# David Pérez-Castrillo

## IBD Amphi

AMU - AMSE

5-9 boulevard Maurice Bourdet

13001 Marseille

Sarah Flèche : sarah.fleche[at]univ-amu.fr

Agnès Tomini : agnes.tomini[at]univ-amu.fr

In the one-sided assignment game any two agents can form a partnership and decide on the sharing of the surplus created. Thus, an outcome involves a matching and a vector of payoffs. In this market, stable outcomes often fail to exist. We introduce the idea of simple outcomes: they are individually rational outcomes where no matched agent can form a blocking pair with any other agent, neither matched nor unmatched. We propose the set of Pareto optimal (PO) simple outcomes, which is the set of the maximal elements of the set of simple outcomes, as a natural solution concept for this game. We prove several properties of the simple outcomes and of the PO simple outcomes. In particular, we show that each element in the set of PO simple payoffs provides the maximum surplus out of the set of simple payoffs, the set is always non-empty, and it coincides with the core when the core is non-empty. We further support the set of PO simple outcomes as a natural solution concept by suggesting an idealized dynamic environment that leads to these outcomes. In this process, coalitions are formed sequentially under the premise of optimal behavior and two agents only reach an agreement if both believe that more favorable terms will not be obtained in any future negotiations.