1993 Reports

# Limited Arbitrage, Gains from Trade and Arrow's Theorem

"The expression 'limited arbitragers' used to describe economies where only bounded,

or limited, opportunities for gains are available to the traders from their initial endowments.

This concept was rigorously defined in [4], [5] and shown to be central

to the problem of resource allocation; it is also linked to the social diversity of the

economy [7]. It turns out that a simple geometric interpretation can be given to limited

arbitrage: here I show that it is equivalent to bounding the gains from trade,

namely the sum of utilities increases which the traders can achieve from their initial

endowments (Proposition 2, Section 1). From this geometry a somewhat unexpected

new link emerges: a close connection with Arrow's impossibility theorem [1]. I establish

that markets have limited arbitrage if and only in they have no Condorcet triples

beyond certain utility levels (Proposition 3, Section 3). This means that on choices of

great importance, irrational or intransitive behavior does not arise. Since Condorcet

triples are the building blocks of Arrow's theorem, limited arbitrage appears to be at

the core of social choice theory. The connection between limited arbitrage and the

concept of no-arbitrage used in financial markets is discussed in Section 2."

## Subjects

## Files

- econ_9394_685.pdf application/pdf 475 KB Download File

## More About This Work

- Academic Units
- Economics
- Publisher
- Department of Economics, Columbia University
- Series
- Department of Economics Discussion Papers, 685
- Published Here
- February 28, 2011

## Notes

December 1993.