Effects of Interagent Communications on the Collective

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Effects of Inter-agent Communications on the
Collective
Emergence of robust leadership structure and
market efficiency
Zoltán Toroczkai
(Complex Systems Group, LANL)
Marian Anghel (CNLS-LANL)
György Korniss (Rensellaer Pol. Inst.)
Kevin Bassler (U. Houston)
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Resource limitations lead in human, and most
biological populations to competitive dynamics.
The more severe the limitations, the more fierce
the competition.
Amid competitive conditions certain agents may
have better venues or strategies to reach the
resources, which puts them into a distinguished
class of the few, or elites. Elites form a
minority group.
In spite of the minority character, the elites
can considerably shape the structure of the whole
society
since they are the most successful (in the given
situation), the rest of the agents will tend to
follow (imitate, interact with) the elites
creating a social structure of leadership in the
agent society.
Definition a leader is an agent that has at
least one follower at that moment. The influence
of a leader is measured by the number of
followers it has. Leaders can be following other
leaders or themselves.
The non-leaders are coined followers.
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Agent-system (society)
-- a set of discrete, autonomous entities
(individuals, agents, players) with a certain
degree of intelligence, adaptability, and
flexibility in the choice of their actions in
response to external stimulus, or to follow
personal goals (maximize or minimize a set of
utility functions). -- there is no (or very
little) centralized control -- there is a
globally available world utility function which
rates the past performance of the collective
(world history function). -- the choice of
response function of an agent couples to ?
the world utility function ? information
gathered from neighboring agents on the social
network, via Reinforcement Learning.
D.H. Wolpert, K. Tumer (2000) COIN
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The El Farol bar problem
W. B Arthur(1994)
A
B

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A binary (computer friendly) version of the El
Farol bar problem
The Minority Game (MG)
Challet and Zhang (1997)
A 0 (bar ok, go to the bar) B 1 (bar
crowded, stay home)
latest bit
? l ? 0,1,..,2m-1
World utility(history)
(011..101)
m bits
S(i)1(l)
S(i)2(l)
(Strategies)(i)
(Scores)(i) C (i)(k), k 1,2,..,S.
?
S(i)S(l)
(Prediction) (i)
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A(t)
t
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Attendance time-series for the MG
World Utility Function
Agents cooperate if they manage to produce
fluctuations below (N1/2)/2 (RCG).
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Some macroscopic properties

• Predictability (Phase transition)

• Unused strategies - freezing

• Persistence Anti-persistence

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The El Farol bar game on a social network
A
B

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The Minority Game on Networks (MGoN)
Agents communicate among themselves.
Social network
2 components
1) Aquintance (substrate) network G
(non-directed, less dynamic)
2) Action network A (directed and dynamic)
G
A ? G
A
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Communication types (more bounded rationality)
Minority rule
Majority rule
(not rational)
(not rational)
Critics rule an agent listens to the
OPINION/PREDICTION of all neighboring agents on
G, scores them (self included) based on their
past predictions, and ACTS on the best score.
(more rational, uses reinforcement learning)
(Links)(i)
(Scores)(i) F (i)(j), j 1,2,..,K.
?
i
(Prediction) (i)
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Social Networks
How do they look like?
1. Degree distribution (number of acquitances a
person has)
- it is strongly peaked around a mean degree
there is a recurring cost in terms of time and
effort for maintaining a connection. This is a
resource as well a cognitive limitation. MEJ
Newman, D. Watts, S. Strogatz, PNAS, 99, 2566,
(2002) .
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Data EpiSims Census data, from Portland Oregon,
1.6 mill. people
H. Guclu, Z. Toroczkai, (2002)
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MEJ Newman, D. Watts, S. Strogatz, PNAS, 99,
2566, (2002) .
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2. Small world-ness it takes only a small
number of acquaintances to reach almost anyone in
the world D ? log (N), where D is the number of
steps, N is the number of vertices (people) in
the graf.
Milgrams experiment J. Travers, S. Milgram,
Sociometry 32, 425 (1969).
D ? 6-7.
D.J. Watts et. al. , Science, 296, 1302 (2002)
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- search in social networks is effective because
of the high dimensionality of the social space
(provides shortcuts).
3. Clustering or transitivity
A
Very likely!
B
C
ki5
Clustering distribution
ni3
Ci0.3
i
Average clustering coefficient
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People-people network is very strongly clustered
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Location networks
People move around. Two locations are connected
by an edge if a person went from A to B.
A
B
Not very likely
C
- expect much less clustering
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H. Guclu, Z. T., (2002)
Power law tail, exponent 2.4
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H. Guclu, Z. T., (2002)
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Network types
1) Regular network with node degree k
2) Erdös-Rényi Random networks with link
probability p.

• shows the small-world effect

3) Small-world networks generated from regular
networks (Watts, Strogatz,
Newman) .
4) Scale-free networks (Albert-Barabási).
(irrelevant here)
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Minority Rule on a ring (k2)
Majority Rule on a ring (k2)
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Critics Rule on a regular network
Uniform aggregation does not pay off!
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Critics Rule on Erdos-Renyi network.
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Network Effects Possibility for Improved Market
Efficiency

• A networked, low trait diversity system
• is more effective as a collective
• than a sophisticated group!

• Can we find/evolve networks/strategies
• that achieve almost perfect volatility
• given a group and their strategies
• (or the social network on the group)?

Improved market efficiency
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Macroscopic Properties Network Effects

• Reduced persistence

• The network is very efficient at
• removing any arbitrage opportunities!

• Reduced predictability and phase
• separation followers and leaders

• Unused links freezing on action network and
  persistence

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Emergence of scale-free leadership structure
m6

• Robust leadership hierarchy

• RCG on the ER network produces the scale-free
• backbone of the leadership structure

• The influence is evenly distributed
• among all levels of the leadership
• hierarchy.

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• The followers (sheep) make up most of the
  population (over 90) and their number scales
  linearly with the total number of agents.

• Structural un-evenness appears in the leadership
  structure for low trait diversity.

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N101, S2

• Leadership position Symmetric-Asymmetric phase
  transition

M3
M2

• In low m regime, where trait diversity is low
  (as in a dictatorship) leaders leave longer!

M6
M8
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SOME CONCLUSIONS

• We modeled the inter-agent communications across
  a social network which forms the skeleton for
  information passing in a competitive game with
  bounded rationality.

• The game evolves the active network by coupling
  via reinforcement learning
• on the agent-level. The game is influenced by
  the inter-agent communications.

• A robust leadership structure emerges naturally.
  The structure is scale-free
• and evenly distributed for large trait
  diversities. The more even is the distri-
• bution the more de-correlated are the agents
  choices in the strategy space.

• The leaders position is more persistent/stable
  the lower the trait diversity.

• Networking can lead to a more efficient
  collective for low-trait diversity
• agents. It is detrimental for large trait
  diversities.