An%20Experimental%20Investigation%20of%20Aggregate%20Information%20Revelation%20in%20the%20Centipede%20Game.

1
An Experimental Investigation of Aggregate
Information Revelation in the Centipede Game.

• Zacharias Maniadis

2
The Basic Question

• Is aggregate information about how the public
  behaves always good for society? When does
  self-censoring make sense?

3
The Answer

• Our experiment suggests that revealing
  information about the aggregate data reduces
  social welfare in our model economy. This is
  contrary to theoretical expectations.

4
The Four-Move Centipede Game.

• P1 P2 P3
  P4

1
2
1
2
(9.6, 2,4)
T1
T2
T4
T3
(0.3, 1.2)
(0.6, 0.15)
(2.4, 0.6)
(1.2, 4.8)
Two-person trust game. Players take turns in
choosing whether to take or pass an escalating
pile of money.
5
The Equilibrium.

• The unique Nash equilibrium outcome in this game
  is for player 1 to Take at her first choice.
• This has been widely regarded a problematic
  solution, and many experiments have been
  conducted to test it.
• If it was known that more that 1/7th of player
  2s would pass in the last decision node, the
  result would be overturned.

6
Previous Results from Experiments of the
Centipede Game.

• McKelvey and Palfrey (1992) found Nash
  equilibrium play (fraction of matches where
  player 1 takes immediately) around 8, even in
  late rounds.
• Nagel and Tang (1998), using the equivalent
  normal form of the game, find relative
  frequencies of equilibrium play not exceeding 5.
  

7
Is it a Good Idea to Release Aggregate
Information About this Economy?

• In the data of MP(1992) many people pass in the
  last decision node (18).
• Fudenberg-Levine (1997) argue that many people
  fail to experiment enough to learn this, so
  they take in early rounds.
• It seems like a good idea to reveal this
  information these people will be induced to
  pass more.

8
The Experiment.

• Took place in CASSEL laboratory with UCLA
  students.
• Six sessions with different subjects were
  conducted.
• Common features for each session
• Subjects were split into 2 groups of player 1s
  and player 2s.
• Played 15 or 14 rounds of the four-move centipede
  game.
• A rotating matching scheme was used.
• 3 practice rounds.

9
The New Treatment Information Revelation.

• Subjects saw the Pass and Take fractions in
  each decision node in the previous round.
• Full Information Revelation (FIR) treatment
  subjects saw these fractions for all nodes.
• Partial Information Revelation (PIR) treatment
  subjects saw the fractions in the nodes of the
  other group only.

10
The Sessions.
Session Subjects Aggregate information Number of total matches
NIR1 30 NO 225
NIR2 28 NO 196
FIR1 30 FULL 225
FIR2 30 FULL 225
PIR1 30 OTHER GROUP ONLY 225
PIR2 28 OTHER GROUP ONLY 196
PIR3 30 OTHER GROUP ONLY 225
11
The Main Features of the Data.

1. In the sessions with information revelation,
   Nash equilibrium play was very frequently played
   in the late rounds, except in session PIR1.
2. When information was provided, subjects passed
   less in the last decision node.
3. The conditional take probabilities increase as
   we get closer to the last move.

12
Behavior in the Last Decision Node.

• In the four-move sessions of MP(1992) and in our
  No Information session, 3-9 of the total
  matches end in node P4. In almost all
  Information sessions, this fraction is less
  than 1.
• Furthermore, the Take probability, conditional
  on that the last decision node was reached, was
  lower in the information sessions.

13
For all Rounds , Pooling our Results with MPs
4-Move Sessions

• 31/802 matches ended in the last terminal node in
  experiments without information revelation and
  only 8/1096 matches with aggregate information.
• Given that the last decision node was reached,
  8/112 passed in the sessions with information,
  and 31/124 in the sessions without information.

14
Signaling was Not Important.

• Note that given the necessary restrictions in the
  number of subjects, signaling is possible. A
  subject may Pass to affect the behavior of the
  people in the other group in the future.
• In fact, signaling was used very little. Perhaps
  subjects did not realize that it was potentially
  profitable to signal.

15
Conclusions.

• Revealing true information about a society may
  not be a good Idea.
• Although there were reasons to believe that
  providing aggregate information would be
  beneficial, social surplus actually fell
  significantly.

16
Late-Round Play in the FIR Sessions.
17
Late-Pound Play in the PIR Sessions.
18
Late-Round Play in the NIR Sessions