Modeling

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Modeling
Playing Dynamic Games in MATLAB
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We start young
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And keep clapping
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Outline

• Motivations
• Observed Dynamics
• Model design
• Results
• Makin it real (complicating the model)
• Dynamic games
• La Ola

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Why do We Clap, and When?

• We clap to express our approval or praise.
• Clapping provides an emotional payoff
• Caveat Clapping at the right time provides an
  emotional payoff
• Clapping at the wrong time can lead to
  embarrassment.
• We clap when the payoff outweighs the cost

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Observed Dynamics

• Casual observations of audiences reveal
• Onset time is shorter than offset

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Observed Dynamics
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Observed Dynamics

• Onset time is shorter than offset
• Onset has a marked beginning. Offset requires
  monitoring of people.
• If an applauder isnt joined by others, they stop
  applauding.
• Embarrassment of being the odd one out generally
  keeps people clapping in line with others.

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Benefits

• Events offer varying benefits to applauders
• Applause level of the event where A ? 0, 1.
  Funnier or more impressive events produce higher
  As
• Individuals have applause thresholds
• Higher thresholds (pi ? 0, 1) offer greater
  benefits for the same event. Thresholds are
  normally distributed
• benefit A pi

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Costs

• Physical Cost
• People pay a constant energy cost c for clapping,
  proportional to the amount of time theyve been
  clapping
• Physical cost c ti2
• Embarrassment Cost
• Cost decreases as proportion of people clapping
  (n/N) increases
• People with higher pi are less easily embarrassed
• Embarrassment cost (1 - n/N)(1-pi)
• total costs c ti2 (1 - n/N)(1-pi)

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Decision

• Clap when Benefit ? Costs
• If A pi ? c ti2 (1 - n/N)(1-pi)
• Mi,t1
• else
• Mi,t0
• n (number of people clapping) sum(M,t)

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Modeled Sequence

• An event occurs with an applause level A
• People with high thresholds, pi, begin to
  applaud.
• If the decrease in the embarrassment cost is not
  enough to cause other people to clap, the
  clapping quickly dies down due to an increase in
  physical costs.
• Otherwise, the decrease in embarrassment causes
  other people begin clapping, which in turn causes
  a cascade of applause.
• People get tired of clapping and stop (physical
  cost begins to outweigh the benefits). This
  increases the cost of embarrassment for others,
  eventually causing everyone to stop clapping.

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Main Predictions

• More impressive events cause more people to
  clap longer
• Onset faster than offset
• Time it takes for people to start clapping is
  shorter than the time it takes to stop clapping

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Effect of Applause Level
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Effect of Group Size
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Effect of Group Size
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Effect of Group Size
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Effect of Group Size
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Proportion clapping vs. A
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Applause Level vs. A
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When time is not enough

• What if clapping with everyone for a long time is
  not satisfying enough?
• Whistling
• Standing ovation
• Slower, so dynamics more obvious.
• Higher embarassment cost
• Slower updates (have to visually scan the
  audience)
• Distance is more important.
• Making those changes

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Standing Ovation
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Adding Distance

• People are clapping in real space
• Clappers are closer to some than others
• Assumption clappers are more affected by their
  neighbors than by distant individuals
• If 5 people are clapping on the other side of the
  room, but no one around me is clapping, Ill
  still be embarrassed

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Effect of Distance
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169 People clapping
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Makin it real

• Allow breaks
• A way to cheat the physical cost?
• Add graded intensity
• Can one tell the difference between forced and
  enthusiastic applause?
• Apparently, yes

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Synchrony of Applause Z. Néda, E. Ravasz, Y.
Brechet, T.Vicsek and A.L. Barabasi (2000) "The
sound of many hands clapping", NATURE, vol. 403,
849

• Globally coupled oscillators to model synchrony
  of clappers
• Mode I vs. Mode II clapping
• Intensity through change in frequency.
• Rhythmic applause ? doubling of the period,
  halfing of the variance
• Both are Gaussian distributions

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Synchrony of Applause

• In communist times it was a common habit to
  applaud by rhythmic applause the "great" leader
  speech. During this rhythmic applause these
  synchronization was almost never lost. This is a
  very nice evidence of the face that spectators
  were not enthusiastic enough and were satisfied
  with the obtained global noise intensity level,
  having no desire to increase it. Frustration was
  not present in this system.

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Dynamic Games

• Queuing behavior of Caribbean spiny lobsters.
  Herrnkind, W. (1969) Queuing behavior of spiny
  lobsters. Science 163 1425-1427.
• The Brave Leader Game and Cooperative Queuing in
  Spiny Lobsters (Reeve Herrnkind. unpublished
  manuscript)
• It pays to wait longer in larger groups because
  of the increased chance that someone else will
  become the leader
• Variance also increases with group size.
• Harder to establish fairness in larger groups ?
  have to continuously monitor others.

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Mexican WavesI. Farkas, D. Helbing, T.
Vicsek,Mexican waves in an excitable
medium.Nature 419, 131 (2002).
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Summary of Findings

• Onset faster than offset
• Everyone applauds past a certain threshold.
• Dependent on distribution of thresholds
• Larger groups are less variable--have more
  momentum.
• If youre on the sidelines, youll be less
  embarassed