Related papers: Concave many-to-one matching
Large-scale, two-sided matching platforms must find market outcomes that align with user preferences while simultaneously learning these preferences from data. Classical notions of stability (Gale and Shapley, 1962; Shapley and Shubik,…
This paper has two objectives. One is to give a linear time algorithm that solves the stable roommates problem (i.e., obtains one stable matching) using the stable marriage problem. The idea is that a stable matching of a roommate instance…
This paper characterizes equilibrium properties of a broad class of economic models that allow multiple heterogeneous agents to interact in heterogeneous manners across several markets. Our key contribution is a new theorem providing…
There are only limited classes of multi-player stochastic games in which independent learning is guaranteed to converge to a Nash equilibrium. Markov potential games are a key example of such classes. Prior work has outlined sets of…
We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classic definition of stability by Gale and Shapley (1962). Informally speaking, robustness…
School choice is the two-sided matching market where students (on one side) are to be matched with schools (on the other side) based on their mutual preferences. The classical algorithm to solve this problem is the celebrated deferred…
Consider a one-to-one two-sided matching market with workers on one side and single-position firms on the other, and suppose that the largest individually rational matching contains $n$ pairs. We show that the number of workers employed and…
Within the context of stochastic probing with commitment, we consider the online stochastic matching problem; that is, the one-sided online bipartite matching problem where edges adjacent to an online node must be probed to determine if…
We use the indirect evolutionary approach to study evolutionarily stable preferences against multiple mutations in single- and multi-population matching settings, respectively. Players choose strategies to maximize their subjective…
We study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models. For a given instance, we call a matching $k$-stable if no other matching exists that is more…
The word stable is used to describe a situation when mathematical objects that almost satisfy an equation are close to objects satisfying it exactly. We study operator-algebraic forms of stability for unitary representations of groups and…
The Stable Marriage Problem is to find a one-to-one matching for two equally sized sets of agents. Due to its widespread applications in the real world, especially the unique importance to the centralized match maker, a very large number of…
In many empirical studies of a large two-sided matching market (such as in a college admissions problem), the researcher performs statistical inference under the assumption that they observe a random sample from a large matching market. In…
Behavioral diversity, expert imitation, fairness, safety goals and others give rise to preferences in sequential decision making domains that do not decompose additively across time. We introduce the class of convex Markov games that allow…
Within the context of stochastic probing with commitment, we consider the online stochastic matching problem; that is, the one sided online bipartite matching problem where edges adjacent to an online node must be probed to determine if…
An approximation of strategyproofness in large, two-sided matching markets is highly evident. Through simulations, one can observe that the percentage of agents with useful deviations decreases as the market size grows. Furthermore, there…
This paper examines equilibria in dynamic two-sided matching games, extending Gale and Shapley's foundational model to a non-cooperative, decentralized, and dynamic framework. We focus on markets where agents have utility functions and…
Evolutionary game theory is an abstract and simple, but very powerful way to model evolutionary dynamics. Even complex biological phenomena can sometimes be abstracted to simple two-player games. But often, the interaction between several…
In this paper we develop the theory of how to count, in thin concurrent games, the configurations of a strategy witnessing that it reaches a certain configuration of the game. This plays a central role in many recent developments in…
This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is…