This short paper isolates a non-trivial class of games for which there exists a monotone relation between the size of pure strategy spaces and the number of pure Nash equilibria (Theorem). This class is that of two- player nice games, i.e., games with compact real intervals as strategy spaces...

Alvin Roth et Lloyd Shapley ont reçu en 2012 le prix de sciences économiques de la Banque Royale de Suède à la mémoire d'Alfred Nobel, pour leurs travaux sur l'organisation centralisée de certains marchés économiques, qui dépendent de l'appariement d'agents de deux types distincts (des...

In a school choice context we show that considering only schools' priorities and the set of acceptable schools for each student - but not how these schools are ranked in their preferences - we can restrict the set of possible stable matchings that can arise for any preference profile of the...

This paper studies a decentralized job market model where firms (academic departments) propose sequentially a (unique) position to some workers (Ph.D. candidates). Successful candidates then decide whether to accept the offers, and departments whose positions remain unfllled propose to other...

We identify in this paper two conditions that characterize the domain of single-peaked preferences on the line in the following sense: a preference profile satisfies these two properties if and only if there exists a linear order L over the set of alternatives such that these preferences are...

Alvin Roth and Lloyd Shapley have received in 2012 the Sveriges Riksbank prize in economic sciences in memory of Alfred Nobel, for their work on the centralized organization of some economic markets, which rely on the matching of agents of two different types (students and schools, for...

We consider non-cooperative environments in which two players have the power to gradually and unilaterally rule out some of their actions. Formally, we embed a strategic-form game into a multi-stage game, in which players can restrict their action spaces in all but the final stage, and select...

Recently, several school districts in the US have adopted or consider adopting the Student-Optimal Stable mechanism or the Top Trading Cycles mechanism to assign children to public schools. There is evidence that for school districts that employ (variants of) the so-called Boston mechanism the...

Contrary to most countries, the recruitment of assistant professors in France is centralized: recruitment committees submit a ranking of candidates to the Ministry of Education, the candidates submit their own ranking over the faculties that rank them and the Ministry compute the final match...