Game-Theoretic Multi-LLM Routing for Safer Agents in the Wild

We propose \textsc{SRLA} (Stackelberg-Routed Leverage-Score Aggregation), a multi-LLM framework in which routing, traffic equilibrium, and output aggregation each carry a game-theoretic guarantee. We model the agent population as a routing graph whose node latencies combine prediction loss and congestion: a Stackelberg-pinned parallel-path topology bounds the price of anarchy by a constant, and online gradient descent on the mixture log-loss converges to a proximal correlated equilibrium with rank-dependent regret. The same bounds yield concrete \emph{safety} and \emph{fairness} properties: the price-of-anarchy bound caps any single agent's worst-case influence on the system, so a misbehaving or compromised agent cannot dominate the decisions. The proximal correlated equilibrium and the leverage-score weighting together certify $\delta$-robustness of the deployed weights and resist the failure mode in which a single overconfident, biased agent hijacks the ensemble.