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We present algorithms of two flavors—one rooted in constraint satisfaction problems (CSPs) and the other in learning dynamics—to compute pure-strategy Nash equilibrium (PSNE) in k-dimensional congestion games (k-DCGs) and their variants. The two algorithmic approaches are driven by whether or not a PSNE is guaranteed to exist. We first show that deciding the existence of a PSNE in a k-DCG is NP-complete even when players have binary and unit demand vectors. For general cost functions (potentially non-monotonic), we devise a new CSP-inspired algorithmic framework for PSNE computation, leading to algorithms that run in polynomial time under certain assumptions while offering exponential savings over standard CSP algorithms. We further refine these algorithms for variants of k-DCGs. Our experiments demonstrate the effectiveness of this new CSP framework for hard, non-monotonic k-DCGs. We then provide learning dynamics-based PSNE computation algorithms for linear and exponential cost functions. These algorithms run in polynomial time under certain assumptions. For general cost, we give a learning dynamics algorithm for an (α, β)-approximate PSNE (for certain α and β). Lastly, we also devise polynomial-time algorithms for structured demands and cost functions.more » « lessFree, publicly-accessible full text available July 16, 2025
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We study pure-strategy Nash equilibrium (PSNE) computation in 𝑘-dimensional congestion games (𝑘-DCGs) where the weights or demands of the players are 𝑘-dimensional vectors. We first show that deciding the existence of a PSNE in a 𝑘-DCG is NP-complete even for games when players have binary and unit demand vectors. We then focus on computing PSNE for 𝑘-DCGs and their variants with general, linear, and exponential cost functions. For general cost functions (potentially non-monotonic), we provide the first configuration-space framework to find a PSNE if one exists. For linear and exponential cost functions, we provide potential function-based algorithms to find a PSNE. These algorithms run in polynomial time under certain assumptions. We also study structured demands and cost functions, giving polynomial-time algorithms to compute PSNE for several cases. For general cost functions, we give a constructive proof of existence for an (𝛼, 𝛽)-PSNE (for certain 𝛼 and 𝛽), where 𝛼 and 𝛽 are multiplicative and additive approximation factors, respectively.more » « lessFree, publicly-accessible full text available May 6, 2025
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We study the group-fair obnoxious facility location problems from the mechanism design perspective where agents belong to different groups and have private location preferences on the undesirable locations of the facility. Our main goal is to design strategyproof mechanisms that elicit the true location preferences from the agents and determine a facility location that approximately optimizes several group-fair objectives. We first consider the maximum total and average group cost (group-fair) objectives. For these objectives, we propose deterministic mechanisms that achieve 3-approximation ratios and provide matching lower bounds. We then provide the characterization of 2-candidate strategyproof randomized mechanisms. Leveraging the characterization, we design randomized mechanisms with improved approximation ratios of 2 for both objectives. We also provide randomized lower bounds of 5/4 for both objectives. Moreover, we investigate intergroup and intragroup fairness (IIF) objectives, addressing fairness between groups and within each group. We present a mechanism that achieves a 4-approximation for the IIF objectives and provide tight lower bounds.
Free, publicly-accessible full text available March 25, 2025 -
We propose a game-theoretic approach to generalizing the classical Schelling model. At the core of our model are two features that did not receive much attention before. First, we allow multiple individuals to occupy the same location. Second, each individual’s choice of location is influenced by their social network neighbors that also choose the same location. In addition, an individual’s choice is influenced by others in the adjacent locations in a network-structured way, which captures the main spirit of the classical Schelling model and its numerous extensions. Our solution concept is a stable configuration represented as a pure-strategy Nash equilibrium (PSNE). We show that even for various special cases of the problem, computing or counting PSNE is provably hard. We give algorithms for computing PSNE, including efficient algorithms for several special cases. We highlight some of the attractive features of our model, such as predicting very few PSNE, through experiments.more » « less