arXiv subjects

Motoki Otsuka

Publications and source records attributed to Motoki Otsuka.

3 recordsLinked to original sources

arXiv2026

Banach-valued graph limits: Graphon representability and Banach-space structure

We study a graph-limit problem for Banach-decorated graphs. Given a sequence of $X$-decorated graphs whose homomorphism densities converge against all $X^*$-decorated test graphs, we ask whether the limiting densities are represented by an $X$-valued graphon. The results connect this graph-limit problem with Banach-space structure. If $X^*$ is separable, then the graphon representation property for graph sequences uniformly bounded in $L^p$ for every finite $p$ holds if and only if $X$ is reflexive. For Banach lattices, it is equivalent to the Radon--Nikod\'ym property. For dual Banach spaces, it is equivalent to the conjunction of the Radon--Nikod\'ym property and weak sequential completeness. In the bounded setting, the same characterization extends to arbitrary Banach spaces: for every Banach space $X$, the representation property for uniformly $L^\infty$-bounded graph sequences holds if and only if $X$ has the Radon--Nikod\'ym property and is weakly sequentially complete.

math.FA↗

arXiv2025

Regularity properties of distributions of correspondences without countable generation: applications to large games

We show that each of the regularity properties of regular conditional distributions of correspondences (convexity, closedness, compactness, and preservation of closed graphs) is equivalent to the condition of nowhere equivalence. This result does not require any countable-generation assumptions. As an application, we establish the existence of a pure-strategy equilibrium for large games with general trait spaces. The trait space may be an arbitrary measurable space. As a corollary, we obtain the existence of a pure-strategy equilibrium in semi-anonymous settings in which payoffs depend, in addition to agents' own actions, on the joint distribution over the space of agents and actions.

math.PR↗

arXiv2025

Graphon games and an idealized limit of large network games

Graphon games are a class of games with a continuum of agents, introduced to approximate the strategic interactions in large network games. The first result of this study is an equilibrium existence theorem in graphon games, under the same conditions as those in network games. We prove the existence of an equilibrium in a graphon game with an infinite-dimensional strategy space, under the continuity and quasi-concavity of the utility functions. The second result characterizes Nash equilibria in graphon games as the limit points of asymptotic Nash equilibria in large network games. If a sequence of large network games converges to a graphon game, any convergent sequence of asymptotic Nash equilibria in these large network games also converges to a Nash equilibrium of the graphon game. In addition, for any graphon game and its equilibrium, there exists a sequence of large network games that converges to the graphon game and has asymptotic Nash equilibria converging to the equilibrium. These results suggest that the concept of a graphon game is an idealized limit of large network games as the number of players tends to infinity.

econ.TH↗