Decentralized Matching Markets of Various Sizes: Similarly Stable Solutions with High Proportions of Equal Splits

In two-sided matching markets where direct negotiations take place over the division of profits between the partners, the appropriate solution concept is the core. Only a minority of the experimentally observed bargaining results are within the core, and the number of core solutions further decreases with an increase in market complexity. For differently-sized matching markets, two adjustments to the core requirements are introduced. Projected cores from smaller markets (partial condition core) are confirmed in larger markets. The possibility of Pareto improvements from the perspective of individual players (individual condition core) does not vanish but may even increase with market size. In all the investigated experimental markets, a high percentage of equal profit splits between matching partners in face-to-face bargaining was found, especially in larger, decentralized matching markets.