Behavioral Stable Marriage Problems.

The stable marriage problem (SMP) is a mathematical abstraction of two-sided matching markets with many practical applications including matching resident doctors to hospitals and students to schools. Several preference models have been considered in the context of SMPs including orders with ties, incomplete orders, and orders with uncertainty, but none have yet captured behavioral aspects of human decision making, e.g., contextual effects of choice. We introduce Behavioral Stable Marriage Problems (BSMPs) , bringing together the formalism of matching with cognitive models of decision making to account for multi-attribute, non-deterministic preferences and to study the impact of well known behavioral deviations from rationality on two core notions of SMPs: stability and fairness. We analyze the computational complexity of BSMPs and show that proposal-based approaches are affected by contextual effects. We then propose and evaluate novel ILP and local-search-based methods to efficiently find optimally stable and fair matchings for BSMPs.