Decentralized Matching with Transfers: Experimental and Noncooperative Analyses

In our matching experiment, the main intervention is the features of the surplus configurations. In total we have four different configurations. The configurations differ in two ways: the “assortativity level” and “whether equal split is in the core”. Surplus configuration is either assortative or non-assortative, and equal split is either in the core or not. This gives in total four (two by two) different types of configurations. We call them positive assortative (assortative, equal split in the core), negative assortative (assortative, equal split not in the core), mixed equal (non-assortative, equal split in the core) and mixed nonequal (non-assortative, equal split not in the core), respectively.

The secondary intervention is the balance of the matching market. We have in total two balance conditions: The balanced one has 3 subjects on each side of the market; the non-balanced one has 3 versus 4 subjects on each side of the market. For both the balanced and non-balanced markets, we perform the main intervention within the balance type.

2019-05-14

2021-06-30

There are three main outcomes variables: 1. At market level, the rate of matching; 2. At market level, the rate of stable matching; 3. At market level, the rate of surplus achieved. 4. At individual level, the payoff gained if matched.

1. The rate of matching equals to the number of matched pairs divided by the number of maximal matched pairs (3 pairs in all cases); 2. The rate of stable matching equals to the number of stable matched pairs divided by the number of maximal matched pairs (3 pairs in all cases); 3. The rate of surplus achieved equals to the surplus achieved from the matched pairs divided by the total maximal surplus. 4. The payoffs of two individuals in a matched pair are determined by the division of surplus proposed and accepted.

1. Number of proposals 2. Detailed information of all the proposals by individual and matching group level, including the time a proposal is made/rejected/accepted; the proposed division of surplus of each proposal; and whether it is rejected/accepted by which player.

1. At each market, the number of proposals indicates how active the markets are. 2. The detailed information of all the proposals enables us to construct different measures to understand the market behavior.

In our experimental design, we use four different surplus configurations. Each surplus configuration represents a different matching market. We vary the configurations in two dimensions: (1) whether the stable matching pattern is assortative, and (2) whether equal split is in the core. We also design the surpluses in a way that the maximum total surplus that all agents can obtain is 200, the average total surplus that all agents can obtain is 180 if they are all matched randomly, and the minimum total surplus they can obtain is 160, which is constant across all four markets. Maximum total surplus is obtained only under stable matching. Hence, the rate of stable matching serves as a measure of efficiency.

We employ a within-subject treatment design. All the subjects play the four different matching markets (surplus configurations), but they play them in different orders. According to the Latin square method, we have in total four different treatment, which differ in the order of markets played by the subjects. The four treatments orders are described below.

1. Positive assortative, negative assortative, mixed equal, mixed nonequal.
2. mixed nonequal, positive assortative, negative assortative, mixed equal.
3. Mixed equal, mixed nonequal, positive assortative, negative assortative.
4. Negative assortative, mixed equal, mixed nonequal, positive assortative.

At the beginning of the experiment, six subjects are randomly selected to form a group, and it is fixed throughout the experiment. Subjects within a group play the four markets in the order corresponding to their assigned treatment. Each market is played for 7 rounds, so they play a total of 28 periods. In the beginning of each round, each subject is randomly assigned a color that represents their role. A cold color can only be matched with a warm color.

Each market lasts 3 minutes. Within the 3-minute market, anyone can propose to anyone on the opposite side. To propose, a subject clicks the color they wish to propose to, and decides the division of surplus. The receiver of a proposal has 30 seconds to accept or to reject. When the proposer is waiting for the response from the receiver, the proposer cannot make a new proposal to anyone. If a proposal is rejected, both sides are free to make new offers.
If a proposal is accepted, a temporary match is reached; the information of the temporary match and division of the surplus is shown to everyone in the market.

When a temporary match is reached, both subjects can still make and receive proposals. One can always break their current temporary match by reaching a new temporary match (either by proposing to a new person and being accepted, or by accepting another proposal).

A market ends at 3-minutes mark, all temporary match become permanent, unless someone gets released from a temporary match in the last 15 seconds, they have 15 seconds to make a new proposal. Subjects can also see the history of final matches in the previous rounds.

Within each experiment session, multiple treatment orders are implemented by randomization; the randomization is pre-determined.

Subjects who sign up for the experiment receive a seat number randomly before entering the laboratory; the seat number determines the order of the four payoff configurations subjects will experience.

Individual-level randomization

No

We are aiming to collect about 36 subjects in each of the 4 treatment orders for the balanced markets, and 42 subjects for each of the 4 treatment orders for the non-balanced markets.

About 300 individuals, recruited via the subject pool of the Economic Lab of the Shanghai University of Finance and Economics.

6-7 matching markets (36-42 subjects) per treatment arm.