Trends in Mathematics Research Perspectives CRM Barcelona Vol.6 Josep Díaz Lefteris Kirousis Luis Ortiz-Gracia Maria Serna Editors Extended Abstracts Summer 2015 Strategic Behavior in Combinatorial Structures; Quantitative Finance Trends in Mathematics Research Perspectives CRM Barcelona Volume Series editors Enric Ventura Antoni Guillamon Since 1984 the Centre de Recerca Matemàtica (CRM) has been organizing scientific events such as conferences or workshops which span a wide range of cutting-edge topics in mathematics and present outstanding new results In the fall of 2012, the CRM decided to publish extended conference abstracts originating from scientific events hosted at the center The aim of this initiative is to quickly communicate new achievements, contribute to a fluent update of the state of the art, and enhance the scientific benefit of the CRM meetings The extended abstracts are published in the subseries Research Perspectives CRM Barcelona within the Trends in Mathematics series Volumes in the subseries will include a collection of revised written versions of the communications, grouped by events More information about this series at http://www.springer.com/series/4961 Extended Abstracts Summer 2015 Strategic Behavior in Combinatorial Structures Josep Díaz Lefteris Kirousis Maria Serna Editors Quantitative Finance Luis Ortiz-Gracia Editor Editors Josep Díaz Departament de CiJencies de la Computació Universitat PolitJecnica de Catalunya Barcelona, Spain Lefteris Kirousis Department of Mathematics National and Kapodistrian University Zografos, Greece Luis Ortiz-Gracia Department of Econometrics University of Barcelona Barcelona, Spain Maria Serna Departament de CiJencies de la Computació Universitat PolitJecnica de Catalunya Barcelona, Spain ISSN 2297-0215 Trends in Mathematics ISBN 978-3-319-51752-0 DOI 10.1007/978-3-319-51753-7 ISSN 2297-024X (electronic) ISBN 978-3-319-51753-7 (eBook) Library of Congress Control Number: 2017932282 Mathematics Subject Classification (2010): First part: 05C80, 34E10, 37N99, 52C45, 60C05, 68W40, 68Q32, 68W20, 82B26, 90B15, 90B60, 91B15; Second part: 62P05, 60G07, 60E10, 65T60, 91B02, 91G60, 91G80 © Springer International Publishing AG 2017 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Printed on acid-free paper This book is published under the trade name Birkhäuser, www.birkhauser-science.com The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Contents Part I Strategic Behavior in Combinatorial Structures On the Push&Pull Protocol for Rumour Spreading Hüseyin Acan, Andrea Collevecchio, Abbas Mehrabian, and Nick Wormald Random Walks That Find Perfect Objects and the Lovász Local Lemma Dimitris Achlioptas and Fotis Iliopoulos Logit Dynamics with Concurrent Updates for Local Interaction Games Vincenzo Auletta, Diodato Ferraioli, Francesco Pasquale, Paolo Penna, and Giuseppe Persiano 11 17 The Set Chromatic Number of Random Graphs Andrzej Dudek, Dieter Mitsche, and Paweł Prałat 23 Carpooling in Social Networks Amos Fiat, Anna R Karlin, Elias Koutsoupias, Claire Mathieu, and Rotem Zach 29 Who to Trust for Truthful Facility Location? Dimitris Fotakis, Christos Tzamos, and Emmanouil Zampetakis 35 Metric and Spectral Properties of Dense Inhomogeneous Random Graphs Nicolas Fraiman and Dieter Mitsche On-Line List Colouring of Random Graphs Alan Frieze, Dieter Mitsche, Xavier Pérez-Giménez, and Paweł Prałat 41 47 v vi Contents Approximation Algorithms for Computing Maximin Share Allocations Georgios Amanatidis, Evangelos Markakis, Afshin Nikzad, and Amin Saberi 55 An Alternate Proof of the Algorithmic Lovász Local Lemma Ioannis Giotis, Lefteris Kirousis, Kostas I Psaromiligkos, and Dimitrios M Thilikos 61 Learning Game-Theoretic Equilibria Via Query Protocols Paul W Goldberg 67 The Lower Tail: Poisson Approximation Revisited Svante Janson and Lutz Warnke 73 Population Protocols for Majority in Arbitrary Networks George B Mertzios, Sotiris E Nikoletseas, Christoforos L Raptopoulos, and Paul G Spirakis 77 The Asymptotic Value in Finite Stochastic Games Miquel Oliu-Barton 83 Almost All 5-Regular Graphs Have a 3-Flow Paweł Prałat and Nick Wormald 89 Part II Quantitative Finance On the Short-Time Behaviour of the Implied Volatility Skew for Spread Options and Applications Elisa Alòs and Jorge A León 97 An Alternative to CARMA Models via Iterations of Ornstein–Uhlenbeck Processes 101 Argimiro Arratia, Alejandra Cabaña, and Enrique M Cabaña Euler–Poisson Schemes for Lévy Processes 109 Albert Ferreiro-Castilla On Time-Consistent Portfolios with Time-Inconsistent Preferences 115 Jesús Marín-Solano A Generic Decomposition Formula for Pricing Vanilla Options Under Stochastic Volatility Models 121 Raúl Merino and Josep Vives A Highly Efficient Pricing Method for European-Style Options Based on Shannon Wavelets 127 Luis Ortiz-Gracia and Cornelis W Oosterlee A New Pricing Measure in the Barndorff-Nielsen–Shephard Model for Commodity Markets 133 Salvador Ortiz-Latorre Part I Strategic Behavior in Combinatorial Structures Foreword The Workshop on Strategic Behavior and Phase Transitions in Random and Complex Combinatorial Structures was held in the Centre de Recerca Matemàtica (CRM) in Bellaterra (Barcelona) from June 8th to 12th, 2015 This workshop was part of a research activity in CRM under the umbrella name Algorithmic Perspectives in Economics and Physics extended from April 7th to June 19th, 2015 Besides CRM, this research activity was funded by several Catalan organizations (Institut d’ Estudis Catalans, Institució Centres de Recerca de Catalunya, Universitat Autònoma de Barcelona, and Generalitat de Catalunya) and by the Simons Institute for the Theory of Computing The organizer committee for the program consisted of Dimitris Achlioptas (Department of Computer Science, UC Santa Cruz), Josep Díaz (Department of Computer Science, Universitat Politècnica de Catalunya), Lefteris Kirousis (Department of Mathematics, National and Kapodistrian University of Athens), and María Serna (Department of Computer Science, Universitat Politècnica de Catalunya) The main research theme of the workshop was to explore possible ties between phase transitions on one hand, and game theory on the other To be more specific, note that an important research area of the last decade is how atomic agents, acting locally and microscopically, lead to discontinuous macroscopic changes This point of view has proved to be especially useful in studying the evolution of random and usually complex combinatorial objects (typically, networks) with respect to discontinuous changes in global parameters like connectivity Naturally, there is a strategic element in the formation of a transition: the atomic agents seek “selfishly" to optimize a local microscopic parameter aiming at macroscopic changes that optimize their utility Investigating the question of whether the connection of microscopic strategic behavior with macroscopic phase transitions is a legitimate and meaningful research objective was the scope of the workshop The workshop was attended by more than thirty registered participants, several of which were Ph.D students or early career post-doctoral researchers Because of the no-fee, open access policy that the organizers opted for, there were many more I Strategic Behavior in Combinatorial Structures non-registered participants The conference followed a rather relaxed timetable that encouraged impromptu discussions and interactions The formal program comprised of some twenty presentations, more or less equally divided between the areas of random graphs and phase transitions on one hand, and game theory on the other The organizers actively sought to have renowned researchers give some of the talks and at the same time to draw from the pool of early career, promising researchers to present their current work Given the diverse background of the audience, presentations at a trans-thematic style and at a non specialized, high level were encouraged Barcelona, Spain Athens, Greece Barcelona, Spain September 2015 Josep Díaz Lefteris Kirousis Maria Serna On the Push&Pull Protocol for Rumour Spreading Hüseyin Acan, Andrea Collevecchio, Abbas Mehrabian, and Nick Wormald Abstract The asynchronous push&pull protocol, a randomized distributed algorithm for spreading a rumour in a graph G, is defined as follows Independent exponential clocks of rate are associated with the vertices of G, one to each vertex Initially, one vertex of G knows the rumour Whenever the clock of a vertex x rings, it calls a random neighbour y: if x knows the rumour and y does not, then x tells y the rumour (a push operation), and if x does not know the rumour and y knows it, y tells x the rumour (a pull operation) The average spread time of G is the expected time it takes for all vertices to know the rumour, and the guaranteed spread time of G is the smallest time t such that with probability at least 1=n, after time t all vertices know the rumour The synchronous variant of this protocol, in which each clock rings precisely at times 1; 2; : : : , has been studied extensively We prove the following results for any n-vertex graph: in either version, the average spread time is at most linear even if only the pull operation is used, and the guaranteed spread time is within a logarithmic factor of the average spread time, so it is O.n log n/ In the asynchronous version, both the average and guaranteed spread times are log n/ We give examples of graphs illustrating that these bounds are best possible up to constant factors We also prove the first theoretical relationships between the guaranteed spread times in the two versions Firstly, in all graphs the guaranteed spread time in the asynchronous version is within an O.log n/ factor of that in the synchronous version, and this is tight Next, we find examples of graphs whose asynchronous spread times are logarithmic, but the synchronous versions are polynomially large Finally, we H Acan ( ) • N Wormald School of Mathematical Sciences, Monash University, Clayton, VIC, Australia e-mail: huseyin.acan@monash.edu; nick.wormald@monash.edu A Collevecchio School of Mathematical Sciences, Monash University, Clayton, VIC, Australia Ca’ Foscari University, Venice, Italy e-mail: andrea.collevecchio@monash.edu A Mehrabian Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada e-mail: amehrabi@uwaterloo.ca © Springer International Publishing AG 2017 J Díaz et al (eds.), Extended Abstracts Summer 2015, Trends in Mathematics 6, DOI 10.1007/978-3-319-51753-7_1 ... events More information about this series at http://www.springer.com/series/4961 Extended Abstracts Summer 2015 Strategic Behavior in Combinatorial Structures Josep Díaz Lefteris Kirousis Maria... amehrabi@uwaterloo.ca © Springer International Publishing AG 2017 J Díaz et al (eds.), Extended Abstracts Summer 2015, Trends in Mathematics 6, DOI 10.1007/978-3-319-51753-7_1 H Acan et al show for any... fotis.iliopoulos@berkeley.edu © Springer International Publishing AG 2017 J Díaz et al (eds.), Extended Abstracts Summer 2015, Trends in Mathematics 6, DOI 10.1007/978-3-319-51753-7_2 11 12 D Achlioptas and F