AI summaryⓘ
The authors explain that traditional game theory assumes players' thoughts always reflect reality, but in AI systems, these thoughts can disconnect and form stable, self-reinforcing patterns unrelated to the real world. They introduce the Causal Mirage Equilibrium (CME), a new way to describe these detached mental states in games where many similar agents interact and consider risk. The authors prove that such detached states can exist stably and that when self-reinforcement becomes stronger than real-world grounding, the system shifts to these disconnected patterns naturally. This work shows that certain stable yet unrealistic behaviors in AI are not errors but expected outcomes of the system's dynamics.
game theorymean-field gamesequilibrium conceptssemantic representationrisk sensitivityfixed-point theoremepistemic decouplingautoregressive dynamicsmirage intensitybifurcation
Abstract
Classical game-theoretic solution concepts assume that agents' internal representations remain causally linked to external states. In generative machine intelligence, this assumption fails: semantic representations can decouple from physical reality, stabilizing into self-reinforcing, operationally robust configurations. This paper introduces the risk-sensitive mean-field-type \emph{Causal Mirage Equilibrium} (CME), a solution refined concept formalizing endogenous epistemic decoupling within a risk-sensitive mean-field-type game. Unlike Nash, Bayesian, self-confirming, or robust equilibria, CME stabilizes detached semantic representation manifolds rather than optimization strategies or observational beliefs. To quantify this phenomenon, we define a dimensionless parameter, the \emph{mirage intensity} which measures semantic detachment as the ratio of an agent's endogenous reinforcement-confidence product to its causally grounded reality alignment. Under compactness, convexity, and continuity assumptions on the game primitives, we prove the existence of an CME using the Kakutani-Glicksberg-Fan fixed-point theorem on the space of joint probability measures. We establish a non-linear mirage bifurcation theorem: when endogenous reinforcement dominates causal grounding, the unique grounded fixed point becomes unstable, giving rise to a stable invariant manifold of ungrounded states. Our results demonstrate that synthetic consensus and causally detached semantic configurations are not transient optimization anomalies, but structurally stable, risk-aware attractors generated by recursive autoregressive dynamics.