Dynamic Matching and Interactions: Theory and Experiments – DynaMITE

Theoretical models are built on game theory. In the three sub-projects (matching, vote and the formation of social networks), theoretical models will conform to the standard models in economic theory, involving rational agents maximizing objective functions. Because of interaction among agents, game theory is the adequate tool to capture individual decisions. Because decisions involve a dynamic element represented by a Markov process, the resolution of theoretical models require the use of methods from dynamic optimization, closely related to methods used in operations research. The experimental studies conform to the standard of experimental work in economics: subjects are paid according to their performance and experiments are run on the basis of complete ingenuity and honesty.

Results are expected on two fronts:
- scientific work published in top journals in economics
- recommandations to public decision makers concerning matching processes and votes

The project is decomposed into three sub-projects which deal with Dynamic Matching (DynaMatch), Dynamic Voting (DynaVote) and Dynamic Networks (DynaNet). All three sub-projects share the same objective (the extension of static studies to dynamic environments) and the same methodology (the construction of theoretical models based on Markovian decision processes, the validation of the model through large scale experimentation). The project is based in three research centers: CREST (at Paris Saclay), , CES (at University Paris I), GATE (at the Universities of Saint-Etienne and Lyon). However, the objective of the project is not to support independent research in each of the three centers, but instead to foster integration and coordination of the researchers in the three locations. Each of the sub-projects is implemented by a team consisting of researchers in at least two centers. A large part of the funding is devoted to integration between the three centers, through the financing of travel, conferences and “revolving post-doctoral positions”, where the post-doctoral researcher will be asked to divide her/his time between two of the three research centers. Our ultimate goal is to structure a long standing network of French scientists working on dynamic interaction problems.

The project has led to advances in the study of dynamic opinion formation models in networks, and dynamic properties of sharing solutions in networks. The project developed two dynamic matching models, one applied to the assignment of Masters of Conference in universities, the other to the allocation of social housing in Paris. The project finally gave rise to a new theory of voting and approval-based negotiation, supported by experimental laboratory results and natural experiments in real votes.

There are about 80 publications related to the project, which specifically mention the funding in acknowledgements. These publications concern network dynamics (for 50 of them), dynamic matching (for about 15) and voting (for about 15). These publications are in many outlets, but there are a large number (about twenty) of publications in high-ranking journals, such as American Economic Journal: Microeconomics (2), Games and Economic Behavior (3), Social Choice and Welfare (2), Mathematical Social Sciences (5).

Many decisions taken by rational economic agents do not involve markets, but the design of matching and voting procedures, or the use of groups and social networks. The allocation of students to schools, the choice of cases taken up by the Supreme Court or the measure of influence of social agents are all examples of issues which have recently been studied by microeconomic theorists beyond the realm of markets. Moving beyond the strict boundaries of markets and prices, economic theorists now join forces with political scientists, psychologists and computer scientists to better understand the functioning of matching, voting and network institutions. With a few exceptions, theoretical and empirical models of matching, voting and network formation are static. The objective of this project is to develop a new generation of theoretical models of dynamic matching, voting and networks by embedding static decisions in dynamic models represented by Markov processes. The project is subdivided into three sub-projects. Dynamatch is devoted to the study of dynamic matching problems, and will examine multi-stage assignment models with an initial phase of courtship, the assignment of subsidized housing to queuing agents, and of positions in high school and universities to overlapping generations of teachers. Driven by concrete applications in market design, the project involves a dialog with practitioners in social housing and teacher assignment. Dynavote focuses on dynamic voting models, and analyzes the design of multi-stage electoral rules in continuous time, models of optimal apportionment and evolutionary learning of voters over repeated elections. Dynanet is a project on dynamic formation of networks, with applications to networks of influence and networks of innovation. In addition, models of dynamic coalition formation and allocations in cooperative games will be studied in this project. Because dynamic models involve sophisticated behavior on the part of agents, we plan to test the predictions of theoretical models in the laboratory. We plan to implement a series of experiments on school choice, voting and network formation. In the long run, the objective of the project is to advance the research frontier in economic theory, to engineer matching procedures in concrete applications and to cement a community of researchers in France dedicated to matching, voting and network theories.