Related papers: Conditions for Stability in Strategic Matching
In the stable marriage problem (SM), a mechanism that always outputs a stable matching is called a stable mechanism. One of the well-known stable mechanisms is the man-oriented Gale-Shapley algorithm (MGS). MGS has a good property that it…
We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are…
The resident matching algorithm, Gale-Shapley, currently used by SF Match and the National Residency Match Program (NRMP), has been in use for over 50 years without fundamental alteration. The algorithm is a 'stable-marriage' method that…
We present a mechanism for computing asymptotically stable school optimal matchings, while guaranteeing that it is an asymptotic dominant strategy for every student to report their true preferences to the mechanism. Our main tool in this…
We show that given a SM instance G as input we can find a largest collection of pairwise edge-disjoint stable matchings of G in time linear in the input size. This extends two classical results: 1. The Gale-Shapley algorithm, which can find…
We analyse the computational complexity of finding Nash equilibria in stochastic multiplayer games with $\omega$-regular objectives. While the existence of an equilibrium whose payoff falls into a certain interval may be undecidable, we…
Many allocation problems in multiagent systems rely on agents specifying cardinal preferences. However, allocation mechanisms can be sensitive to small perturbations in cardinal preferences, thus causing agents who make ``small" or…
Suppose $n$ boys and $n$ girls rank each other at random. We show that any particular girl has at least $({1\over 2}-\epsilon) \ln n$ and at most $(1+\epsilon)\ln n$ different husbands in the set of all Gale/Shapley stable matchings defined…
With respect to probabilistic mixtures of the strategies in non-cooperative games, quantum game theory provides guarantee of fixed-point stability, the so-called Nash equilibrium. This permits players to choose mixed quantum strategies that…
We study a full implementation problem with a state unknown to the designer but known to agents, where agents have uncertain evidence privately drawn from state-dependent distributions. Stochastic evidence enables ``perfect deceptions,''…
The Stable Marriage problem (SM), solved by the famous deferred acceptance algorithm of Gale and Shapley (GS), has many natural generalizations. If we allow ties in preferences, then the problem of finding a maximum stable matching becomes…
We consider a voting setting where candidates have preferences about the outcome of the election and are free to join or leave the election. The corresponding candidacy game, where candidates choose strategically to participate or not, has…
We address Nash equilibrium problems in a partial-decision information scenario, where each agent can only exchange information with some neighbors, while its cost function possibly depends on the strategies of all agents. We characterize…
A fundamental shortcoming of the concept of Nash equilibrium is its computational intractability: approximating Nash equilibria in normal-form games is PPAD-hard. In this paper, inspired by the ideas of smoothed analysis, we introduce a…
In a stable matching problem there are two groups of agents, with agents on one side having their individual preferences for agents on another side as a potential match. It is assumed silently that agents can freely and costlessly ``switch"…
The classic Stable Roommates problem (which is the non-bipartite generalization of the well-known Stable Marriage problem) asks whether there is a stable matching for a given set of agents, i.e. a partitioning of the agents into disjoint…
We study organizational elections in which each group nominates one candidate and receives as payoff its members expected utility under a probabilistic winning rule. We empirically justify a standard monotonicity assumption by simulating…
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
We address the generalized Nash equilibrium seeking problem in a partial-decision information scenario, where each agent can only exchange information with some neighbors, although its cost function possibly depends on the strategies of all…
A description of static equilibria in the noisy binary choice (Ising) game on complete and random graphs resulting from maximisation of the likelihood of system configurations is presented. An equivalence of such likelihood equilibria to…