What price stability? Social welfare in matching markets

• We formalize the concept of social welfare functions for matching markets.
• Stability can involve a price in terms of other notions of social welfare.
• We show some price tags are very very likely.
• We also show that price tags can be substantial.

In two-sided matching markets, stability can be costly. We define social welfare functions for matching markets and use them to formulate a definition of the price of stability. We then show that it is common to find a price tag attached to stability, and that the price of stability can be substantial. Therefore, when choosing a matching mechanism, a social planner would be well advised to weigh the price of stability against the value of stability, which varies from market to market.