Introduction to Experimental Economics

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Introduction to Experimental Economics

• Lecture 5
• John Hey

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Game Theory

• Where do we begin?
• Equilibrium concepts.
• Nash Equilibrium.
• Backward Induction.
• Knowledge.
• Rationality.
• Assumptions about other players.

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Game Theory

• Prisoners Dilemma.
• Dictator Game.
• Ultimatum Game.
• Coordination Games.
• Trust Games.
• Guessing games Beauty Contests.
• Centipede Games.
• .......

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Game Theory site

• There is an excellent site at
• http//gametheory.tau.ac.il
• You need to register.
• You will need to enter the course number which is
  1611 and your E-mail address.
• The initial password is t235542Yu , but you will
  need to select a new personalised password.
• You will then play an introductory game.

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Basic concepts

• The starting point is that of a Nash
  Equilibrium...
• ... In which everyone is doing what is best for
  themselves given what everyone else is doing.
• There may be one or more equilibria in either
  pure or mixed strategies.
• Are they plausible?

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First simple game
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Second simple game
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Third simple game
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Fourth simple game
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Another game variant 1
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Another game variant 2
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Another game variant 3
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Another game variant 4
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Centipede Games

• As there have been literally thousands of
  experiments on games of various types, I have to
  be selective.
• I have therefore chosen centipede games.
• Here you will find a link to Mckelvey R D and
  Palfrey T R (1992), "An Experimental Study of the
  Centipede Game" Econometrica, 60, 803-836, of
  which you should read the non-technical part.

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Predictions of Game Theory

• The first subject should Take.
• This conclusion can be reached by Backward
  Induction
• Starting at the final decision node, Player 2
  will Take.
• Given that, Player 1 should Take at the
  penultimate node...
• ...and so on.

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Experimental Protocols

• Subjects played either the four or six move game.
• Groups of 20 (18) subjects who played 10 times
  each against a different other player.
• This guarantees that there should be no strategic
  effects from one repetition to another...
• ...while guaranteeing lots of observations.

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Note what the authors say

• Thus it was common knowledge that no subject was
  ever matched with another subject more than once.
  In fact we used a rotating matching scheme which
  insures that no player i ever plays against a
  player who has previously played someone who has
  played someone that i has already played.
  (Further, for any positive integer n, the
  sentence which replaces the phrase "who has
  previously played someone who has played someone"
  in the previous sentence with n copies of the
  same phrase is also true.) In principle, this
  matching scheme should eliminate potential
  super-game or cooperative behavior, yet at the
  same time allow us to obtain multiple
  observations on each individual's behavior.

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Notation fi is the proportion of games ending at
the ith terminal node.
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Observations

• Data clearly inconsistent with the notion of the
  game theoretic equilibrium Pr(T1) ? 1.
• We note that Pr(Tt) pt increases with t.
• People getting nervous?
• We also note that as experience accrues pt
  increases (for fixed t).
• Notice that there are no strategic reasons for
  this must be learning?

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What McKelvey and Palfrey do

• Too sophisticated for this module.
• Essentially tries to explain the data with a
  model in which
• There exist selfish and altruistic subjects
• Subjects have to learn how many of each
• Optimal behaviour is a mixed strategy
• Errors in beliefs and in actions.
• It is instructive to read what they write...

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Conclusions

• Raw game theoretic prediction based on selfish
  individuals does not do too well (though they
  might be approaching it).
• Including a small number of altruists (and belief
  of their existence) explains a lot of the
  results.
• Errors are important.