Illusion of Control in Minority and Parrondo Games

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Illusion of ControlinMinority and Parrondo Games

• Jeffrey Satinover1, Didier Sornette2
• Condensed Matter Physics Laboratory, University
  of Nice, France, Dept.of Politics, Princeton
  University jsatinov_at_princeton.edu
• Chair of Entrepreneurial Risk, Swiss Federal
  Institute of Technology, Zurich, Switzerland,
  .
  dsornette_at_ethz.ch

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I. Message

• Optimization often yields perverse results
• (In economic policy-making
• Law of Unintended Consequences)
• but not always When and why?
• Attempt to formally characterize conditions that
  yield perverse outcomes under optimization

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II. Overview THMG

• 10 Time-Horizon MG (THMG) Pro/Con
• In general, agents underperform strategies for
  reasonable t (no impact)
• Agent performance declines with dH
• Agent evolution dH ? 0
• Counteradaptive agents perform best

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III. Parrondo Games Briefly

• 10 effect 2 losing games win if alternated
• History-dependent games
• Attempt to optimize this effect inverts it
• Shown in unusual multi-player setting
• Here in natural single-player setting

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IV. Other Briefly

• Cycle decomposition of THMG
• Cycle predictor for real-world 1D series
• Status Minority Game

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A. 10 Time-Horizon MG (THMG) Pro/Con

• Pro
• MG unreasonable teq
• Many real-world series not stationary
• Many real-world trading strategies use short or
  declining-valued t (expon. damping)
• Certain kinds of tractability due to reasonable
  t

• Con
• Far from equilibrium
• Arguendo many real-world series effectively at
  equilibrium (high-freq data?)
• Analytic solutions more difficult for finite t
• Very complex finite-size effects, e.g., s2
  periodic in t

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THMG Markov Chain
(EPJB, B07270)
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THMG Markovian
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THMG Markovian
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THMG Markovian

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THMG Markovian

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B. agents underperform strategies for
reasonable t (no impact)
.
All N, m, S and
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B. agents underperform strategies for
reasonable t (no impact)
m, S, N2,2,31
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B. agents underperform strategies for
reasonable t (no impact)
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B. agents underperform strategies for
reasonable t (no impact)
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B. agents underperform strategies for
reasonable t (no impact)
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B. agents underperform strategies for
reasonable t (no impact)
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B. agents underperform strategies for
reasonable t (no impact)
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B. agents underperform strategies for
reasonable t (no impact)
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B. agents underperform strategies for
reasonable t (no impact)
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B. agents underperform strategies for
reasonable t (no impact)
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B. agents underperform strategies for
reasonable t (no impact)
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B. agents underperform strategies for
reasonable t (no impact)
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B. agents underperform strategies for
reasonable t (no impact)

• Do we underestimate the extent to which
  real-world financial systems are so difficult
  simply because they are far-from equilibrium?

in a THMG composed entirely of impact-accounting
agents, with N31, S2, a near equilibrium state
is attained for 10gttgt100. For t1 or 10,
strategies outperform their agents as we have
described. For t100, the reverse is true.
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C. Agent performance declines with dH
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D. At all a, agent performance declines with dH
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D. Agent Evolution

• If agents are allowed to evolve strategies (e.g.,
  adaptive evolution, GA)
• dH ? 0

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Agent performance declines with dHbut,

• for MG proper (equilibrium), for agt ac,
• Agent performance increases with dH
• dH ? 1

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E. Counteradaptive agentsperform best
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E. Counteradaptive agentsperform best (they
choose worst strategy)

• Carefully designed privileges can yield superior
  results for a subset of agents
• An important question We pose it carefully so as
  to avoid introducing either privileged agents or
  learning Is the illusion-of-control so powerful
  that inverting the optimization rule could yield
  equally unanticipated and opposite results?
• The answer is yes If the fundamental
  optimization rule of the MG is symmetrically
  inverted for a limited subset of agents who
  choose their worst-performing strategy instead of
  their best, those agents systematically
  outperform both their strategies and other
  agents. They also can attain positive gain.

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E. Counteradaptive agentsperform best (they
choose their worst strategy)
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E. Counteradaptive agentsperform best (they
choose their worst strategy)
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E. Counteradaptive agentsperform best (they
choose their worst strategy)
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E. Counteradaptive agents
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Parrondo Games(Physica A, 386,1339-344)

• 10 effect 2 losing games win if alternated
• Capital-dependent ? History-dependent
• Attempt to optimize this effect inverts it
• Shown in unusual multi-player setting
• Here (ref.) in natural single-player setting
• Choose worst partially restores PE

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Parrondo Games(Physica A, 386,1339-344)
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Parrondo Games(Physica A, 386,1339-344)
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Parrondo Games(Physica A, 386,1339-344)
Under optimization (choose best) 8 X 8
transition matrix
Under choose worst
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IV. Other Briefly

• Cycle decomposition of THMG
• Cycle predictor for real-world 1D series
• Status Minority Game

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Status MG LMG? SMGmobile agents
competition for topsimple definition of
social

• Boundary conditions reflective, random, fixed
  But NOT circular
• Neighborhood size, heterogeneity
• Role for different neighborhood functions