A general framework for endowment effects in combinatorial markets

Abstract

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.