Disc Game Dynamics: A Latent Space Perspective on Selection and Learning in Games
Pablo Lechon-Alonso, Andrew Dennehy, Ruizheng Bai, Nicolas Sanchez, Derek K. Wise, David Sewell, David Rosenbluth, Alexander Strang

TL;DR
This paper introduces a latent space representation for symmetric zero-sum games, enabling simplified analysis of learning dynamics and revealing Hamiltonian structures in evolutionary processes.
Contribution
It develops a novel disc game embedding that transforms complex game dynamics into linear combinations of simple games, facilitating analysis and numerical simulation.
Findings
Replicator dynamics reduce to Hamiltonian oscillators in latent space
Exact finite-dimensional closure for finite-rank games
Embedding generalizes to metapopulation and differentiable dynamics
Abstract
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 axiomatically derive a latent space representation for pairwise, symmetric, zero-sum games by seeking a coordinate space in which the optimal training direction for an agent responding to an opponent depends only on their opponent's coordinates. The associated embedding represents the original game as a linear combination of copies of a simple game, the disc game, in a new coordinate space. In this article, we show that disc-game embedding is useful for studying learning dynamics. We demonstrate that a series of classical evolutionary processes simplify to constrained oscillator equations in the latent space. In particular, the continuous replicator equation…
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Taxonomy
TopicsEvolutionary Game Theory and Cooperation · Game Theory and Applications · Experimental Behavioral Economics Studies
