this line of work…

Computer Science and Game Theory · Computer Science 2015-07-07 Moran Feldman , Moshe Tennenholtz , Omri Weinstein

We introduce and analyze several variations of Penney's game aimed to find a more equitable game.

Simultaneous ascending auctions present agents with the exposure problem: bidding to acquire a bundle risks the possibility of obtaining an undesired subset of the goods. Auction theory provides little guidance for dealing with this…

Computer Science and Game Theory · Computer Science 2012-07-09 Anna Osepayshvili , Michael P. Wellman , Daniel Reeves , Jeffrey K. MacKie-Mason