Final Report Summary - NSMP (A New Solution to Matching Problems) The extant literature on matching theory and market design assumes that institutions (e.g. schools, hospitals) have deterministic priorities over the other side of the problem, which is agents (e.g. students or doctors). While it is clear that this supposition significantly decreases the theoretical scope of the studies, the same is true on practical ground as there are many real-life market examples where the relevant institutions have random, rather than deterministic, priorities. Some of such market examples are elementary and secondary school choice programs in Belgium, Ireland, and Italy; the centralized medical graduates market in Scotland; and the college admission programs in Germany, Hungary, and Turkey.Given this important handicap of the literature, this project is the first to generalize the existing matching models by letting priorities to be random, as opposed to restricting them to be deterministic. While this generalization greatly enriches the theoretical scope of the existing literature, it is also more able to represent real-life markets. After this generalization, the project introduces a stability notion, which fits to its formulation. This notion is more general than the conventional stability notion of Gale and Shapley (1962), and they become the same in the deterministic priority case.The next research direction that the project pursues is a mechanism design that satisfies the project's stability notion as well as some other desirable properties. In the conventional deterministic priority setting, the celebrated deferred-acceptance mechanism of Gale and Shapley (1962) not only satisfies their stability property but also some other very strong properties. Hence, it is deemed as the best mechanism in the deterministic setting. Given this, the project first considers the deferred-acceptance mechanism and verifies that it satisfies the project's stability notion. However, it is also found that it has an important efficiency handicap in that it fails to be efficient within the class of mechanisms that satisfy the project's stability property. This necessitates a new mechanism design, which avoids such inefficiencies. To this end, the project next introduces a new mechanism design, and shows that it is well-defined in the sense that it stops in finite number of steps and produces an outcome. It is shown that the mechanism satisfies the project's stability notion as well, and it does not admit an efficiency handicap as the deferred-acceptance mechanism. That is, it is efficient within the class of mechanisms that satisfy the project's stability notion.In order to understand more about the project's mechanism, a set of desirable axioms are determined to compare the deferred-acceptance and the project's mechanism. Specifically, these axioms are efficiency, fairness, and strategic-concerns related. This comparison shows that the project's mechanism performs better than the deferred-acceptance mechanism in terms of efficiency and fairness, whereas the converse is true in terms of strategic issues. Moreover, an axiomatic characterization of the project's mechanism is provided. This result singles out it by demonstrating that the project's mechanism is the unique one that satisfies the stability as well as some certain desirable efficiency and fairness properties.After having obtained all the theoretical results above, in order to show the practical relevance of the project, I find some real-life matching market examples that fit to the project's model rather than those of the existing ones. These are markets where the relevant institutions have non-deterministic priorities. Some of them are school choice programs in Belgium, Ireland, and Italy; the centralized medical graduates market is Scotland; and the college admissions in Turkey, Hungary. There are examples from the United States as well, including school choice programs in Boston and New York. The theoretical richness and practical relevance of the project makes its dissemination more important. In order to disseminate the project findings, I organized talks, attended prestigious conferences, invited well-known researchers to the host institution. Below is the list of conferences/workshops I attended and presented the project findings or related works.* Meeting of the Society for Social Choice and Welfare, June 2014, Boston College, USA (Presenter)* International Workshop on Game Theory and Economic Applications of the Game Theory Society, Sao Paulo University, Brazil, July 2014 (Presenter)* First Market Design and Matching Theory Workshop at Sabanci University, Istanbul, Turkey, 2014 (Organizer and Presenter)* All Istanbul Meeting, May 2015, Turkey (Presenter)* Conference on Economic Design 2015, July 2015, Turkey (Presenter)* Bosphorus Workshop on Economic Design, Bodrum, Turkey, 2015 (Presenter)* East Asian Game Theory Conference 2015, August 2015, Tokyo, Japan (Presenter)* 37th Bosphorus Workshop on Economic Design, August 2016, Bodrum, Turkey (Presenter).* 2016 Biennial Meeting of the Society for Social Choice and Welfare, June 2016, Lund University, Lund, Sweden (Presenter).* 12th Workshop Matching in Practice, December 2016, Hungarian Academy of Science, Budapest, Hungary (Presenter).* Workshop on Matching Markets, December 2016, Istanbul Technical University, Istanbul, Turkey (Presenter & Co-organizer).* The 10th Conference on Economic Design, June 2017, York, United Kingdom (Presenter).* 13th Workshop of Matching in Practice, August 2017, Universite Libre de Bruxelles, Belgium (Presenter).These conference/workshops organizations have significantly contributed to the dissemination of the project. I had also chance to talk to well-known researchers at those conferences, which has helped me to improve myself and widen my academic network. They also provided knowledge transfer. I invited well-known researchers to the host institution. Some of them are Prof. Bertan Turhan (Boston College), Prof. Rahmi Ilkilic (Bilkent University), Prof. Herve Moulin (University of Glasgow), Prof. Anna Bogomolnaia (University of Glasgow), Prof. Alex Westkamp (University of Cologne), Prof. Battal Dogan (University of Lausanne), Prof. Levent Kockesen (Koc University), Prof. Nejat Ambarcı (Deakin University), Prof. Hulya Eraslan (Rice University), and Prof. Tugce Cuhadaroglu (University of St Andrews). These talk organizations provided knowledge transfer to (and from) host institution as well, contributed to my academic improvement and network as well.In addition to the above dissemination activities, I wrote the project findings as a journal article, and submitted to top journals. This article has successfully received a minor revision request from a top Economic theory journal--Games and Economic Behavior. Unless something highly unexpected will happen, it will be published there. This publication will make the project findings totally visible and accessible. In order to reach public at large and put the project findings into work, I contacted various real-life matching market administrators, such as Hungarian and Turkish student placement administrators. I mentioned the project to let them know about it. In the long run, as the project mechanism admits desirable efficiency and fairness properties, the implementation of the project findings would lead those market to work more efficiently and in a fair way. As such an implementation would increase the efficiency of markets, it would contribute to society at large in various aspects, including economic and sociological.