Learning in matching markets with incomplete information

In our experiment of matching markets with one-sided incomplete information, we employ 2x2 matching markets with 3 state profiles, which means there are two workers who know the state of the market, two firms who initially do not know the state of the market, and there are in total 3 possible states with equal probability. The primary intervention is the learning types/features of the matching market. In total we have five primary learning types: Plain, Conditional Evaluation (CE), Learning from Blocking (LB), Learning from No Blocking (LNB), and Compound (Conditional Evaluation plus LB/LNB). Plain is the benchmark treatment, in which people do not need to learn from outcomes in the matching market. Conditional Evaluation means that the players without complete information need to learn the state of the market from receiving a proposal by some player at the other side of the markets (who have complete information). Learning from Blocking means that players need to learn the state of the market by observing the match formed by others in the market. Learning from No Blocking means that players need to learn the state of the market by observing no match formed by others in the market. Finally, Compound means that both Conditional Evaluation and Learning from Blocking/Learning from No Blocking are required for players to learn the state of the market.

The secondary intervention is whether players can pin down the state of the matching markets from learning (the “sub-learning type”). Plain has no subtype. For CE, LB, and LNB, there are two subtypes: (i) players can be certain of the state of the matching markets after learning, in other words, they know exactly which state they are in after learning; and (ii) players can learn that the state of the matching markets has to be one of two possible states (instead of one of three possible states before learning), but they cannot know which one. For Compound, the two subtypes are CE+LB and CE+LNB.

2025-09-01

2026-08-31

There are three primary outcome variables: 1. At market level, whether the market reaches Bayesian stable matchings, 2. At market level, the rate of surplus achieved, compared to theory. 3. At individual level, whether the individual reaches the correct matching outcome. 4. At individual level, whether players of different learning difficulties reach the correct matching outcome.

1. Whether the market reaches Bayesian stable matchings: 1 if the market’s matching outcomes is identical to the theoretical predictions of Bayesian stable matchings, and 0 otherwise. 2. At market level, the rate of surplus achieved equal the actual achieved surplus divided by the total surplus in Bayesian stable matchings. 3. Whether an individual reaches the correct matching outcome: 1 if his or her matching outcome is the same as predicted by Bayesian stable matching, and 0 otherwise. 4.We classify players in each matching market based on whether they need to engage in active learning: 2 workers do not need to engage in learning at all, one firm engages in a very simple learning approach (easier firms), and the other firm undertakes a harder learning approach (harder firms), the type of which varies across treatments.

Detailed information of all the proposals at individual level and market level, including (1) the time a proposal is made/rejected/accepted, (2) the proposer and recipient of each proposal, (3) the outcome of each proposal (reject or accepted).

The detailed information of all the proposals enables us to construct different measures to understand the market behavior.

In our experimental design, we use five learning types of markets that vary in how people learn in the markets. The details of the five types are stated in the primary interventions.

We employ a within-subject treatment design. All the subjects play the five matching markets types, but they play them in different orders. In total, there are 20 rounds of markets, and they all have different payoff matrices. These 20 rounds consist of the 5 learning types, with each type having 4 different payoff matrices. The 20 rounds can be divided into 4 blocks, each consisting of 5 different types. According to the Latin square method, we have in total four different treatment orders, which differ in the order of markets played by the subjects. Note that we only consider the primary intervention variable in designing treatment orders, while the secondary intervention variable is determined randomly within each learning type. To control for potential order effect of the subtypes, our (pre-)randomization ensures a balanced distribution along two dimensions: first, an equal number of realizations of each subtype within each type; second, an equal number of realizations across the two halves of the experiment. The four treatments orders are described below.

Treatment order 1: Block A, B, C, D
Treatment order 2: Block B, C, D, A
Treatment order 3: Block C, D, A, B
Treatment order 4: Block D, A, B, C

And the detailed sequence of block A-D are described below. Note that, all the block starts with the Plain type, as the Plain is the benchmark with no learning required.

Block A: Plain-CE-LB-LNB-Compound
Block B: Plain-LB-LNB-Compound-CE
Block C: Plain-LNB-Compound-CE-LB
Block D: Plain-Compound-CE-LB-LNB

Workers and firms: At the beginning of the experiment, 12 subjects are randomly selected to form a random matching group, and it is fixed throughout the experiment. Subjects within a random matching group play the 20 rounds of the game in one of four treatment orders. Among the 12 subjects, 6 are randomly assigned the role of the worker, and the rest are assigned the role of the firm. These roles are kept throughout the experiment. At the beginning of each round, 12 subjects are randomly divided into 3 matching markets, each consisting of 2 workers and 2 firms. The workers are denoted by the names “Lemon” and “Mango”, and firms are denoted by the names “Yellow” and “Green”. In each round, the subject with the role of worker could be either Lemon or Mongo, with equal chance; while the subject with the role of firm could be either Yellow or Green, with equal chance (Our pre-randomization ensures that, across 20 rounds, each subject experiences a balanced mix of easier firm roles and harder firm roles (as described in primary outcome variable 4). A worker can only be matched with a firm, or one can choose not to be matched with anyone.

States of the matching markets: In each matching market, there are three possible states, denoted as “Sunny”, “Cloudy” or “Rainy”. The probability of each state is one third. The workers are always informed of the state, while firms are not. Across the 20 rounds, the states are randomly and independently determined (pre-randomization). All the players can view the payoff matrix of the matching market, which shows the payoffs of the worker and the firm, for each possible match under each possible state. The payoffs of not matching with anyone is 10; the matching payoffs can be greater or smaller than 10.

The matching protocol: In each matching market, both firms and workers can propose to each other, they can only propose to one opponent each time. When a proposal is sent out, the receiver has 15 seconds to reject/accept; if no response in 15 seconds, it will be automatically rejected. As long as the market does not end, the matching status is temporary, any person can still propose and/or accept proposals. When a new match is reached between agents A and B, their previous matches become invalid. The market runs for a minimum of 60 seconds. A counter and a matrix showing all possible matching payoffs are displayed in a public info area. When two agents form or dissolve a match, their joint payoff cell lights up or dims, respectively, and the counter restarts from 60 seconds. The market ends either when the counter runs out or when everyone in a group clicks the ‘End’ button, which becomes available after the initial 60s.

Earnings: At the end of the experiment, we randomly select 4 rounds for final payment. We choose the payoff number carefully such that the expected earnings (as predicted by theory) of workers and firms do not vary. Subjects also receive a show-up fee.

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 five market types subjects will experience.

Individual-level randomization

No

We are aiming to collect about 48 subjects in each of the 4 treatment orders.

About 200 individuals, recruited via the subject pool of the Economic Lab of the Shanghai University of Finance and Economics.

4-5 matching groups of 12 subjects (48-60 subjects) per treatment order.