We implement the matching market studied by Kagel and Roth (2000).1 Groups are split evenly between medical residents and hospitals who interact in a number of matching rounds, in of a number of independent markets (Periods). Without intervention, matches occur inefficiently early (and those that match early receive a penalty). Instructors can then introduce one of two clearinghouse mechanisms: a stable matching algorithm (based on Gale and Shapley’s2 deferred-acceptance algorithm) that has successfully reduced market unraveling, and the priority matching algorithm which is not stable, and has often failed to deter early matching.
Note: Matching is stable if there is no hospital-resident pair who would both prefer to be matched together rather than accept the proposed matching.
In a matching market, the risk of being unmatched (e.g. due to congestion and coordination failures) induces participants to match early. This will be inefficient when there are costs to early matching (e.g. match quality uncertainty or loss of flexibility).
Good experiences with a clearinghouse employing a stable matching algorithm reduces the incentive to match early, leading to a decrease in early matching.
Less than desirable results from a clearinghouse using an unstable matching algorithm maintains incentives to match early, and thus, does not seem reduce early matching.
Half of each group are hospitals, half are residents. Half of each role are high quality, half are low quality. A player matching with a high quality parter earns High Payoff=150 plus a partner-specific payment drawn uniformly from 1 to 10, and earns Low Payoff=50 plus a partner-specific payment for matching with a low quality partner.3 By default, there are three Rounds of Matching. Each round, each unmatched hospital can make, at most, one offer, without knowing which residents have previously matched. A resident then receives all offers, if any, for the round. An unmatched resident can accept at most one offer in each round (or pass on all), while an already matched resident rejects all new offers. A player unmatched after the final round (i.e., graduation year) receives a payoff of zero, while a player matching before the final round pays Early Match Cost=10 for each round they match early.
We recommend a Group Size of either 8 or 12 in order to have an equal number of highs and lows for each role and to have match-specific payoffs fit comfortably on student screen. By setting Periods=10, you should see significant unraveling (i.e., early matches).
Note: A player maintains the same role and quality across all periods, but partner-specific payoffs vary across periods.
Specifying a Clearinghouse changes the final round of each period. Unmatched players submit a rank-ordered list of partners, and resulting matches are determined by one of two algorithms. Stable Matching uses the deferred-acceptance matching algorithm to produce stable matches, whereas the Priority Matching algorithm (which ranks potential matches according to the product of rankings) does not always produce stable matches.
After running a ten-period game without a clearinghouse, run a ten-period game with either of the clearinghouses. By using one of the replay options after completing the first game, you can more easily compare results across games. At the end of a game, click Replay. If you then click Random, role and group assignments are randomly determined. Alternatively, choosing Rotate Role keeps students in the same group but causes hospitals to become residents (and vice versa). For further details on replay options, click here.
While you should expect to see players learn to trust a clearinghouse that uses the deferred-acceptance algorithm, it is likely that a clearinghouse using the priority algorithm will not be successful in reducing early matching.
Results are focused on assessing early matching. If you used one of the Replay options, you can switch between these linked games by clicking Results from the last of these replayed games and using the View menu.
For each game, the first panel summarizes a game’s results across all market periods (Figure 1). The first table reports each role’s likelihood of not matching. The second reports the likelihood of each match type (High-High, High-Low, and mixed) across matching rounds. Because the denominator includes all outcomes, including no match, the entries in this table will sum to less than 100%.
The next set of results for each game are found in the Per Market Period panel. The first graph (Figure 2) shows for each period the early-matching cost incurred by an average group. Without a clearinghouse, market unraveling should cause early-matching costs to increase as students gain experience. For stable matching, especially when introduced after not using a clearinghouse, you should see costs from early matching decrease as students learn to trust clearinghouse matches.
The second graph in this panel (Figure 3) shows the likelihood of each outcome across matching periods. You should expect to see relatively few mixed matches, and failures to match should be concentrated in early periods.
Finally, if you used one of the Replay options, access Results from the last of these replayed games and choose Across Games from the View menu. The table (Figure 4) displays the distribution of match timing for each replayed game. If game 1 is no clearinghouse and game 2 is a clearinghouse using the deferred-acceptance algorithm, then game 2 should have fewer early-round matches and potentially fewer non-matches.