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Emergence of two-phase behavior in markets through interaction and learning in agents with bounded rationality . Sitabhra Sinha The Institute of Mathematical Sciences, Chennai, India in collaboration with: S. Raghavendra Madras School of Economics, Chennai, India.

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slide1

Emergence of two-phase behavior in markets through interaction and learning in agents with bounded rationality

Sitabhra Sinha

The Institute of Mathematical Sciences, Chennai, India

in collaboration with:

S. Raghavendra

Madras School of Economics, Chennai, India

market behavior the problem of collective decision
Market Behavior : The Problem of Collective Decision
  • Process of emergence of collective decision
    • in a society of agents free to choose….
    • but constrained by limited information and having heterogeneous beliefs.
  • Example:

Movie popularity.

  • Movie rankings according to votes by IMDB users.
collective decision a naive approach
Collective Decision: A Naive Approach
  • Each agent chooses randomly - independent of all other agents.
  • Collective decision: sum of all individual choices.
  • Example: YES/NO voting on an issue
  • For binary choice

Individual agent: S = 0 or 1

Collective decision: M = Σ S

  • Result: Normal distribution.

NO

YES

0 % Collective Decision M 100%

slide4
But…
  • Prevalence of bimodal distributions across social domains:

Movies

Elections

Financial Markets

Plerou, Gopikrishna, Stanley (2003)

collective choice interaction among agents
Collective Choice: Interaction among Agents
  • Modeling social phenomena : Emergence of collective properties from agent-level interactions.
  • Approach : Agent Interaction Dynamics
  • Assumption: Bounded Rationality of Agents
    • Limited perception: information about choice behavior of the entire system is limited to agent’s immediate neighborhood.
    • Perfect rationality:

Neighborhood ≡ entire system → complete information.

The agents quickly synchronize their decisions.

background
Background

Physica A 323 (2003)

  • Weisbuch-Stauffer Binary Choice Model
  • Agents interact with their ‘social neighbors’ [e.g., in square lattice with 4 nearest neighbors] …
  • …and their own belief.
  • Belief changes over time as a function of previous decisions.
  • Result:
    • Very small connected groups of similar choice behavior.
    • On average, equal number of agents with opposite choice preferences.
slide7

100 x 100 lattice of agents in the Weisbuch-Stauffer model.

No long-range order : Unimodal distribution

so what s missing
So what’s missing ?
  • 2 factors affect the evolution of an agent’s belief
  • Adaptation (to previous choice):

Belief increases on making a positive choice and decreases on making a negative choice

  • Global Feedback (by learning):

The agent will also be affected by how her previous choice accorded with the collective choice (M).

  • Influence of mass media ?
the model adaptive field ising model
The Model:‘Adaptive Field’ Ising Model
  • Binary choice :2 possible choice states (S = ± 1).
  • Choice dynamics of the ith agent at time t:
  • Belief dynamics of the ith agent at time t:

is the collective decision

where

  • μ: Adaptation timescale
  • λ: Global feedback timescale
results
Results
  • Long-range order for λ > 0
slide12

μ =0.1

λ = 0: No long-range order

N = 1000, T = 10000 itrns

Square Lattice (4 neighbors)

slide13

μ =0.1

λ > 0: clustering

λ = 0.05

N = 1000, T = 200 itrns

Square Lattice (4 neighbors)

results1
Results
  • Long-range order for λ > 0
  • Self-organized pattern formation
slide15

μ =0.1

Ordered patterns emerge asymptotically

λ = 0.05

results2
Results
  • Long-range order for λ > 0
  • Self-organized pattern formation
    • Multiple ordered domains
    • Behavior of agents belonging to each such domain is highly correlated –
    • Distinct ‘cultural groups’ (Axelrod).
    • These domains eventually cover the entire system. [dislocation lines at the boundary of two domains]
slide17

μ =0.1

Pattern formation even for randomly distributed λ

λ = uniform distribution [0,0.1]

slide18

μ =0.1

Pattern formation in higher dimensions

λ = 0.05

3-D

100 × 100 ×100 : 50000 iterations

results3
Results
  • Long-range order for λ > 0
  • Self-organized pattern formation
    • Multiple ordered domains
    • Behavior of agents belonging to each such domain is highly correlated –
    • Distinct ‘cultural groups’ (Axelrod).
    • These domains eventually cover the entire system. [dislocation lines at the boundary of two domains]
  • Phase transition
    • Unimodal to bimodal distribution as λ increases.
slide20

Behavior of collective decision M with increasing λ

λ=0.0

λ=0.05

μ =0.1

λ=0.1

λ=0.2

  • As λ increases the system gets locked into either positive or negative M
  • Reminiscent of lock-in due to positive feedbacks in economies (Arthur 1989).
ok but does it explain reality
OK… but does it explain reality ?

Rank distribution:

Compare real data with model

US Movie Opening Gross

Model: randomly distributed λ

Model

outlook
Outlook
  • Two-phase behavior of financial markets
  • Efficiency of marketing strategies:

Mass media campaign blitz vs targeted distribution of free sample

  • The Mayhew Effect: Bimodality in electoral behavior
  • Evolution of co-operation and defection:

Each individual is rational and cooperates some of the time;

But society as a whole gets trapped into non-cooperative mode and vice versa

  • How does a paper become a "citation classic" ?

S. Redner, "How popular is your paper?", E P J B 4 (1998) 131. The role of citation indices in making a paper a citation classic.