  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.
