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COMMENTS

on

Modeling Bounded Rationality in Economic Theory: Four Examples

by

Ariel Rubinstein

• Preliminary note
• Rubinstein writes that he is not a big fan of abstract methodological discussion
• Unfortunately, my comments will be largely methodological because of the interdisciplinary audience (and because I am not an expert in bounded rationality)
• I will try to refer to specific models any time I am able to do it

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• What are Models of Bounded Rationality in Economic Theory
• Economic Theory at most clarify concepts and provides non-exclusive explanations of economic phenomena
• In many respects a model in Economic Theory is no different than a story: both are linked to reality in an associative way
• Models of Bounded Rationality are models that includes explicit references to procedural aspects of decision making which are crucial for the derivation of the analytical results

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• My observations will focus on
1. The role of models in economic theory
2. The role of BR in economic models
3. Questions derived by comments 1 & 2

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1. Observations on models - 1
1. Economists organize their thoughts using models.
2. Rubinstein view on models is that models are a sort of “fable” or “fairy tale”, because
• Models as fables draw a parallel to a situation in real life
• Both have some moral to impart
• Fables as models can be dismissed as being unrealistic or simplistic, but being free of details is also their advantage to try to clearly discern what cannot always be seen in the real world.

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1. Observations on models - 2
1. Criteria for good models:
• As for fables, a good model in economic theory identifies a number of themes and elucidates them
• These thought exercises are only loosely connected to reality and that have been stripped of most of their real-life characteristics.
• However, in a good model, something significant remains
2. But then how to evaluate what is a good model?
3. This is a relevant question especially for BR models that in some sense should be “realistic”

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1. Observations on models - 3
1. To answer this question, consider models as “stories linked to reality in an associative way”
2. “associative” is necessarily vague, it doesn’t explain when association is good
3. Observations in the paper
1. Rejection of common criticism of models of BR as more specific and arbitrary since all models make very specific assumptions
2. a good model of BR should include a procedure of reasoning that
1. Makes sense
2. Somewhat related to what we observe in real life

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1. Observations on models - 4
1. On making sense: what does it mean?
2. On relationship with reality:
• The connection between the models in economic theory and reality is tricky.

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• Conclusion: when should we change a model?

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• Maybe the idea of non arbitrary assumptions should still have a role, e.g. many behavioral models assume “arbitrary” payoff functions

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1. Observations on models - 5
1. Examples of alternative models with FR or BR:
1. What is the right model to explain the experimental evidence on the dictator game?
• Rule rationality ?
• Specific payoff functions?
• Incomplete information?
2. Consumer allocating α and 1- α of income to two goods:
• Rule of thumb
• Maximization of Cobb-Douglas?

With Cobb-Douglas there are other interesting implications such as elasticity

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1. Observations on models - 6
1. Further example of alternative explanations:
3. Superstition as Self Confirming Equilibrium or as bounded rational beliefs?
• SCE as limit of rational learning provides interesting empirical predictions/explanations

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2. Observations on models of BR as characterized by explicit references to procedural aspects of decision making - 1
1. It is a very useful demarcation criterium that distinguish bounded rationality models from behavioral models
• It is important to distinguish between the two approaches
• However, BR models share a common characteristic with behavioral economic models, i.e., the fact that most of the time the modeler may manipulate the agents of the model
• EXAMPLES:
1. “Agents with different models in mind”, where a sophisticated manipulator can use agents’ limited ability to sort out them
2. “Multiple self and hyperbolic discount”

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Probably due to the influence of behavioral/cognitive psychology.

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2. Observations on models of BR as characterized by explicit references to procedural aspects of decision making - 2
1. In many standard fully rational models there is an explicit reference to procedural aspects of decision making
• Rationalizability is based on chain of justification, which can be interpreted as a procedure of thinking leading to strategic decisions
• Learning processes may be fully rational or include possibility of fully rational models

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• My view is that reduction of complexity should play a role in distinguishing BR from FR models

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1. Example of situation where reduction of complexity seems to me crucial:
• Chess
1. Chess is a finite perfect information game, thus it has a subgame perfect equilibrium that in principle can be fully calculated by backward induction

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• However, it is too “complex”
• just to sketch the “complexity”
• After both players make the first move, 400 possible board setups exist.
• After the second pair of turns, there are 197,742 possible games,
• after three moves, 121 million
• Shannon 1950 in the paper "Programming a Computer for Playing Chess“ estimated the number of possible positions of the general order of about 10⁴³ possible games
• Allis in 1994 PhD thesis estimated the game-tree complexity to be at least 10¹²³. As a comparison, the number of atoms in the observable universes roughly estimated to be 10⁸⁰

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• Chess complexity suggests three problems:
1. Is complexity in the sense of computer science the “right” concept of complexity?
2. How to model analogical reasoning?
3. More, generally how to model, modelling reasoning ?

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2. Observations on models of BR as characterized by explicit references to procedural aspects of decision making - 3
1. A traditional view of BR (e.g. Aumann 1997) is that a model with BR is a model where agents are not maximizers
• Simon 1952 idea of satisficing behavior
• Radner 1980 ε equilibria
2. What is the connection between this classic view of BR and the one proposed in this paper?

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