We introduce a new matching model to mimic two-sided exchange programs such as tuition and worker exchanges, in which export-import balances are required for longevity of programs. These exchanges use decentralized markets, making it difficult to achieve this goal. We introduce the two-sided top trading cycles, the unique mechanism that is balanced-efficient, worker-strategy-proof, acceptable, individually rational, and respecting priority bylaws regarding worker eligibility. Moreover, it encourages exchange, because full participation induces a dominant-strategy equilibrium for firms. We extend it to dynamic settings permitting tolerable yearly imbalances and demonstrate that its regular and tolerable versions perform considerably better than models of current practice.

We show that in the presence of admissions reserves, the effect of the precedence order (i.e., the order in which different types of seats are filled) is comparable to the effect of adjusting reserve sizes. Either lowering the precedence of reserve seats at a school or increasing the school’s reserve size weakly increases reserve-group assignment at that school. Using data from Boston Public Schools, we show that reserve and precedence adjustments have similar quantitative effects. Transparency about these issues—in particular, how precedence unintentionally undermined intended policy—led to the elimination of walk zone reserves in Boston’s public school match.