Upper bound on the number of steady states

Determine whether the canonical Aiyagari model can possess more than three steady states, beyond the three-state multiplicity established by the explicit parameter example.

Background

The paper proves that a two-income-state canonical Aiyagari economy can have at least three steady states and reports a numerical example with three computed equilibria. This establishes multiplicity but does not characterize the total number of possible steady states.

The authors note that their analysis does not exclude additional steady states, and they report that an extensive computational search in related work did not find examples with more than three. Whether three is a universal upper bound therefore remains unresolved.

References

I have not ruled out that there could be more steady states, but \citet{WalshYoung2026} never found an example with more than three in their extensive search.

— Proof of Steady-State Multiplicity in Aiyagari  (2609.03730 - Walsh, 3 Sep 2026) in Section 3, Multiplicity, footnote to the concluding paragraph