Yasushi Kawase

Shunta Akiyama, Mitsuaki Obara, Yasushi Kawase

Lotteries are a prevalent form of gambling between a seller and buyers. Designing a lottery requires a model of how buyers make decisions when confronted with uncertain outcomes. Cumulative prospect theory (CPT) is a descriptive model that captures people's propensity to overestimate extreme events and their different attitudes toward gains and losses. In this study, we design a lottery that maximizes the seller's profit when the buyers' decision-making adheres to the CPT framework. The main difficulty is the nonconvexity of the CPT framework, which we overcome by reformulating the problem as a three-level optimization problem and characterizing its optimal solution. Based on the analysis, we propose a linear-time algorithm that computes the optimal lottery. Furthermore, we present an efficient algorithm applicable to a broader setting with a ticket price constraint. This is the first study to employ the CPT framework in designing an optimal lottery with more than two outcomes.

Yasushi Kawase, Warut Suksompong, Hanna Sumita et al.

In random assignment, fairness is often captured by stochastic-dominance envy-freeness (SD-EF). We observe that assignments satisfying SD-EF may admit decompositions that result in each agent envying another agent with high probability. To address this, we introduce decomposition envy-freeness (Dec-EF), which is a property of a decomposition rather than of an assignment matrix. We show that an SD-EF assignment matrix always admits a Dec-EF decomposition when there are at most three agents or the agents have at most two distinct preferences.

Tsubasa Harada, Yasushi Kawase, Hanna Sumita

We study the repeated optimal stopping problem, which generalizes the classical optimal stopping problem with an unknown distribution to a setting where the same problem is solved repeatedly over $T$ rounds. In this framework, we aim to design algorithms that guarantee a competitive ratio in each round while also achieving sublinear regret across all rounds. Our primary contribution is a general algorithmic framework that achieves these objectives simultaneously for a wide array of repeated optimal stopping problems. The core idea is to dynamically select an algorithm for each round, choosing between two candidates: (1) an empirically optimal algorithm derived from the history of observations, and (2) a sample-based algorithm with a proven competitive ratio guarantee. Based on this approach, we design an algorithm that performs no worse than the baseline sample-based algorithm in every round, while ensuring that the total regret is bounded by $\tilde{O}(\sqrt{T})$. We demonstrate the broad applicability of our framework to canonical problems, including the prophet inequality, the secretary problem, and their variants under adversarial, random, and i.i.d. input models. For example, for the repeated prophet inequality problem, our method achieves a $1/2$-competitive ratio from the second round on and an $\tilde{O}(\sqrt{T})$ regret. Furthermore, we establish a regret lower bound of $Ω(\sqrt{T})$ even in the i.i.d. model, confirming that our algorithm's performance is almost optimal with respect to the number of rounds.

Yasushi Kawase, Ryoga Mahara

We study the problem of allocating indivisible goods among agents with additive valuation functions to achieve both fairness and efficiency under the constraint that each agent receives exactly the same number of goods (the \emph{balanced constraint}). While this constraint is common in real-world scenarios such as team drafts or asset division, it significantly complicates the search for allocations that are both fair and efficient. Envy-freeness up to one good (EF1) is a well-established fairness notion for indivisible goods. Pareto optimality (PO) and its stronger variant, fractional Pareto optimality (fPO), are widely accepted efficiency criteria. Our main contribution establishes both the existence and polynomial-time computability of allocations that are simultaneously EF1 and fPO under balanced constraints in two fundamental cases: (1) when each agent has a personalized bivalued valuation, and (2) when agents have at most two distinct valuation types,. Our algorithms leverage novel applications of maximum-weight matching in bipartite graphs and duality theory, providing the first polynomial-time solutions for these cases and offering new insights for constrained fair division problems.

Yasushi Kawase, Bodhayan Roy, Mohammad Azharuddin Sanpui

This paper explores the fair allocation of indivisible items in a multidimensional setting, motivated by the need to address fairness in complex environments where agents assess bundles according to multiple criteria. Such multidimensional settings are not merely of theoretical interest but are central to many real-world applications. For example, cloud computing resources are evaluated based on multiple criteria such as CPU cores, memory, and network bandwidth. In such cases, traditional one dimensional fairness notions fail to capture fairness across multiple attributes. To address these challenges, we study two relaxed variants of envy-freeness: weak simultaneously envy-free up to c goods (weak sEFc) and strong simultaneously envy-free up to c goods (strong sEFc), which accommodate the multidimensionality of agents' preferences. Under the weak notion, for every pair of agents and for each dimension, any perceived envy can be eliminated by removing, if necessary, a different set of goods from the envied agent's allocation. In contrast, the strong version requires selecting a single set of goods whose removal from the envied bundle simultaneously eliminates envy in every dimension. We provide upper and lower bounds on the relaxation parameter c that guarantee the existence of weak or strong sEFc allocations, where these bounds are independent of the total number of items. In addition, we present algorithms for checking whether a weak or strong sEFc allocation exists. Moreover, we establish NP-hardness results for checking the existence of weak sEF1 and strong sEF1 allocations.

Yasushi Kawase, Bodhayan Roy, Mohammad Azharuddin Sanpui

A Latin square is an $n \times n$ matrix filled with $n$ distinct symbols, each of which appears exactly once in each row and exactly once in each column. We introduce a problem of allocating $n$ indivisible items among $n$ agents over $n$ rounds while satisfying the Latin square constraint. This constraint ensures that each agent receives no more than one item per round and receives each item at most once. Each agent has an additive valuation on the item--round pairs. Real-world applications like scheduling, resource management, and experimental design require the Latin square constraint to satisfy fairness or balancedness in allocation. Our goal is to find a partial or complete allocation that maximizes the sum of the agents' valuations (utilitarian social welfare) or the minimum of the agents' valuations (egalitarian social welfare). For the problem of maximizing utilitarian social welfare, we prove NP-hardness even when the valuations are binary additive. We then provide $(1-1/e)$ and $(1-1/e)/4$-approximation algorithms for partial and complete settings, respectively. Additionally, we present fixed-parameter tractable (FPT) algorithms with respect to the order of Latin square and the optimum value for both partial and complete settings. For the problem of maximizing egalitarian social welfare, we establish that deciding whether the optimum value is at most $1$ or at least $2$ is NP-hard for both the partial and complete settings, even when the valuations are binary. Furthermore, we demonstrate that checking the existence of a complete allocation that satisfies each of envy-free, proportional, equitable, envy-free up to any good, proportional up to any good, or equitable up to any good is NP-hard, even when the valuations are identical.

Yasushi Kawase, Yuko Kuroki, Atsushi Miyauchi

Aggregating responses from crowd workers is a fundamental task in the process of crowdsourcing. In cases where a few experts are overwhelmed by a large number of non-experts, most answer aggregation algorithms such as the majority voting fail to identify the correct answers. Therefore, it is crucial to extract reliable experts from the crowd workers. In this study, we introduce the notion of "expert core", which is a set of workers that is very unlikely to contain a non-expert. We design a graph-mining-based efficient algorithm that exactly computes the expert core. To answer the aggregation task, we propose two types of algorithms. The first one incorporates the expert core into existing answer aggregation algorithms such as the majority voting, whereas the second one utilizes information provided by the expert core extraction algorithm pertaining to the reliability of workers. We then give a theoretical justification for the first type of algorithm. Computational experiments using synthetic and real-world datasets demonstrate that our proposed answer aggregation algorithms outperform state-of-the-art algorithms.