Haneesha Kella

Matching refers to the part of economics that assigns buyers and sellers in the economy to better allocate scarce goods. The notion of stable matching is the eccentric drive for the economy and aids in fixing market failures. Market failures are caused by the lack of efficient distribution of scarce resources in the market, which can be fixed by changing the market’s design. Studying the principles of matching is essential for certain markets to succeed as it allows high comprehensibility of a market’s structure. David Gale and Lloyd Shapeley concluded that instability, the notion that an applicant and a university that both prefer each other in higher precedence over other applicants, should be avoided based on the constraints. In the marriage problem, they conclude that there will always be a stable set of marriages despite the unequal number of men and women. They prove this theorem by an iterative process where they generate two algorithms: MPDA (men-proposing deferred acceptance) and WPDA(women-proposing deferred acceptance). These follow the Gale-Shapley algorithm, which has been implemented in many coding languages to emphasize the optimality of certain markets. The compatibility constraints in this area of study are binary since a match between a couple is either “compatible” or “not compatible”. Suppose for each couple, the compatibility constraints could be more varied like: "highly compatible", "moderately compatible" or "not compatible". If the input preferences regarding these new compatibility constraints were to be randomly generated, would the match probabilities of MPDA and WPDA still be identical?