Combinatorial auctions with endowment effect

We study combinatorial auctions with bidders that exhibit an endowment effect. In most of the previous work on cognitive biases in algorithmic game theory 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 fail to exist in more general settings, e.g., when the valuations are submodular. 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.