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List of invited speakers and abstracts
Please click on the name of the invited speakers to see details on their talks.go to the schedule page
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- Laurent Desvillettes (CMLA, ENS Cachan) slides
- Serge Galam (CREA Polytechnique) article
- Ansgar Jungel (Mainz, Germany) slides
- Hervé Maillot (Univ. Orleans) slides
- Vincent Merlin (CREM, Caen) slides figures
- Jean-Pierre Nadal (EHESS, Paris) slides
- Giovanni Naldi (Dipartimento di Matematica, Milano) slides
- A. K. Naimzada (Dipartimento Economia Politica, Milano-Bicocca) slides
- Cyrille Piatecki (LEO, Univ. Orleans) slides
- Jean-Louis Rouet (ISTO, Orleans) slides
- Giuseppe Toscani (Dipartimento di Matematica, Pavia)
slides of talk 1
slides of talk 2
Laurent Desvillettes (web page, CMLA, ENS Cachan)[go up]
Title: Infinite-dimensional reaction diffusion equations for population dynamics in the context of an artificial selective pressure
Abstract: We present an approach for the study of structured populations based on the so-called "Infinite-dimensional reaction diffusion equations", where the unknown is the density of individuals having a certain quantitative trait (for example related to their size). In this talk, we describe the situation when the individuals (for example, fishes) are a resource which is exploited with an intensity which depends on their trait.
Serge Galam (web page, CREA, Ecole Polytechnique)[go up]
Title: When Sociophysics becomes predictive: The recent french referendum and The hung fifty-fifty elections.(Minority opinion spreading, heterogeneous believes and contrarian behavior)
Abstract: In 2005, for the first time, a highly improbable political vote outcome was predicted using a model of sociophysics. Moreover the prediction was made several months ahead of the actual vote against all polls and analyses predictions. The model deals with the dynamics of spreading of a minority opinion in public debates using a two sate variable system. It applies to a large spectrum of issues including national votes like the recent French vote, behavior changes like smoking versus non-smoking, support or opposition to a military action like the war in Iraq, rumors like the French hoax about September eleven, and reform proposals. It articulated around successive local opinion updates combining majority rule and the possible existence of doubt. In case of a local doubt, collective beliefs are activated to make a choice. The emergence of a stable collective opinion is found to obey a threshold dynamic. It is the degree of heterogeneity in the distribution of common beliefs which determines the current value of the threshold which may well vary from ten percents to ninety percents. Accordingly the expected democratic character of a free public debate may turn onto a dictatorial machine to propagate the opinion of a tiny minority against the initial opinion of the overwhelming majority. Extension to include a contrarian effect is shown to provide an explanation for the recent occurrence of hung elections at fifty-fifty.
S. Galam, « Heterogeneous beliefs, segregation, and extremism in the making of public opinion », Phys. Rev. E 71, 046123 (2005)
P. Le Hir, « Les mathématiques s'invitent dans le débat européen », Le Monde/Samedi 26 Fevrier 2005/23
S. Galam, « Contrarian deterministic effect: the hung elections scenario », Physica A 333, 453-460 (2004)
C. Borghesi and S. Galam, « Chaotic, staggered, and polarized dynamics in opinion forming: The contrarian effect », Physical Review E 73, 066118 (2006)
Ansgar Jungel (web page, Mainz, Germany)[go up]
Title: Some mathematical results for Black-Scholes-type equations for financial derivatives
Hervé Maillot (Orléans, France)[go up]
Title: Modelling issues for developing countries agriculture, and distribution systems.
Abstract: One deals with issues araising in the economical field and focusing on regulation of exchanges and flows strategies. As examples, we present two problems concerned with agricultural policy and mass retail organization. The mathematical study of them takes place in a more global project of an International Initiative proposed and supported by the IRG and the FPH , two Institutions of the civil society. This Initiative carried out by a multidisciplinary group is an open space for debates and dialogue where researchers and stakeholders involved in decision-making process for institutions and business (corporations, government agencies, and non-profit organizations) attempt to formalize new economic research topics. In this framework the need of mathematical modelization and numerical simulation is clearly identified and collaborations with mathematicians (senior researchers as well as students) is seeked.
Vincent Merlin (web page, CREM, Caen)[go up]
Title:Majority Efficient Representation of the Citizens in a Federal Union
Abstract: All the federal unions, like the United States of America or the European Union face the issue of finding a ``good'' two step voting mechanism. In particular, a crucial question is to know how many mandates should be given to each country or state in a two tiers voting system, given that the majority rule is used at each level. We here propose a new normative criterion to evaluate these voting rules: An apportionment of the seats among the states is majority efficient if the probability of electing the candidate who receives less than 50\% of the votes in a two candidate competition over the whole union is minimized. Using computer simulations, we suggest that either the proportional or the square root rule can emerge as an optimal apportionment method depending on the probability model we use to describe the electoral process. As a byproduct, we also study the influence of unequal populations on the probability of picking a minority candidate through two-tiers voting mechanisms.
Jean-Pierre Nadal (web page, EHESS, Paris)[go up]
Title: Choice under social influence: the curse of coordination.
Abstract: We explore the effects of social influence in a simple market model in which a large number of agents face a binary choice: to buy/not to buy a single unit of a product at a price posted by a single seller (monopoly market). We consider the case of positive externalities: an agent is more willing to buy if other agents make the same decision. The heterogeneity among agents is fixed (random utility framework) - in Physics this is a particular case of "quenched disorder" models known as random field Ising model, at zero temperature.
We study analytically the equilibrium properties of the market in the limiting case where each agent is influenced by all the others. We show that generically, if the social influence is strong enough, there is a range of prices for which the aggregate demand is multivaluated - a situation similar to the one arising in stag hunt-type coordination games.
Considering the optimisation of the profit by the seller, we exhibit a regime where, if the mean willingness to pay increases and/or the production costs decrease, the seller's optimal strategy jumps from a solution with a high price and a small number of buyers, to another one with a low price and a large number of buyers. This regime, usually modelled with ad-hoc bimodal distributions of the idiosyncratic heterogeneity, arises here for general monomodal distributions if the social influence is strong enough. In addition, we show that for a large range of parameters the optimal price (for the seller) falls in the region where the demand is not unique: the optimal profit will be realized only if the agents coordinate.
Work done with Mirta B. Gordon, Denis Phan, Viktoriya Semeshenko and Jean Vannimenus, within the project "ELICCIR" supported by the Program "Complex Systems in Human and Social Sciences" (CNRS and French Ministry of Research).
Biblio:
- Mirta B. Gordon, Jean-Pierre Nadal, Denis Phan and Jean Vannimenus, "Seller's dilemma due to social interactions between customers", Physica A: Statistical Mechanics and its Applications, Volume 356, Issues 2-4, 15 October 2005, Pages 628-640.
- Jean-Pierre Nadal, Denis Phan, Mirta B. Gordon and Jean Vannimenus, "Multiple equilibria in a monopoly market with heterogeneous agents and externalities", Quantitative Finance, Vol. 5, No. 6, December 2005, 557-568.
- Mirta B. Gordon and Jean-Pierre Nadal and Denis Phan and Viktoriya Semeshenko, "Discrete Choices under Social Influence: Generic Properties", In preparation.
- Mirta B. Gordon and Jean-Pierre Nadal and Denis Phan and Viktoriya Semeshenko, "Monopoly market with externalities: the curse of coordination", In preparation.
Ahmad K. Naimzada (Dipartimento di Economia Politica, Università Milano Bicocca) [go up]
Title: Heterogeneous Fundamentalists and Complex Dynamics
Abstract: Developing a model with a switching mechanism, we show how complex dynamics can be generated even though heterogeneity arises among agents with the same trading rules (fundamentalists). We assume that there are two experts which are imitated by other operators. We show that (i) market instability and periodic, or even, chaotic price fluctuations can be generated; (ii) conditions exist under which an expert can drive another expert out of the market; (iii) two experts can survive when the dynamic system either generates a period doubling bifurcation around an attractor or when an homoclinic bifurcation leads to the merging of the two attractors; (iv) a central role is played by the reaction to misalignment of both market makers and agents.
This is a common work with Giorgio Ricchiuti (Dipartimento Scienze Economiche, Università degli Studi di Firenze
Giovanni Naldi (web page, Dipartimento di Matematica, Milano)[go up]
Title: Fokker-Planck equations for opinion formation: modeling, analysis and asymptotics
Abstract: Microscopic models of both social describing collective behaviors and self organization in a society have been recently introduced and analyzed by several authors (see e.g. [1-6] The leading idea is that collective behaviors of a society composed by a sufficiently large number of individuals (agents) can be hopefully described using the laws of statistical mechanics as it happens in a physical system composed of many interacting particles. The details of the social interactions between agents then characterize the emerging statistical phenomena. We study certain nonlinear continuous models of opinion formation derived from a kinetic description [7] involving exchange of opinion between individual agents. These models imply that the only possible final opinions are the extremal ones, and are similar to models of pure drift in magnetization. Both analytical and numerical methods allow to recover the final distribution of opinion between the two extremal ones. We also describe some possible developments. The work reported here will appear in a forthcoming paper [8].
[1] Galam S., Gefen Y., Shapir Y.: Sociophysics:a new approach of sociological collective behavior. J. Math. Sociology 9, (1982) 1.
[2] Ochrombel R.: Simulation of Sznajd sociophysics model with convincing single opinions. Int. J. Mod. Phys. C 12 (2001) 1091.
[3] Slanina F., Lavi˘cka H.: Analytical results for the Sznajd model of opinion formation, Eur. Phys. J. B 35 (2003) 279.
[4] Stauffer D.: Percolation and Galam theory of minority opinion spreading. Int. J. Mod. Phys. C 13 (2002) 315.
[5] Sznajd-Weron K., Sznajd J.: Opinion evolution in closed community, Int. J. Mod. Phys. C 11 (2000) 1157.
[6] Weidlich W.: Sociodynamics: A systematic approach to mathematical modelling in the social sciences, Harwood Academic Publishers, 2000.
[7] G. Toscani, Kinetic models of opinion formation, Comm. Math. Sci. 4 (3) (2006) 481-496G.
[8] G. Aletti, G. Naldi, G. Toscani, First-order continuous models of opinion formation, SIAM J. Appl. Math. (in press) (2007).
Jean-Louis Rouet (web page, ISTO, Orléans)[go up]
Title:Using voting probabilistic models in the EU case
Abstract: Departing from the traditional axiomatic approach, probabilistic models have proved to be useful for the analysis of voting rules. In Social Choice theory, the Impartial Culture model (IC) and the Impartial Anonymous Culture model (IAC) are the two main probabilistic assumptions commonly used.
Using the Impartial Culture assumption to model the voting behavior, suggests that the EU could only take a decision in 2% of the cases with its current voting mechanisms. The Impartial Anonymous Culture assumption we consider here is an alternative of this first model and gives more reasonable results. Moreover, we go beyond this point and we show that these two main assumptions are unified using a double probabilistic approach, defining the Generalized Impartial Anonymous Culture, IC and IAC being special cases.
Using these models, the probability of approval for the asymptotic case (reached when the number of countries $N$ goes to infinity) is computed. Next with computer enumerations and Monte Carlo simulations, we evaluate the probability to act for the European Union with 27 members. We consider both the Treaty of Nice and some proposals for the European Constitution. The asymptotic results will be compared to those obtained with the 27 states of the European Union.
Giuseppe Toscani (web page, Dipartimento di Matematica, Pavia)[go up]
Title:Kinetic models for economy: The conservative case (Part 1)
Title:Formation of tails in non conservative kinetic models (Part 2)
