Unit IV: Thinking about Thinking

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Unit IV Thinking about Thinking

• Choice and Consequence
• Fair Play
• Learning to Cooperate
• Summary and Conclusions

4/25
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Choice and Consequence

• The Limits of Homo Economicus
• Bounded Rationality
• We Play Some Games
• Tournament Update
•  

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The Limits of Homo Economicus

• Schellings Errant Economics
• The Intimate Contest for Self-Command (1984
  57-82)
• The Mind as a Consuming Organ (328-46)
• The standard model of rational economic man is

• Too simple
• Assumes time consistent preferences
• Susceptible to self deception and sour grapes
• Is overly consequentialist
• Ignores labelling and framing effects

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The Limits of Homo Economicus

• Schellings Errant Economics
• The Intimate Contest for Self-Command (1984
  57-82)
• The Mind as a Consuming Organ (328-46)
• Schellings views are not merely critical
  (negative) his concerns foreshadow much current
  research on improving the standard model

• Behavioral economics/cognitive psychology
• Artificial Intelligence
• Learning models Inductive reasoning

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The Limits of Homo Economicus

• Experiments in behavioral economics have shown
  people routinely do not behave the way the
  standard model predicts
• reject profitable bargains they think are
  unfair
• do not take full advantage of others when they
  can
• punish others even when costly to themselves
• contribute substantially to public goods
• behave irrationally when they expect others to
  behave even more irrationally
• (Camerer, 1997)

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Bounded Rationality

• Game theory usually assumes unbounded, perfect,
  or Olympian rationality (Simon, 1983).
  Players
• have unlimited memory and computational
  resources.
• solve complex, interdependent maximization
  problems instantaneously! subject only to
  the constraint that the other player is also
  trying to maximize.
• But observation and experimentation with human
  subjects tell us that people dont actually make
  decisions this way. A more realistic approach
  would make more modest assumptions bounded
  rationality.

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Bounded Rationality

•  

Game theory usually assumes players are
deductively rational. Starting from certain
givens (sets of actions, information, payoffs),
they arrive at a choice that maximizes expected
utility. Deductive rationality assumes a high
degree of constancy in the decision-makers
environment. They may have complete or
incomplete information, but they are able to form
probability distributions over all possible
states of the world, and these underlying
distributions are themselves stable. But in
more complex environments, the traditional
assumptions break down. Every time a decision is
made the environment changes, sometimes in
unpredictable ways, and every new decision is
made in a new environment (S. Smale).
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Bounded Rationality

•  

In more complicated environments, the
computational requirements to deduce a solution
quickly swamp the capacity of any human
reasoning. Chess appears to be well beyond the
ability of humans to fulfill the requirements of
traditional deductive reasoning. In todays
fast economy a more dynamic theory is needed.
The long-run position of the economy may be
affected by our predictions! On Learning and
Adaptation in the Economy, Arthur, 1992, p. 5
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Bounded Rationality

•  

The standard model of Homo Economics break down
for two reasons (i) human decision making is
limited by finite memory and computational
resources. (ii) thinking about others thinking
involves forming subjective beliefs and
subjective beliefs about subjective beliefs, and
so on.
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Bounded Rationality
There is a peculiar form of regress which
characterizes reasoning about someone elses
reasoning, which in turn, is based on assumptions
about one's own reasoning, a point repeatedly
stressed by Schelling (1960). In some types of
games this process comes to an end in a finite
number of steps . . . . Reflexive reasoning, . .
. folds in on itself, as it were, and so is not
a finite process. In particular when one makes
an assumption in the process of reasoning about
strategies, one plugs in this very assumption
into the data. In this way the possibilities
may never be exhausted in a sequential
examination. Under these circumstances it is not
surprising that the purely deductive mode of
reasoning becomes inadequate when the reasoners
themselves are the objects of reasoning. (Rapo
port, 1966, p. 143)

•  
•  

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Bounded Rationality

• In the Repeated Prisoners Dilemma, it has been
  suggested that uncooperative behavior is the
  result of unbounded rationality, i.e., the
  assumed availability of unlimited reasoning and
  computational resources to the players
  (Papadimitrou, 1992 122). If players are
  bounded rational, on the other hand, the
  cooperative outcome may emerge as the result of a
  muddling process. They reason inductively and
  adapt (imitate or learn) locally superior
  stategies.
• Thus, not only is bounded rationality a more
  realistic approach, it may also solve some deep
  analytical problems, e.g., resolution of finite
  horizon paradoxes.

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We Play Some Games

• An offer to give 2 and keep 8 is accepted

PROPOSER RESPONDER Player ____ Player
____ Offer 2 or 5 Accept
Reject (Keep 8 5)
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Fair Play
8 0 5 0 8 0 2 0 2 0 5 0 2 0 8 0
GAME A GAME B
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Fair Play
8 0 8 0 8 0 10 0 2 0 2 0 2 0 0 0
GAME C GAME D
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Fair Play
2/4
Rejection Rates, (8,2) Offer
50 40 30 20 10 0
3/7
4/18/01, in Class. 24 (8,2) Offers 2 (5,5)
Offers N 26
1/4
0/9
A B C D
(5,5) (2,8) (8,2) (10,0)
Alternative Offer
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Fair Play
5/7
2/3
1/2
Rejection Rates, (8,2) Offer
50 40 30 20 10 0
4/15/02, in Class. 24 (8,2) Offers 6 (5,5)
Offers N 30
2/12
A B C D
(5,5) (2,8) (8,2) (10,0)
Alternative Offer
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Fair Play
Rejection Rates, (8,2) Offer
50 40 30 20 10 0
Source Falk, Fehr Fischbacher, 1999
A B C D
(5,5) (2,8) (8,2) (10,0)
Alternative Offer
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Fair Play

• What determines a fair offer?
• Relative shares
• Intentions
• Endowments
• Reference groups
• Norms, manners, or history

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Fair Play

• These results show that identical offers in an
  ultimatum game generate systematically different
  rejection rates, depending on the other offer
  available to Proposer (but not made). This may
  reflect considerations of fairness
• i) not only own payoffs, but also relative
  payoffs matter
• ii) intentions matter.
• (FFF, 1999, p. 1)

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What Counts as Utility?

• Own payoffs Ui(Pi)
• Others payoffs Ui(Pi Pj) sympathy

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What Counts as Utility?

• Own payoffs Ui(Pi)
• Others payoffs Ui(Pi - Pj) envy

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What Counts as Utility?

• Own payoffs Ui(Pi)
• Others payoffs Ui(Pi , Pj)
• Equity Ui(Pi Pi/Pj)
• Intentions ?

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Tournament Assignment

• Design a strategy to play an
• Evolutionary Prisoners Dilemma Tournament.
• Entries will meet in a round robin tournament,
  with 1 noise (i.e., for each intended choice
  there is a 1 chance that the opposite choice
  will be implemented). Games will last at least
  1000 repetitions (each generation), and after
  each generation, population shares will be
  adjusted according to the replicator dynamic, so
  that strategies that do better than average will
  grow as a share of the population whereas others
  will be driven to extinction. The winner or
  winners will be those strategies that survive
  after at least 10,000 generations.
•  

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Tournament Assignment

• To design your strategy, access the programs
  through your fas Unix account. The Finite
  Automaton Creation Tool (fa) will prompt you to
  create a finite automata to implement your
  strategy. Select the number of internal states,
  designate the initial state, define output and
  transition functions, which together determine
  how an automaton behaves. The program also
  allows you to specify probabilistic output and
  transition functions. Simple probabilistic
  strategies such as GENEROUS TIT FOR TAT have been
  shown to perform particularly well in noisy
  environments, because they avoid costly sequences
  of alternating defections that undermine
  sustained cooperation.

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Preliminary Tournament Results
After 5000 generations (as of 4/25/02)
Avg. Score (x10)
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Preliminary Tournament Results
After 5000 generations (10pm 4/27/02)
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Preliminary Tournament Results
After 20000 generations (7am 4/28/02)