A General Framework for Endowment Effects in Combinatorial Markets

The endowment effect, coined by Nobel Laureate Richard Thaler, posits that people tend to inflate the value of items they own. Recently, Babaioff, Dobzinski and Oren [EC'18] introduced the notion of endowed valuations --- valuations that capture the endowment effect --- and studied the stability and efficiency of combinatorial markets with endowed valuations. They showed that under a specific formulation of the endowment effect, an endowed equilibrium --- market equilibrium with respect to endowed valuations --- is guaranteed to exist in markets with submodular valuations, but fails to exist under XOS valuations. We harness the endowment effect further by introducing a general framework that captures a wide range of different formulations of the endowment effect. The different formulations are (partially) ranked from weak to strong, based on a stability-preserving order. We then provide algorithms for computing endowment equilibria with high welfare for sufficiently strong endowment effects, and non-existence results for weaker ones. Among other results, we prove the existence of endowment equilibria under XOS valuations, and show that if one can pre-pack items into irrevocable bundles then an endowment equilibrium exists for arbitrary markets.