Dynamics of social networks (the rise and fall of a networked society)
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1 Dynams of soal networks (the rse and fall of a networked soety Matteo Marsl, ICTP Treste Frantsek Slanna, Prague, Fernando Vega-Redondo, Alante Motvaton & Bakground Soal nteraton and nformaton Smple model of soal network dynams Mean feld soluton Conlusons M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004
2 M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004 Bakground Soal aptal/non-market nteratons are mportant to understand soo-eonom phenomena (e.g. ob market (Putnam, Granovetter, Topa, Game theoret approah to endogenous network formaton (Bala&Goyal, Jakson&Wolnsk, Determnst set up, no volatlty Empral studes of networks stylzed fats + smple models of random graphs (Barabas, Watts&Strogatz, Mendes, Vespgnan, No mro-eonom foundaton
3 Networks and Informaton I Market nteraton Impersonal (need not know/trust others Informaton from pres Need nsttuton Low volatlty market M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004
4 Networks and Informaton II Soal/non-market nteraton (e.g. ob ontat networks Personal (trust/reputaton No nsttuton Informaton through ontats Hgh volatlty! Network arres both payoffs and nformaton! Informaton s rual n a volatle world when lnks may deay due to envronmental shoks It needs all the runnng you an do to keep n the same plae (Red Queen effet M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004
5 M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004 What s a lnk? What nformaton does t arry? Mutually proftable ollaboraton Requres trust. Ths s why nformaton through frend s mportant: beleves that k wll do what he promses, beause ths s what he has done wth. The nteraton k reveals the type of k to That s why long range lnk are rare Implt osts of establshng a lnk. Payoff needs to be strtly postve
6 M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004 How do networked soetes form from soal nteraton? market Poverty trap Mssng nsttutons/markets Low soal aptal Hgh volatlty Developed Countres Effent nsttutons/markets Hgh soal aptal Low volatlty Mrales and ant-mrales?
7 A model soety A soety of N agents Eah par of agents (, an have a mutually proftable ollaboraton opportunty. In ths ase, f they get to know eah other they form a lnk. Agents searh for proftable nteratons Typally (at a rate ξ through neghbors: ask at one of hs frends* about one of hs frends* rarely (at a rate η by random enounters: meets, randomly drawn from the populaton Agents lve n a volatle envronment A proftable ooperaton may turn unproftable wth some rate λ the orrespondng lnk s deleted M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004 * taken at random, f any
8 M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004 Three parameters Global searh η k k Loal searh ξ Volatlty λ (tme resalng elmnates one parameter
9 Observables: Average degree onnetvty average number of frends Clusterng oeffent qprobablty that two frends of an agent are also frend of eah other densty of Sze of largest omponent M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004
10 M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004 Numeral results η/λ0.01 Fraton of agents n Gant omponent q dereases as ξ nreases!
11 M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004 Mean feld theory Assumpton: Master equaton: Soluton: { }{ } ( N q q t p t q P 1 (, (,, δ k F k q w F P q w > (1 1 ( 1 { (1, ( 2 1 ( ξ γ ξ β γ βθ η e p s s p s log 0 ( (1 2 (1 2 ( ( γ µ µ µ γ η β γ η β π + + '(1 (0]/ [1 (1 '(1] '(0 / [1 (1 π π ξ γ π π ξ β q q q there s only 1 soluton! Need eq. for q Self-onsstent equatons: n.b. no sale-free when lnks ost!
12 M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004 Equaton for q: Q # pars of frend of whh are also frend of eah other Compute transton rates w(q Q ±1, e.g.: { } + { k k } k k Statonary ondton: w( Q Q + 1 w( Q qπ ''(1 ξ (1 q[2 Q 1 π '(0 π (0] 1 π '(1
13 M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004 Soluton of self-onsstent equaton q q dereases wth ξ n the dense phase!
14 M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004 λ~t: Lqud-gas transton λ < λ λ λ λ > λ lqud gas
15 M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004 Conluson I An attempt to understand the performane of a soety must nlude a proper aount of the fores governng the dynams of ts soal network. Soal networks may respond n a very non-lnear way to smple proesses: Soetes may not follow a smooth path of development Phase oexstene: a networked soety may not materalze even under favourable ondtons. By ontrast, t may dsplay a sgnfant reslene to deteroratng ondtons Densty of lques (q does not neessarly nreases wth nentves (ξ
16 M.Marsl, F. Slanna & F. Vega-Redondo, Pro. Nat. Aad. S. 101: (2004 Conlusons II New soo-eonom questons: What type of network strutures emerge from ndvdual nentves? What s the mpat of markets on soety (globalzaton Non-market nteratons (fashons, ob searh, rmnalty New questons n statstal physs: Interaton network as a degree of freedom max u ( F,graph, F {neghbors of F e.g. u ( F,graph F 1 N d, } + K
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