# The Edgeworth Conjecture with Small Coalitions and Approximate Equilibria in Large Economies

## TL;DR

This paper explores the relationship between bargaining outcomes and approximate Walrasian equilibria in large economies, showing that certain allocations are computationally tractable to verify even when finding exact equilibria is hard.

## Contribution

It establishes that allocations unblocked by small coalitions are approximate equilibria and can be efficiently identified, linking bargaining concepts with computational economics.

## Key findings

- Unblocked allocations are approximate Walrasian equilibria.
- Deciding approximate equilibrium status is polynomial-time solvable.
- Results connect bargaining stability with computational tractability.

## Abstract

We revisit the connection between bargaining and equilibrium in exchange economies, and study its algorithmic implications. We consider bargaining outcomes to be allocations that cannot be blocked (i.e., profitably re-traded) by coalitions of small size and show that these allocations must be approximate Walrasian equilibria. Our results imply that deciding whether an allocation is approximately Walrasian can be done in polynomial time, even in economies for which finding an equilibrium is known to be computationally hard.