Combinatorial Auctions with Endowment Effect

TL;DR

This paper demonstrates that in combinatorial auctions, the endowment effect among bidders can ensure the existence of Walrasian equilibria in settings where they typically do not exist, such as with submodular valuations.

Contribution

It shows that even a mild endowment effect guarantees Walrasian equilibria in submodular valuation settings, linking local optima to equilibrium allocations.

Findings

Endowment effect ensures Walrasian equilibria with submodular valuations.

Any local optimum can serve as an equilibrium allocation.

Lower bounds on the endowment effect needed for equilibrium existence.

Abstract

We study combinatorial auctions with bidders that exhibit endowment effect. In most of the previous work on cognitive biases in algorithmic game theory (e.g., [Kleinberg and Oren, EC'14] and its follow-ups) the focus was on analyzing the implications and mitigating their negative consequences. In contrast, in this paper we show how in some cases cognitive biases can be harnessed to obtain better outcomes. Specifically, we study Walrasian equilibria in combinatorial markets. It is well known that Walrasian equilibria exist only in limited settings, e.g., when all valuations are gross substitutes, but fails to exist in more general settings, e.g., when the valuations are submodular. We consider combinatorial settings in which bidders exhibit the endowment effect, that is, their value for items increases with ownership. Our main result shows that when the valuations are submodular, even a mild degree of endowment effect is sufficient to guarantee the existence of Walrasian equilibria. In fact, we show that in contrast to Walrasian equilibria with standard utility maximizing bidders -- in which the equilibrium allocation must be efficient -- when bidders exhibit endowment effect any local optimum can be an equilibrium allocation. Our techniques reveal interesting connections between the LP relaxation of combinatorial auctions and local maxima. We also provide lower bounds on the intensity of the endowment effect that the bidders must have in order to guarantee the existence of a Walrasian equilibrium in various settings.