arXiv subjects

Chuang-Chieh Lin

Publications and source records attributed to Chuang-Chieh Lin.

9 recordsLinked to original sources

arXiv2026

EF1-Constrained Nash Social Welfare with Identical Additive Valuations: Complexity, Guarantees, and Experiments

We study the allocation of indivisible goods among agents with identical additive valuations, focusing on envy-freeness up to one good (EF1) and Nash social welfare (NSW). Since every maximum-NSW allocation is EF1 under additive valuations, the associated threshold problem inherits the known strong NP-hardness of NSW maximization under identical additive valuations and is strongly NP-complete. We therefore focus on welfare guarantees satisfied by arbitrary EF1 allocations. Although every such allocation is known to achieve an $e^{-1/e}$-approximation to the unrestricted optimal NSW, we identify conditions yielding stronger guarantees. Under uniform valuations, every EF1 allocation is NSW-optimal. Under an $\varepsilon$-small-item condition, every EF1 allocation achieves an explicit approximation ratio $ρ_n(\varepsilon)$ satisfying $ρ_n(\varepsilon) = 1-O(\varepsilon^2)$ as $\varepsilon\to 0$ for fixed $n$. We further consider the stronger sequential requirement that $\operatorname{EF1}$ be maintained after every item assignment. For this setting, we introduce \emph{PriorityNet}, a deep reinforcement learning framework trained with Proximal Policy Optimization (PPO) and equipped with prospective $\operatorname{EF1}$ action masking, which guarantees prefix-wise $\operatorname{EF1}$ by construction. Across 3,000 test instances in each of the offline full-information and random-order online regimes ($n\in[2,20]$, $m\in[5,100]$), PriorityNet achieves mean normalized $\operatorname{NSW}$ values of $0.9911$ and $0.9701$, respectively. Relative to the offline Longest Processing Time (LPT) heuristic and the online least-valued-bundle rule, it attains instance-wise win-minus-loss rates of $+27.10\%$ and $+17.87\%$. Its aggregate welfare matches the offline LPT baseline to four decimal places and modestly improves upon the online baseline, from $0.9694$ to $0.9701$.

cs.GT↗

arXiv2026

Resolving Envy by Adding Goods with Bounded Supply: A Type-Count Dichotomy and Two-Agent Hardness

We study envy elimination by adding goods (EEAG) when the additional pool has bounded supply and no separate budget bound. We establish a sharp type-count dichotomy for binary additive valuations. With one additional item type, EEAG is polynomial-time solvable for any number of agents. More generally, our algorithm permits arbitrary nonnegative integer per-copy values. The envy constraints form a system of difference constraints, and Bellman--Ford returns the componentwise least feasible extension. In contrast, with exactly two additional item types, EEAG is \textsf{NP}-complete even when both types have positive finite supply and the approvers of one type form a subset of the approvers of the other. This closes the two-type case left open by Bentert et al. Separately, we prove weak \textsf{NP}-completeness even for two agents with identical additive valuations, one initially endowed good, and a growing number of unit-supply item types. Thus, bounded-supply hardness appears both with two item-types and many agents and with two agents and many item-types.

cs.GT↗

arXiv2026

Dynamics and Convergences for Markov Coevolutionary Opinion Formation Games in Dynamic Social Networks

While deterministic variants of the coevolutionary opinion formation games such as the K-Nearest Neighbor (K-NN) game, e.g., in Bhawalkar et al., in a dynamic social network can sometimes be shown to stabilize using potential functions or localized smoothness arguments, introducing stochasticity fundamentally changes the mathematical landscape. In the "K-NN Markov game", network topologies evolve via a time-varying, randomized selection process. Proving whether such a system, as a special case of general-sum Markov games, converges to an equilibrium is a profoundly non-obvious and challenging theoretical question. Multiagent reinforcement learning has been shown to derive Nash (minimax) equilibria in two-player zero-sum Markov games and Markov potential games (along with some price-of-anarchy types of results). In recent work, optimistic dynamics are shown to converge to correlated equilibria in general-sum Markov games while the price-of-anarchy bounds are unknown. We thus analyze playing specific no-regret algorithms in general-sum Markov games for convergence to a stricter set than correlated equilibria. We integrate the convergence analysis techniques from multi-agent reinforcement learning in works of Wei et al. and online learning in a recent work of Anagnostides et al. Specifically in (general-sum) Markov games, since the regret of the optimistic gradient ascent algorithm would have extra positive terms coming from Q-values, taking care of these terms requires non-trivial extra work setting an appropriate range of our learning rate and deriving the threshold on the number of iterations for convergence or a bounded price of anarchy, significantly different from those in the assumption in a main technical theorem of Anagnostides et al. We analyze a weaker sense of convergences to approximate Nash equilibria by playing optimistic gradient ascents in general-sum Markov games.

cs.GT↗

arXiv2026

Testing Full Quartet Consistency: Adaptive Reconstruction, Random Verification, and Constant-Query Testability

We study dense property testing for full systems of resolved quartet topologies on $n$ taxa: determining whether a system is induced by a phylogenetic tree or is $\varepsilon$-far from every tree-induced system. Our main result is an explicit polynomial-time adaptive one-sided-error tester. It reconstructs a candidate tree through anchored quartet queries and verifies the candidate using uniformly random quartet queries. With error probability $δ$, it uses $O\!\left(n\log n+\varepsilon^{-1}\log(1/δ)\right)$ queries. We also give a non-adaptive cached-anchor variant using $\binom{n-1}{3}+O\!\left(\varepsilon^{-1}\log(1/δ)\right)$ queries. Both improve the previous explicit $O(n^3/\varepsilon)$ query bound. Since the input contains $\binom{n}{4}=Θ(n^4)$ quartet entries, both testers use $o\!\left(\binom{n}{4}\right)$ queries for fixed~$\varepsilon$ and~$δ$. We additionally encode full quartet systems, equivariantly under relabeling, as directed, three-colored $4$-ary structures. Hereditary directed-hypergraph testing then yields an $n$-independent one-sided-error tester, although its dependence on $\varepsilon$ is quantitatively impractical. Finally, we prove lower bounds. In ordinary property testing, every adaptive randomized tester, even with two-sided error, requires asymptotically at least $\ln((1-δ)/δ)/\ln(1/(1-\varepsilon))$ queries as $n\to\infty$. Every one-sided-error tester requires $\ln(1/δ)/\ln(1/(1-\varepsilon))$ queries, matching the random-verification term up to rounding. For the stronger reconstruct-or-reject task, our upper bounds are optimal up to constant factors: the adaptive and non-adaptive complexities are $Θ(n\log n+\varepsilon^{-1}\log(1/δ))$ and $Θ(n^3+\varepsilon^{-1}\log(1/δ))$, respectively.

cs.DS↗

arXiv2026

Computing Pure-Strategy Nash Equilibria in a Two-Party Policy Competition: Existence and Algorithmic Approaches

We formulate two-party policy competition as a two-player non-cooperative game, generalizing Lin et al.'s work (2021). Each party selects a real-valued policy vector as its strategy from a compact subset of Euclidean space, and a voter's utility for a policy is given by the inner product with their preference vector. To capture the uncertainty in the competition, we assume that a policy's winning probability increases monotonically with its total utility across all voters, and we formalize this via an affine isotonic function. A player's payoff is defined as the expected utility received by its supporters. In this work, we first test and validate the isotonicity hypothesis through voting simulations. Next, we prove the existence of a pure-strategy Nash equilibrium (PSNE) in both one- and multi-dimensional settings. Although we construct a counterexample demonstrating the game's non-monotonicity, our experiments show that a decentralized gradient-based algorithm typically converges rapidly to an approximate PSNE. Finally, we present a grid-based search algorithm that finds an $ε$-approximate PSNE of the game in time polynomial in the input size and $1/ε$.

cs.GT↗

arXiv2026

A Computational Analysis of Strategic Nominations: Modeling Equilibrium and Complexity in Organizational Elections

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 two- and three-group elections, finding that a candidates aggregate voter utility correlates monotonically with win probability. For three or more groups, we show that pure-strategy Nash equilibria (PSNE) may fail to exist even under egoistic preferences, and that deciding PSNE existence is NP-complete in a succinct (general form) representation. For cross-monotone winning-probability functions, we give simple sufficient conditions for PSNE existence and an FPT algorithm to compute one, parameterized by the number of irresolute groups and nominating depth. Finally, for crossmonotone, order-preserving winning-probability functions, we bound the price of anarchy of egoistic games by the number of groups.

cs.GT↗

arXiv2024

Robustness of Online Proportional Response in Stochastic Online Fisher Markets: a Decentralized Approach

This study is focused on periodic Fisher markets where items with time-dependent and stochastic values are regularly replenished and buyers aim to maximize their utilities by spending budgets on these items. Traditional approaches of finding a market equilibrium in the single-period Fisher market rely on complete information about buyers' utility functions and budgets. However, it is impractical to consistently enforce buyers to disclose this private information in a periodic setting. We introduce a distributed auction algorithm, online proportional response, wherein buyers update bids solely based on the randomly fluctuating values of items in each period. The market then allocates items based on the bids provided by the buyers. Utilizing the known Shmyrev convex program that characterizes market equilibrium of a Fisher market, two performance metrics are proposed: the fairness regret is the cumulative difference in the objective value of a stochastic Shmyrev convex program between an online algorithm and an offline optimum, and the individual buyer's regret gauges the deviation in terms of utility for each buyer between the online algorithm and the offline optimum. Our algorithm attains a problem-dependent upper bound contingent on the number of items and buyers under stationary inputs in fairness regret. Additionally, we conduct analysis of regret under various non-stationary stochastic input models to demonstrate the algorithm's efficiency across diverse scenarios. The online proportional response algorithm addresses privacy concerns by allowing buyers to update bids without revealing sensitive information and ensures decentralized decision-making, fostering autonomy and potential improvements in buyer satisfaction. Furthermore, our algorithm is universally applicable to many worlds and shows the robust performance guarantees.

cs.GT↗

arXiv2022

Multiagent Learning for Competitive Opinion Optimization

From a perspective of designing or engineering for opinion formation games in social networks, the "opinion maximization (or minimization)" problem has been studied mainly for designing subset selecting algorithms. We define a two-player zero-sum Stackelberg game of competitive opinion optimization by letting the player under study as the leader minimize the sum of expressed opinions by doing so-called "internal opinion design", knowing that the other adversarial player as the follower is to maximize the same objective by also conducting her own internal opinion design. We furthermore consider multiagent learning, specifically using the Optimistic Gradient Descent Ascent, and analyze its convergence to equilibria in the simultaneous version of competitive opinion optimization.

cs.GT↗

arXiv2020

How Good Is a Two-Party Election Game?

In this paper, we propose a simple and intuitive model to investigate the efficiency of the two-party election system, especially regarding the nomination process. Each of the two parties has its own candidates, and each of them brings utilities for the people including the supporters and non-supporters. In an election, each party nominates exactly one of its candidates to compete against the other party's. The candidate wins the election with higher odds if he or she brings more utility for all the people. We model such competition as a "two-party election game" such that each party is a player with two or more pure strategies corresponding to its potential candidates, and the payoff of each party is a mixed utility from a selected pair of competing candidates. By looking into the three models, namely, the linear link, Bradley-Terry, and the softmax models, which differ in how to formulate a candidate's winning odds against the competing candidate, we show that the two-party election game may neither have any pure Nash equilibrium nor a bounded price of anarchy. Nevertheless, by considering the conventional "egoism", which states that any candidate benefits his/her party's supporters more than any candidate from the competing party does, we prove that the two-party election game in both the linear link model and the softmax model always has pure Nash equilibria, and furthermore, the price of anarchy is constantly bounded.

cs.GT↗