Linking multi-agent simulation to experiments in economy

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Linking multi-agent simulation to experiments in
economy

• Re-implementing John Duffys model of speculative
  learning agents

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Experimental economics
Hayek, "The use of knowledge in Society", 1945
Production of a setting where individuals face
an economic situation that is similar to real
ones controlled and easy to reproduce. Limited
possibilities of action Control of motivation of
agents / interaction mode / initial
information Observation of behaviours of real
humans Interpretation of results Comparison of
behaviours with the theoretical setting Drawing
hypothesis explaining the differences
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Simulations to design experiments

• Usual protocol humans interact only through
  computers to get an absolute control of
  communication.
• Choice of parameters to design experiments by
  running tests with only computers
• Test of behavioural hypothesis with learning IA
  in place of humans following the experiments to
  reproduce the results
• Mixing humans and AI in the same environment

• Duffy , J, 2001, Learning to Speculate
  Experiments with Articial and Real Agents, JEDC,
  25, pp 295-319.

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The Kiyotaki and Wright model how to induce
speculative behaviours?
The aim of KW is to find an economy in which the
production and consumption rules would Force
the agents to exchange Have them use a good as
an exchange value (enable them to store a good
that has no direct value to them)
Discretisation of action best response Knowing
possession of the whole population
Kiyotaki N., Wright R., 1989, On money as a
medium of exchange, Journal of Political Economy
97, 924-954.
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Situation of the agents
3 types of agents 1, 2, 3 3 goods 1, 2, 3
Agent i consumes good i Agent i produces good i
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Consumption gt gain in utility u. Agent
produces iff it has just consumed
Production gt exchange gt consumption
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A time-step
storage
At the end of a time-step an agent 1 possesses
only good 2 or 3 Only stores ONE unit of
non-divisible good Storage costs 0lt c1 ltc2 lt
c3 lt u discount factor ? 0lt ?lt 1 end of the
exchange rounds
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A time-step
exchange
Bilateral decentralised negotiation - choose to
exchange or not. No  simple exchange  (A is
forbidden) gt at least three agents have been
involved when everyone is satisfied
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Fundamental and speculative behaviours
Expected gain for agent i (imagine that it will
get good i at time t 1 by exchanging against
the good it possesses now) Possesses good
(i1) ?i 1 - c i 1 ?u. Possesses good
(i2) ?i 2 - c i 2 ?u. Fundamental when
facing an exchange accepts to store the good that
gives the best expected gain. Speculative when
facing an exchange accepts to store the good that
gives the worst expected gain if there is a
higher chance to perform the exchange to get i at
the next time-step. Fundamental for agents 1 and
3 is to refuse to exchange i1 for
i2 Fundamental for agents 2 is to accept to
exchange i1 for i2 Speculative depends on
actual probabilities of exchange
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Fundamental and speculative behaviours
Notation Proportion of agents i possessing the
good they produce pi, and possessing the other
good (1-pi) (s1,s2,s3) the set of strategies
by agents 1, 2 and 3, Si 0 if agents refuses
to get i2 when facing the opportunity Si 1 if
agents accepts to get i2 when facing the
opportunity Solution by KW the agent decides if
it will speculate or not by anticipating its
ability to exchange at the next time-step. gtgt
Strategic equilibrium depending on u, c1, c2, c3,
? and (p1,p2,p3) - either (0,1,0) ou
(1,1,0) Issue for Duffy agents have no
complete knowledge and learn anticipated gain
through experience experience is individual
not all agents of the same type choose the same
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Reproduction of the speculative setting

• Several production of this model put in a
  distributed setting (multi-agent type models)
• Marimon, R., E.R. McGrattan and T.J. Sargent,
  1990, Money as a medium of exchange in an economy
  with artificially intelligent agents, Journal of
  Economic Dynamics and Control 14, 329-373.
• Basci, E., 1999, Learning by imitation, Journal
  of Economic Dynamics and Control 23, 1569-1585.
• Several production of this model put in an
  experimental setting
• Duffy, and J. Ochs, 1999a, Emergence of money as
  a medium of exchange An experimental study,
  American Economic Review 89, 847-877.
• Duffy, J. and J. Ochs, 1999b, Fiat money as a
  medium of exchange Experimental evidence,
  working paper, University of Pittsburgh.

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Duffy getting close to experimental setting for
comparison and extension
Limited number of agents 16 or 24 Short
simulation only repetition of 10 games in a
row Chooses setting where (1,1,0) is the
solution profile agents of type 1 should
play speculative agents of type 2 and 3 should
play fundamental Same setting is used for
artificial agents and humans, Manipulation of the
setting to influence learning change proportion
for different probabilities of meeting automate
some of the behaviours gtgt once the simulation
shows how interesting the setting is, reproduce
it with real humans / mix artificial and real
agents
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Learning algorithm for the agents

• A simulation is a set of 10 games with
  probability ß to stop at each time-step, agents
  cannot exchange when it stops and they start with
  their production good again
• when an agent A meets another agent (B)
• if B proposes the good A owns no exchange
• B has good i A proposes the exchange
• otherwise depends on memory
• ? i1 S (I i1) ?i 1 - S (I i2) ?i 2
• ? i2 S (I i2) ?i 2 - S (I i1) ?i 1
• Where I i1 1 for a time-step where i
  succeeded in getting i 1 with i at start and I
  i1 1 in the opposite case
• x ? i1 - ? i2
• And probability to refuse exp x / (1 exp x)

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Reproducing the learning algorithm in simulations
Homogeneous Simulations Ambiguity to interpret
the algorithm I i1 1 for a time-step where
i succeeded in getting i with i1 at start and I
i1 0 in the opposite case Algo1 any time
the agents has possessed the good Algo2 any
time he could have exchanged and it was refused
(if it had had the other good, the exchange
would have been accepted) Algo3 Algo1 but
doesnt exchange back to get its production
good Constrained simulations Only agents of type
1 have to learn and the others are automated
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Experimental data (8-8-8)
 
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Agents of type 1 algo1
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Agents of type 1 algo2
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Agents of type 1 algo3
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Reasons why comparison hasnt work (but will)

• My mistake in reproducing the setting
• Dependence to random generator
• Not enough meetings or agents to establish
  comparison with experiments
• My simulations same results
• Not enough meetings, possibility to exchange with
  such a simple algorithm
• Comparison at the macro level is not enough gt use
  the actions one-by-one (need of the whole set of
  experimental data).