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We discuss how mathematical semantics has evolved, and suggest some new directions for future work. As an example, we discuss some recent work on encapsulating model comparison games as comonads, in the context of finite model theory.
We prove a theorem computing the number of solutions to a system of equations which is generic subject to the sparsity conditions embodied in a graph. We apply this theorem to games obeying graphical models and to extensive-form games. We…
We investigate uniformity properties of strategies. These properties involve sets of plays in order to express useful constraints on strategies that are not \mu-calculus definable. Typically, we can state that a strategy is…
Pursuing a new approach to the study of infinite games in combinatorics, we introduce the categories $\mathbf{Game}_{A}$ and $\mathbf{Game}_{B}$ and improve some classical results concerning topological games related to the duality between…
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
We exhibit the proximity frames and proximity homomorphisms as a Kleisli category of a comonad whose underlying functor takes a proximity frame to its frame of round ideals. This construction is known in the literature as {\em stable…
We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose…
We construct witnesses that can be used to derive strategies in fixpoint games and provide proof that the least fixpoint of a function is either above or not below some given bound. We rely on a lattice-theoretical approach, including a…
We study strong equilibria in symmetric capacitated cost-sharing games. In these games, a graph with designated source $s$ and sink $t$ is given, and each edge is associated with some cost. Each agent chooses strategically an $s$-$t$ path,…
We consider turn-based game arenas for which we investigate uniformity properties of strategies. These properties involve bundles of plays, that arise from some semantical motive. Typically, we can represent constraints on allowed…
In this paper, we consider combinatorial game rulesets based on data structures normally covered in an undergraduate Computer Science Data Structures course: arrays, stacks, queues, priority queues, sets, linked lists, and binary trees. We…
We introduce a new class of games where each player's aim is to randomise her strategic choices in order to affect the other players' expectations aside from her own. The way each player intends to exert this influence is expressed through…
This study utilizes the game Codenames as a benchmarking tool to evaluate large language models (LLMs) with respect to specific linguistic and cognitive skills. LLMs play each side of the game, where one side generates a clue word covering…
We study games in which every action requires planning and preparation. Moreover, before players act, they can revise their plans based on partially revealing information that they receive on their adversary's preparations. In turn, we…
Evolutionary game theory studies populations that change in response to an underlying game. Often, the functional form relating outcome to player attributes or strategy is complex, preventing mathematical progress. In this work, we…
This paper is a fundamental study of comodules and contramodules over a comonoid in a symmetric closed monoidal category. We study both algebraic and homotopical aspects of them. Algebraically, we enrich the comodule and contramodule…
We consider a repeated sequential game between a learner, who plays first, and an opponent who responds to the chosen action. We seek to design strategies for the learner to successfully interact with the opponent. While most previous…
We study coalition structure formation with intra and inter-coalition externalities in the introduced family of nested non-cooperative simultaneous finite games. A non-cooperative game embeds a coalition structure formation mechanism, and…
One goal of applied category theory is to better understand networks appearing throughout science and engineering. Here we introduce "structured cospans" as a way to study networks with inputs and outputs. Given a functor $L \colon…
We use replicator dynamics to study an iterated prisoners' dilemma game with memory. In this study, we investigate the characteristics of all 32 possible strategies with a single-step memory by observing the results when each strategy…