Research

Publications:

Gender consistent resolving rules in marriage problems, with D. Dimitrov and Y. Yang (Discrete Applied Mathematics, 2018)

The selection of blocking pairs to be matched plays an important role in the study of mechanisms converting arbitrary matchings into stable ones. We assume that a resolving rule guides the selection and show that two axioms (independence and top optimality) transform such a rule into a gender consistent one. That is, the rule is forced by the axioms to follow a linear order over acceptable pairs which is consistent with the preferences of either all men or all women. As shown by Abeledo and Rothblum (1995), stable matchings can be reached when starting from an arbitrary individually rational matching and iteratively satisfying the pair selected by a gender consistent resolving rule.

Condorcet Consistency and the strong no show paradoxes, with H. Peters and D. Vermeulen (Mathematical Social Sciences, forthcoming)

We consider voting correspondences that are, besides Condorcet Consistent, immune against the two strong no show paradoxes. That is, it cannot happen that if an additional voter ranks a winning alternative on top then that alternative becomes loosing, and that if an additional voter ranks a loosing alternative at bottom then that alternative becomes winning. This immunity is called the Top Property in the first case and the Bottom Property in the second case. We establish the voting correspondence satisfying Condorcet Consistency and the Top Property, which is maximal in the following strong sense: it is the union of all smaller voting correspondences with these two properties. The result remains true if we add the Bottom Property but not if we replace the Top Property by the Bottom Property. This voting correspondence contains the Minimax Rule but it is strictly larger. In particular, voting functions (single-valued voting correspondences) that are Condorcet Consistent and immune against the two paradoxes must select from this maximal correspondence, and we demonstrate several ways in which this can or cannot be done.

Working Papers:

Full Farsighted Rationality, with D. Karos (Job market paper)

An abstract game consists of a set of states and specifies what coalitions are allowed to replace one state by another one. Agents are called farsighted if they compare the status quo to the long term outcome following their deviation rather than to the state they actually deviate to. What the literature has ignored so far is that if a coalition does not move out of the status quo, they might still expect another coalition to do so. Specifically, above definition of farsightedness implies that agents ignore this possibility in their reasoning. So, in fact, agents are not fully farsighted. Expectation functions assign to each state a (potentially) different state and a coalition that moves from the former to the latter, thereby creating paths between states. This endows agents with an expectation about what any potential deviation entails, namely the path of the prescribed further moves. We extend these functions by capturing coalitions' expectations about the consequences of not moving out of a state. We impose three stability and optimality axioms on extended expectation functions that reflect full farsightedness and rationality. We then show that an expectation function satisfies our axioms if and only if it can be associated with a non-cooperative equilibrium of the abstract game. We finally apply our solution to games in characteristic function form and matching problems.

Employment experience and stability in two-sided matching, with D. Dimitrov

We consider two-sided matching problems in which firms' preferences are crucially shaped by workers' employment experience. Assuming that experience assigns to each worker a set of firms he has been employed by, we first show that there are experience configurations for which no stable matching exists. We then present a sufficientcondition guaranteeing such existence for any configuration. The condition stipulates the idea that firms are size-sensitive with respect to the experience of each worker and it allows us also to fully describe the set of stable matchings. An example showing that experience size-sensitivity does not assure the existence of a firm optimal stablematching is provided as well.

Work in Progress:

Transfers in dynamic TU-games, with H. Peters and D. Vermeulen

This paper analyzes individuals' behavior if agents have to repeatedly cooperate with others. Although cooperative game theory normally abstracts away of any strategic interaction between players, we argue that in a repeated set up players would act strategically if they could. It seems natural, that, even when conducting projects in groups, individuals try to maximize their own benefit, such as money or power. Also other factors might influence agents' behavior in groups. How should a researcher behave if, due to time constraints, she cannot work at all the projects she agreed on at the same time? We intend to incorporate and predict such (strategic) behavior by modeling non-cooperative games based on a dynamic game with transferable utility and point-wise solution concepts for them. We model the strategic interaction between agents by allowing them to transfer some worth among periods, and, hence, indirectly affect their payoffs, as well as the payoffs of the other players. We discuss different transfer systems, specifying what worth agents can transfer and identify Nash equilibria in the resulting non-cooperative games. Furthermore, we characterize the Nash equilibria and discuss uniqueness of them. We also consider particular classes of TU-games, such as market games and voting games and introduce transfer systems that seem to be suited best for these games: in market games agents can transfer their initial endowment among periods, and in the context of voting games, we allow agents to shift their voting weights over time. Based on this idea we derive non-cooperative games and further discuss existence and uniqueness of Nash equilibria.