1 / 14

Continuously Tunable Pareto Exponent in a Random Shuffling Money Exchange Model

Econophys – Kolkata I. Continuously Tunable Pareto Exponent in a Random Shuffling Money Exchange Model. K. Bhattacharya, G. Mukherjee and S. S. Manna. Satyendra Nath Bose National Centre for Basic Sciences manna@bose.res.in. Random pair wise conservative money shuffling:

lowri
Download Presentation

Continuously Tunable Pareto Exponent in a Random Shuffling Money Exchange Model

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. Econophys – Kolkata I Continuously Tunable Pareto Exponent in a Random Shuffling Money Exchange Model K. Bhattacharya, G. Mukherjee and S. S. Manna Satyendra Nath Bose National Centre for Basic Sciences manna@bose.res.in

  2. Random pair wise conservative money shuffling: A.A. Dragulescu and V. M. Yakovenko, Eur. Phys. J. B. 17 (2000) 723. ● N traders, each has money mi (i=1,N), ∑Ni=1mi=N, <m>=1 ●Time t = number of pair wise money exchanges ●A pair i and j are selected {1 ≤i,j ≤ N, i ≠ j} with uniform probability who reshuffle their total money: ●Result: Wealth Distribution in the stationary state

  3. ●Fixed Saving Propensity (λ) A. Chakraborti and B. K. Chakrabarti, Eur. Phys. J. B 17 (2000) 167. ●Result: Wealth Distribution in the stationary state Gamma distribution: P(m) ~ ma exp(-bm) Most probable value mp=a/b

  4. ●Quenched Saving Propensities (λi, i=1,N) A. Chatterjee, B. K. Chakrabarti, and S. S. Manna, Physica A, 335, 155 (2004) ●Result: Wealth Distribution in the stationary state Pareto distribution: P(m) ~ m-(1+ν)

  5. ●Dynamics with a tagged trader ● N-th trader is assigned λmax and others 0≤λ < λmax for 1 ≤ i ≤ N-1 ● λmax is tuned and <m(λmax)> are calculated for different λ ● <m(λmax)> diverges like:

  6. [<m(λmax)>/N]N-0.125 ~ G[(1-λmax)N1.5] where G[x]→x-δas x→0 with δ ≈ 0.725 <m(λmax)>N-9/8 ~ (1-λmax)-3/4N-9/8 assuming 0.725 ≈ ¾ <m(λmax)> ~ (1-λmax)-3/4 For a system of N traders (1-λmax) ~ 1/N. Therefore <m(λmax)> ~ N3/4

  7. ●Approaching the Stationary State ● As λmax→1, the time tx required for the N-th trader to reach the stationary state diverges. ● Scaling shows that: tx ~ (1-λmax)-1

  8. PRESENT WORK Weighted selection of traders: Rule 1: Probability of selecting the i-th trader is: πi~ miα where α is a continuously varying tuning parameter Rule 2: Trading is done by random pair wise conservative money exchange as before:

  9. Money Distribution in the Stationary State P(m,N) follows a scaling form: Where G(x)→x-(1+ν(α)) as x→0 G(x) →const. as x→1 Results for α=2 η(2)=1 and ζ(2)=2 giving ν(2)=1 Height of hor. part ~ 1/N2 Length of hor. part ~ N Area under hor. part ~ 1/N

  10. Results for α=3/2 η(3/2)=3/2 and ζ(3/2)=1 giving ν(3/2)=1/2

  11. Results for α=1 ν(1)=0

  12. Conclusion ● There are complex inherent structures in the model with quenched random saving propensities which are disturbing. More detailed and extensive study are required. ● Model with weighted selection of traders seems to be free from these problems. Thank you.

More Related