1 / 16

Denis Phan 1 , Stephane Pajot 1 , Jean Pierre Nadal 2 ,

The Monopolist's Market with Discrete Choices and Network Externality Revisited: Small-Worlds, Phase Transition and Avalanches in an ACE Framework. Denis Phan 1 , Stephane Pajot 1 , Jean Pierre Nadal 2 , 1 ENST de Bretagne, Département ESH & ICI - Université de Bretagne Occidentale, Brest

belva
Download Presentation

Denis Phan 1 , Stephane Pajot 1 , Jean Pierre Nadal 2 ,

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Monopolist's Market with Discrete Choices and Network Externality Revisited:Small-Worlds, Phase Transition and Avalanches in an ACE Framework. Denis Phan1, Stephane Pajot1, Jean Pierre Nadal2, 1 ENST de Bretagne, Département ESH & ICI - Université de Bretagne Occidentale, Brest 1 Laboratoire de Physique Statistique, Ecole Normale Supérieure, Paris. denis.phan@enst-bretagne.fr - nadal@tournesol.lps.ens.fr Ninth annual meeting of the Society of Computational Economics University of Washington, Seattle, USA, July 11 - 13, 2003

  2. In this paper, we use Agent-based Computational Economicsand mathematical theorising as complementary toolsOutline of this paper(first investigations) 1 - Modelling the individual choice in a social context • Discrete choice with social influence: idiosyncratic and interactive heterogeneity 2 - Local dynamics and the network structure (basic features) • Direct vs indirect adoption, chain effect and avalanche process • From regular network towards small world : structure matters 3 - « Classical » issues in the « global » externality case • Analytical results in the simplest case (mean field) • « Classical » supply and demand curves static equilibrium 4 - Exploration of more complex dynamics at the global level • « Phase transition », demand hysteresis, andSethna’s inner hysteresis • Long range (static) monopolist’s optimal position and the network’s structure 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  3. Agents make a discrete (binary) choice i in the set :{0, 1} • Surplus : Vi(i) = willingness to pay – price • repeated buying The demand side: I - modelling the individual choice in a social contextDiscrete choice model with social influence : (1) Idiosyncraticheterogeneity • willingness to pay (1) Idiosyncratic heterogeneity : Hi(t) • Two special cases (Anderson, de Palma, Thisse 1992) : • « McFaden » (econometric) :Hi(t) = H + ifor allt ; i~ Logistic(0,) • Physicist’squenched disorder (e.g. Random Field)  used in this paper • « Thurstone » (psychological):Hi(t) = H + i (t)for allt ; i (t)~ Logistic(0,) • Physicist’s annealed disorder (+ad. Assumptions : Markov Random Field) • Also used by Durlauf, Blume, Brock among others… • Properties of this two cases generally differ (except in mean fieldfor this model) 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  4. Myopic agents (reactive) : • no expectations :each agent observes his neighbourhood • In this paper, social influence is assumed to be positive, homogeneous, symmetric and normalized across the neighbourhood) The demand side: I - modelling the individual choice in a social contextDiscrete choice model with social influence(2) Interactive (social) heterogeneity Willingness to pay (2)Interactive (social) heterogeneity: St(-i) • Jik measures the effect of the agent k ’schoice on the agent i ’swillingness to pay: 0 (if k=0) orJik(if k=1) • Jikare non-equivocal parameters of social influence • (several possible interpretations) 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  5. Indirect effect of prices: « chain » or « dominoes » effect Variation in price Variation in price Direct effect of prices ( P1P2) ( P1P2) Change ofagenti Change of agenti Change of agentj Change ofagentk Anavalanche carry on as long as: The demand side: II - Local dynamics and the network structure1 - Direct versus indirect adoption,chain effect and avalanche process 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  6. Regular network (lattice) Total connectivity Small world 1 (Watts Strogatz) Random network The demand side: II - Local dynamics and the network structure2 - From regular network towards small world :structure matters (a) • Milgram (1967) • “ six degrees of separation” • Watts and Strogatz (1998) • Barabasi and Albert, (1999) • “ scale free ”(all connectivity) • multiplicative process  power law • blue agent is “hub ” or “gourou ” 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  7. The demand side: II - Local dynamics and the network structure2 - From regular network towards small world :structure matters (b) 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  8. Demand Side In this case, each agent observes only the aggregate rate of adoption,  Let mthe marginal consumer: Vm= 0 Supply Side Optimal pricing by a monopolist in situation of risk Optimum / implicit derivation gives (inverse) supply curve : for large populations. With F logistic : Aggregate demandmayhave two fixed point for high   low  ; (here = 20) III - « Classical » issues in the « global » externality case 1 -Analytical results in the simplest case:global externality / full connectivity (main field) • H >0 : only one solution • H <0 : two solutions ; results depends on .J 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  9.  = 1 (one single Fixed point) Ps Pd H = 2 Ps H = 0 Pd J = 4 J = 0 J = 4 J=0 Dashed lines J = 0 no externality Ps Ps Pd H = 1.9 H = 1 Pd J = 4 J = 4 J= 0 Low  / high P III - « Classical » issues in the « global » externality case 2 -Inverse curve of supply and demand: comparative static 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  10. P- + P+ +> - +> - + - - III - « Classical » issues in the « global » externality case3 - Phase diagram & profit regime transition Full discussion of phase diagram in the plane .J,  .h, and numerically calculated solutions are presented in: Nadal et al., 2003 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  11. Homogeneous population:Hi = H i P = H + J P = H First order transition (strong connectivity) Chronology and sizes of induced adoptions in the avalanche when decrease from 1.2408 to 1.2407 =5 =20 IV - Exploration by ACEof more complex dynamics at the global level1 - Chain effect, avalanches and hysteresis 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  12. IV - Exploration by ACEof more complex dynamics at the global level2 - hysteresis in the demand curve : connectivity effect 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  13. A B (neighbourhood = 8, H = 1, J = 0.5, = 10) - Sub trajectory : [1,18-1,29] IV - Exploration by ACEof more complex dynamics at the global level(3) hysteresis in the demand curve :Sethna inner hystersis 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  14. Global externality J=0 IV - Exploration by ACEof more complex dynamics at the global levelOptimal long run (static) pricing by a monopolist: the influence of local network structure • optimal static (long run) monopoly prices increase with connectivity and small world parameterq ; higher with scale free than WS. 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  15. Conclusion, extensions & future developments • Even with simplest assumptions (myopic customers, full connectivity, risky situation), complex dynamics may arise. • Actual extensions: long term equilibrium for scale free small world, and dynamic regimes with H<0. • In the future: looking for cognitive agents …. • Dynamic pricing & monopolist’s Bayesian learning process in the case of repeated buying • Dynamic pricing & agent’s learning process in the case of durable good (Coase conjecture) • Dynamic network and monopolist’s learning about the network …. 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

  16. References • Anderson S.P., DePalma A, Thisse J.-F. (1992) Discrete Choice Theory of Product Differentiation, MIT Press, Cambridge MA. • Brock Durlauf (2001) “Interaction based models” in Heckman Leamer eds. Handbook of econometrics Vol 5 Elsevier, Amsterdam • Phan D. (2003) “From Agent-based Computational Economics towards Cognitive Economics”, in Bourgine, Nadal (eds.), Towards a Cognitive Economy, Springer Verlag, Forthcoming.www-eco.enst-bretagne.fr/~phan/moduleco • Phan D.Gordon M.B. Nadal J.P. (2003) “Social interactions in economic theory: a statistical mechanics insight”, in Bourgine, Nadal (eds.), Towards a Cognitive Economy, Springer Verlag, Forthcoming. • Nadal J.P.Phan D.Gordon M.B. Vannimenus J. (2003), "Monopoly Market with Externality: an Analysis with Statistical Physics and ACE", 8th Annual Workshop on Economics with Heterogeneous Interacting Agents, Kiel. Any Questions ? (please speak slowly) 9thSociety of Computational Economics, Seattle denis.phan@enst-bretagne.fr

More Related