In this project, we address the relationship between generative AI and principles of play from a posthuman perspective, drawing on our work in Language-Based Artistic Research. We position Language Arts as a committed expressive practice that is productively distinct from creative writing while capable of generating insights relevant both within artistic domains and beyond. Moving past binary positions of technological apocalypse or uncritical affirmation, we adopt an artistically reflexive approach to generative AI and its cultural, particularly posthuman, implications. To illustrate this relationship, we experiment with large and small language models trained to play a game based on the structure of "Who am I," the experience of which we will demonstrate during our presentation. This approach addresses not only the linguistic expression and linguistic constitution of identity but also examines the underlying principles of play itself. Our artistic research draws on James P. Carse’s (1986) and Simon Sinek’s (2019) models of finite and infinite games and explores the challenges of relating these artistic and theoretical frameworks to one another. In our experimental setting—alongside philosophical considerations, game-related elements such as rules and improvisation, and combinatorial aesthetics—we focus on two key areas for artistic investigation through a posthuman lens: First, we explore principles of playful, polyvalent experimentation that resist orientation toward reproducible results or unambiguous truths in a scientific sense. Second, following Johanna Drucker's reflections (2023), we examine the concept of agency as a more relevant focus for AI than intelligence or sentience, distinguishing between AI's core functions of synthesis and simulation and acknowledging that AI's capabilities align more closely with pattern-based processes than with the human concept of creativity. Through this methodological constellation, we combine our fundamental positioning in Language-Based Artistic Research with game theory frameworks to question how generative AI engages with concepts of playability and artificially generated identities. This research contributes to emerging conversations about the nature of machine agency and the evolving boundaries between human and machine-generated expression.