Related papers: Conditions for Stability in Strategic Matching
Current research in distributed Nash equilibrium (NE) seeking in the partial information setting assumes that information is exchanged between agents that are "truthful". However, in general noncooperative games agents may consider sending…
Nash equilibrium is a central solution concept for reasoning about self-interested agents. We address the problem of synthesizing Nash equilibria in two-player deterministic games on graphs, where players have private, partially-ordered…
Many-to-many matching with contracts is studied in the framework of revealed preferences. All preferences are described by choice functions that satisfy natural conditions. Under a no-externality assumption individual preferences can be…
In IWOCA 2019, Ruangwises and Itoh introduced stable noncrossing matchings, where participants of each side are aligned on each of two parallel lines, and no two matching edges are allowed to cross each other. They defined two stability…
Assume that $n = 2k$ potential roommates each have an ordered preference of the $n-1$ others. A stable matching is a perfect matching of the $n$ roommates in which no two unmatched people prefer each other to their matched partners. In…
We study the existence of mixed-strategy equilibria in concurrent games played on graphs. While existence is guaranteed with safety objectives for each player, Nash equilibria need not exist when players are given arbitrary terminal-reward…
We study the design of one-to-one matching mechanisms that are strategy-proof for both sides and as stable as possible. Motivated by the impossibility result of Roth (1982), we formulate the mechanism design problem as a linear program that…
In stable matching, one must find a matching between two sets of agents, commonly men and women, or job applicants and job positions. Each agent has a preference ordering over who they want to be matched with. Moreover a matching is said to…
In their seminal work on the Stable Marriage Problem, Gale and Shapley describe an algorithm which finds a stable matching in $O(n^2)$ communication rounds. Their algorithm has a natural interpretation as a distributed algorithm where each…
In this paper, we examine the Nash equilibrium convergence properties of no-regret learning in general N-player games. For concreteness, we focus on the archetypal follow the regularized leader (FTRL) family of algorithms, and we consider…
Matching algorithms have demonstrated great success in several practical applications, but they often require centralized coordination and plentiful information. In many modern online marketplaces, agents must independently seek out and…
We study rational synthesis problems for concurrent games with omega-regular objectives. Our model of rationality considers only pure strategy Nash equilibria that satisfy either a social welfare or Pareto optimality condition with respect…
Consider the group of $n$ men and $n$ women, each with their own preference list for a potential marriage partner. The stable marriage is a bipartite matching such that no unmatched pair (man, woman) prefer each other to their partners in…
Colloquially, there are two groups, $n$ men and $n$ women, each man (woman) ranking women (men) as potential marriage partners. A complete matching is called stable if no unmatched pair prefer each other to their partners in the matching.…
We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In…
An instance $I$ of the Stable Matching Problem (SMP) is given by a bipartite graph with a preference list of neighbors for every vertex. A swap in $I$ is the exchange of two consecutive vertices in a preference list. A swap can be viewed as…
We analyse the computational complexity of finding Nash equilibria in turn-based stochastic multiplayer games with omega-regular objectives. We show that restricting the search space to equilibria whose payoffs fall into a certain interval…
In two-sided matching markets, ensuring both stability and strategy-proofness poses a significant challenge; it is impossible when agents' preferences are unrestricted. But what if agents' preferences have specific restricted structures?…
Many two-sided matching markets, from labor markets to school choice programs, use a clearinghouse based on the applicant-proposing deferred acceptance algorithm, which is well known to be strategy-proof for the applicants. Nonetheless, a…
Motivated by growing evidence of agents' mistakes in strategically simple environments, we propose a solution concept -- robust equilibrium -- that requires only an asymptotically optimal behavior. We use it to study large random matching…