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This paper uses category theory to develop an entirely new approach to approximate game theory. Game theory is the study of how different agents within a multi-agent system take decisions. At its core, game theory asks what an optimal…
The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by…
We study stochastic evolution of optional games on simple graphs. There are two strategies, A and B, whose interaction is described by a general payoff matrix. In addition there are one or several possibilities to opt out from the game by…
The aim of this note is to investigate the open-open game of uncountable length. We introduce a cardinal number $\mu(X)$, which says how long the Player I has to play to ensure a victory. It is proved that $\su(X)\leq\mu(X)\leq\su(X)^+$. We…
This paper extends and generalizes the well-known cut-matching game framework and provides a novel cut-strategy that produces constant-hop expanders. Constant-hop expanders are a significant strengthening of regular expanders with the…
This paper proposes concentrated geo-privacy (CGP), a privacy notion that can be considered as the counterpart of concentrated differential privacy (CDP) for geometric data. Compared with the previous notion of geo-privacy [ABCP13, CABP13],…
In this paper, authors prove that if $X$ is a weak Asplund space, then the space $X\times R$ is a weak Asplund space. Thus the author definitely answered an open problem raised by D.G. Larman and R.R. Phelps for 45 years ago (J. London.…
We survey discrete and continuous model-theoretic notions which have important connections to general topology. We present a self-contained exposition of several interactions between continuous logic and $C_p$-theory which have applications…
In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as…
Constrained Markov games offer a formal mathematical framework for modeling multi-agent reinforcement learning problems where the behavior of the agents is subject to constraints. In this work, we focus on the recently introduced class of…
The famous Michael selection theorem deals with the characterisation of paracompact spaces by continuous selections of lower semi-continuous mappings in Banach spaces. In this paper, we will discuss several equivalent forms of this theorem,…
This paper focuses on the relation among the existence of different types of curves (such as directional ones, quasi-geodesic or geodesic rays), the (approximate) fixed point property for nonexpansive mappings, and a discrete lion and man…
We investigate combinatorial issues relating to the use of random orbit approximations to the attractor of an iterated function system with the aim of clarifying the role of the stochastic process during generation the orbit. A Baire…
$c$-realcompact spaces are introduced by Karamzadeh and Keshtkar in Quaest. Math. 41(8), 2018, 1135-1167. We offer a characterization of these spaces $X$ via $c$-stable family of closed sets in $X$ by showing that $X$ is $c$-realcompact if…
In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…
This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [4] to…
The way that people make choices or exhibit preferences can be strongly affected by the set of available alternatives, often called the choice set. Furthermore, there are usually heterogeneous preferences, either at an individual level…
The literature on dynamic discrete games often assumes that the conditional choice probabilities and the state transition probabilities are homogeneous across markets and over time. We refer to this as the "homogeneity assumption" in…
In this paper we continue to study the property of separability of functional space C(X) with the open-point and bi-point-open topologies.
In this paper we study connections between topological games such as Rothberger, Menger and compact-open, and relate these games to properties involving covers by G_{\delta} subsets. The results include: (1) If Two has a winning strategy in…