Generalized three-sided assignment markets: core consistency and competitive prices

Abstract

A generalization of the classical three-sided assignment market is considered, where value is generated by pairs or triplets of agents belonging to different sectors, as well as by individuals. For these markets we represent the situation that arises when some agents leave the market with some payoff by means of a generalization of Owen (1992) derived market. Consistency with respect to the derived market, together with singleness best and individual anti-monotonicity, axiomatically characterize the core for these generalized three-sided assignment markets. When one sector is formed by buyers and the other by two different type of sellers, we show that the core coincides with the set of competitive equilibrium payoff vectors.

Stable Source Connection and Assignment Problems as Multi-Period Shortest Path Problems

“…Many extensions of the assignment problem to m > 2 sides have been proposed, and we focus here on the extensions proposed by Quint (1991) and Atay et al (2016). To simplify notations, we focus here on 3-sided assignment problems, but all results can be extended to m-sided, for any positive integer m. Both extensions consider cases in which we have 3 groups, and value is created by triplets consisting of one member of each group.…”

“…To simplify notations, we focus here on 3-sided assignment problems, but all results can be extended to m-sided, for any positive integer m. Both extensions consider cases in which we have 3 groups, and value is created by triplets consisting of one member of each group. While Quint (1991) supposes that these are the only groups creating value, Atay et al (2016) also allow for pairs to create value. We call the model proposed by Quint (1991) the strict m-sided assignment problem and the one by Atay et al…”

“…Extensions of the assignment problem to m-sides, with m > 2, is where the connection to MSP problems is more useful. Many variants have been proposed and we study the strict m-sided assignment problem of Quint (1991) and the generalized version of Atay et al (2016). In the former, value is created only when we match a group that contains one player from each side, while in the latter there is also some value created when we match smaller groups of agents from different sides.…”

“…Some but not all of these m-sided assignment problems have a corresponding MSP representation, but by our stability result, if an assignment problem can be represented as a MSP problem, it has a non-empty core. We provide sufficient conditions for representability as MSP problems, and thus for non-vacuity of the core, and show that the resulting set of stable games are distinct from those described by Quint (1991) and Atay et al (2016).…”

Multi-Sided Assignment Games on M-Partite Graphs

“…It is clear that for m = 2, multi-sided assignment games on bi-partite graphs coincide with the classical Shapley and Shubik (1972) assignment games. Notice also that for m = 3, multi-sided assignment games on 3-partite graphs are a particular case of the generalized three-sided assignment games in Atay et al (2016), with the constraint that the value of a three-person coalition is the addition of the values of all its pairs.…”