Combinatorial Auctions with Endowment Effect

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 cognitive biases can sometimes be harnessed to improve the outcome.

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 \emph{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 maximizers bidders — in which the equilibrium allocation must be efficient — when bidders exhibit endowment effect any \emph{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 the bidders must have in order to guarantee the existence of a Walrasian equilibrium in various settings.