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Yuma Fujimoto

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

7 papers

1 author row

AAMAS Conference 2026 Conference Paper

Time-Varyingness in Auction Breaks Revenue Equivalence

Yuma Fujimoto
Kaito Ariu
Kenshi Abe

The revenue equivalence theorem states that equilibrium revenue is the same across different auction mechanisms, such as first- and second-price ones. However, the environment in the real-world auctions varies over time and can prevent bidders from reaching such an equilibrium. While second-price auctions allow bidders to automatically maintain equilibrium through truthful bidding, firstprice auctions require bidders to track moving equilibria through continuous learning. We demonstrate that this tracking lag breaks revenue equivalence. Which of the first- and second-price auctions yields higher revenue depends on the correlation between the basis value (the standard price to bid) and the value interval (the width of possible values). This study uncovers a novel phenomenon that can be triggered by time-varying environments in real-world auctions.

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AAMAS Conference 2025 Conference Paper

Global Behavior of Learning Dynamics in Zero-Sum Games with Memory Asymmetry

Yuma Fujimoto
Kaito Ariu
Kenshi Abe

This study examines the global behavior of dynamics in learning in games between two players, X and Y. We consider the simplest situation for memory asymmetry between two players: X memorizes the other Y’s previous action and uses reactive strategies, while Y has no memory. Although this memory complicates their learning dynamics, we characterize the global behavior of such complex dynamics by discovering and analyzing two novel quantities. One is an extended Kullback-Leibler divergence from the Nash equilibrium, a well-known conserved quantity from previous studies. The other is a family of Lyapunov functions of X’s reactive strategy. One of the global behaviors we capture is that if X exploits Y, then their strategies converge to the Nash equilibrium. Another is that if Y’s strategy is out of equilibrium, then X becomes more exploitative with time. Consequently, we suggest global convergence to the Nash equilibrium from both aspects of theory and experiment. This study provides a novel characterization of the global behavior in learning in games through a couple of indicators.

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NeurIPS Conference 2025 Conference Paper

Learning from Delayed Feedback in Games via Extra Prediction

Yuma Fujimoto
Kenshi Abe
Kaito Ariu

This study raises and addresses the problem of time-delayed feedback in learning in games. Because learning in games assumes that multiple agents independently learn their strategies, a discrepancy in optimization often emerges among the agents. To overcome this discrepancy, the prediction of the future reward is incorporated into algorithms, typically known as Optimistic Follow-the-Regularized-Leader (OFTRL). However, the time delay in observing the past rewards hinders the prediction. Indeed, this study firstly proves that even a single-step delay worsens the performance of OFTRL from the aspects of social regret and convergence. This study proposes the weighted OFTRL (WOFTRL), where the prediction vector of the next reward in OFTRL is weighted $n$ times. We further capture an intuition that the optimistic weight cancels out this time delay. We prove that when the optimistic weight exceeds the time delay, our WOFTRL recovers the good performances that social regret is constant in general-sum normal-form games, and the strategies last-iterate converge to the Nash equilibrium in poly-matrix zero-sum games. The theoretical results are supported and strengthened by our experiments.

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AAMAS Conference 2025 Conference Paper

Nash Equilibrium and Learning Dynamics in Three-Player Matching m -Action Games

Yuma Fujimoto
Kaito Ariu
Kenshi Abe

Learning in games discusses the processes where multiple players learn their optimal strategies through the repetition of game plays. The dynamics of learning between two players in zero-sum games, such as Matching Pennies, where their benefits are competitive, have already been well analyzed. However, it is still unexplored and challenging to analyze the dynamics of learning among three players. In this study, we formulate a minimalistic game where three players compete to match their actions with one another. Although interaction among three players diversifies and complicates the Nash equilibria, we fully analyze the equilibria. We also discuss the dynamics of learning based on some famous algorithms categorized into Follow the Regularized Leader. From both theoretical and experimental aspects, we characterize the dynamics by categorizing three-player interactions into three forces to synchronize their actions, switch their actions rotationally, and seek competition.

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AAAI Conference 2025 Conference Paper

Synchronization in Learning in Periodic Zero-Sum Games Triggers Divergence from Nash Equilibrium

Yuma Fujimoto
Kaito Ariu
Kenshi Abe

Learning in zero-sum games studies a situation where multiple agents competitively learn their strategy. In such multi-agent learning, we often see that the strategies cycle around their optimum, i.e., Nash equilibrium. When a game periodically varies (called a ``periodic'' game), however, the Nash equilibrium moves generically. How learning dynamics behave in such periodic games is of interest but still unclear. Interestingly, we discover that the behavior is highly dependent on the relationship between the two speeds at which the game changes and at which players learn. We observe that when these two speeds synchronize, the learning dynamics diverge, and their time-average does not converge. Otherwise, the learning dynamics draw complicated cycles, but their time-average converges. Under some assumptions introduced for the dynamical systems analysis, we prove that this behavior occurs. Furthermore, our experiments observe this behavior even if these assumptions are removed. This study discovers a novel phenomenon, i.e., synchronization, and gains insight widely applicable to learning in periodic games.

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AAAI Conference 2024 Conference Paper

Memory Asymmetry Creates Heteroclinic Orbits to Nash Equilibrium in Learning in Zero-Sum Games

Yuma Fujimoto
Kaito Ariu
Kenshi Abe

Learning in games considers how multiple agents maximize their own rewards through repeated games. Memory, an ability that an agent changes his/her action depending on the history of actions in previous games, is often introduced into learning to explore more clever strategies and discuss the decision-making of real agents like humans. However, such games with memory are hard to analyze because they exhibit complex phenomena like chaotic dynamics or divergence from Nash equilibrium. In particular, how asymmetry in memory capacities between agents affects learning in games is still unclear. In response, this study formulates a gradient ascent algorithm in games with asymmetry memory capacities. To obtain theoretical insights into learning dynamics, we first consider a simple case of zero-sum games. We observe complex behavior, where learning dynamics draw a heteroclinic connection from unstable fixed points to stable ones. Despite this complexity, we analyze learning dynamics and prove local convergence to these stable fixed points, i.e., the Nash equilibria. We identify the mechanism driving this convergence: an agent with a longer memory learns to exploit the other, which in turn endows the other's utility function with strict concavity. We further numerically observe such convergence in various initial strategies, action numbers, and memory lengths. This study reveals a novel phenomenon due to memory asymmetry, providing fundamental strides in learning in games and new insights into computing equilibria.

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IJCAI Conference 2023 Conference Paper

Learning in Multi-Memory Games Triggers Complex Dynamics Diverging from Nash Equilibrium

Yuma Fujimoto
Kaito Ariu
Kenshi Abe

Repeated games consider a situation where multiple agents are motivated by their independent rewards throughout learning. In general, the dynamics of their learning become complex. Especially when their rewards compete with each other like zero-sum games, the dynamics often do not converge to their optimum, i. e. , the Nash equilibrium. To tackle such complexity, many studies have understood various learning algorithms as dynamical systems and discovered qualitative insights among the algorithms. However, such studies have yet to handle multi-memory games (where agents can memorize actions they played in the past and choose their actions based on their memories), even though memorization plays a pivotal role in artificial intelligence and interpersonal relationship. This study extends two major learning algorithms in games, i. e. , replicator dynamics and gradient ascent, into multi-memory games. Then, we prove their dynamics are identical. Furthermore, theoretically and experimentally, we clarify that the learning dynamics diverge from the Nash equilibrium in multi-memory zero-sum games and reach heteroclinic cycles (sojourn longer around the boundary of the strategy space), providing a fundamental advance in learning in games.

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