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cs.DS updates on arXiv.org

PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Strategic play in stable marriage problem
Mircea Adrian Digulescu · 2016-08-27 · via cs.DS updates on arXiv.org

The stable marriage problem, as addressed by Gale and Shapely [1] consists of providing a bipartite matching between n " boys " and n " girls "-each of whom have a totally ordered preference list over the other set-such that there exists no " boy " and no " girl " that would prefer each other over their partner in the matching. In this paper, we analyze the cases of strategic play by the " boys " in the game directly inspired by this problem. We provide an O(n^3) algorithm for determining a matching which is not necessarily stable in the Gale-Shapely sense, but it is coalition-stable, in that no player has a selfish interest to leave the resulting grand coalition to join any potential alternative one which might feasibly form, and is also man-optimal. Thus, under a realistic assumption set, no player has an interest to " destabilize " the matching, even though he theoretically could. The resulting matching is often better than the naïve Gale-Shapely one for some (not all) of the " boys " , being no worse for the rest. This matching is more realistic (stable) than the one produced by top-trading-cycles method, thus offering a qualitative improvement over the latter. Furthermore, we analyze the situation when players are allowed to make strategic threats (i.e. be willing to sacrifice their own outcome to hurt others), offer a relevant example to illustrate the benefits of this form of play, and ultimately provide an exponential time algorithm which tries to determine a good threat-making strategy. We then briefly examine a few other non-conventional possibilities a player has to affect his outcome. Most common variations to the game model are also described and analyzed with regard to applicability of the methods in this paper. Finally, a few examples of real-life problems which can be modeled and solved with the methods in this paper are presented.