Unit IV: Thinking about Thinking

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

4/23

Choice and Consequence

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

 

Schelling’s “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:

The Limits of Homo Economicus

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

Schelling’s “Errant Economics”

“The Intimate Contest for Self-Command” (1984: 57-82) “The Mind as a Consuming Organ” (328-46)

Schelling’s views are not merely critical (negative); his concerns foreshadow much current research on improving the standard model:

The Limits of Homo Economicus

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

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)

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 don’t actually make decisions this way. A more realistic approach would make more modest assumptions: 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).

 

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 today’s “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

 

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.

 

Bounded Rationality

Bounded RationalityThere is a peculiar form of regress which characterizes reasoning about someone else’s 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.

(Rapoport, 1966, p. 143)

 

 

In the Repeated Prisoner’s 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.

Bounded Rationality

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)

Fair Play

8 0 5 0 8 0 2 02 0 5 0 2 0 8 0

GAME A GAME B

Fair Play

8 0 8 0 8 0 10 02 0 2 0 2 0 0 0

GAME C GAME D

Fair Play

A B C D

50%

40

30

20

10

0

3/7

1/4

2/4

0/9

Rejection

Rates,

(8,2) Offer

(5,5) (2,8) (8,2) (10,0) Alternative Offer

4/18/01, in Class.

24 (8,2) Offers 2 (5,5) Offers N = 26

Fair Play

A B C D

50%

40

30

20

10

0

5/72/3

1/2

2/12

Rejection

Rates,

(8,2) Offer

(5,5) (2,8) (8,2) (10,0) Alternative Offer

4/15/02, in Class.

24 (8,2) Offers 6 (5,5) Offers N = 30

Fair Play

A B C D

50%

40

30

20

10

0

Source: Falk, Fehr & Fischbacher, 1999

Rejection

Rates,

(8,2) Offer

(5,5) (2,8) (8,2) (10,0) Alternative Offer

Fair Play

What determines a fair offer?

• Relative shares• Intentions• Endowments• Reference groups• Norms, “manners,” or history

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)

What Counts as Utility?

• Own payoffs Ui(Pi)

• Other’s payoffs Ui(Pi+ Pj) sympathy

What Counts as Utility?

• Own payoffs Ui(Pi)

• Other’s payoffs Ui(Pi - Pj) envy

What Counts as Utility?

• Own payoffs Ui(Pi)

• Other’s payoffs Ui(Pi , Pj)

• Equity Ui(Pi + Pi/Pj)

• Intentions ?

Tournament Assignment

Design a strategy to play an Evolutionary Prisoner’s 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. 

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.

Preliminary Tournament Results

Test.009

0

0.2

0.4

0.6

0.8

1

1.2

Generations (x50)

Po

pu

lati

on

Sh

ares

defect

cooperate

grim

tit4tat

pavlov

random

ataub

bjweiss

bmartin

brill

cgerry

daniels

daniels1

daniels2

daranow

delahuer

demashk

ekent

ekent1

fahl

fahl2

nicer

After 5000 generations

(10pm 4/27/02)