Welcome file

osborne_rubenstein_discussion.md

Discussion and annotation of Osborne and Rubinstein "Models in Microeconomic Theory"

(Discussion between David Reinstein and Britt Li, possibly others)

Chapter 1

1.1 Preferences

A binary relation on a set $X$ specifies, for each ordered pair $(x , y )$ of members of X , whether or not x relates to y in a certain way. For example, “acquaintance” is a binary relation on a set of people. For some pairs (x , y ) of people, the state- ment “x is acquainted with y ” is true, and for some pairs it is false. Another example of a binary relation is “smaller than” on the set of numbers. For some pairs (x,y ) of numbers, x is smaller than y , and for some it is not. For a binary relation R, the expression x R y means that x is related to y according to R. For any pair (x , y ) of members of X , the statement x R y either holds or does not hold. For example, for the binary relation < on the set of numbers, we have 3 < 5, but not7<1.

Britt questions:

• Not sure the meaning of ‘binary relation’. Does it refer to relationships between two objects?

• What does ‘acquaintance’ example mean?

• Given that R stands for relation, what does xRy means? Does it mean the relationship between x and y? If so, what does yRx mean?

• I am still confused with the concept of ‘reflexivity’ after reading these paragraphs. Does it mean all ‘x’ are the same?

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1.2 Preference formation

Britt questions:

• Not sure what this unanimity rule means

1.3 An experiment

Britt questions:

• Everything makes sense to me

1.4 Utility functions

Britt questions:

• I don’t understand the entire sections, since I can’t understand the minimal and maximal alternatives and since the following parts do not make sense to me.