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Life sciences · Preprint
arXiv · August 13, 2026
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This is a preprint presenting theoretical results on the relationship between ordinal preferences in games and the asymptotic behavior of no-regret learning dynamics. The authors show that dynamic stability implies preference stability, but the converse fails in general; they propose resilience under aggregate deviations as a payoff-based condition sufficient for asymptotic stability. The work is foundational and mathematical, raising and partially resolving open questions in multi-agent learning theory rather than providing empirical evidence for clinical or practical application.
Preprint.
The skeleton of every dynamically stable set must be preferentially stable (closed under profitable deviations). Preferences characterize asymptotic stability in subgames (subsets obtained by restricting players' action sets). A three-player counterexample demonstrates that preferences do not suffice for dynamic stability of arbitrary spans of pure strategies.
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This is a theoretical analysis of game dynamics and preference-based solution concepts with no empirical data, experimental validation, or clinical application; it raises mathematical questions about when preferences predict learning outcomes rather than answering them with evidence.
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We examine the interplay between ordinal, preference-based solution concepts in games and the long-run behavior of game dynamics, asking in particular to what extent the combinatorial data of a game -- its preference graph -- determine the outcomes of no-regret learning dynamics -- such as follow-the-regularized-leader (FTRL). In one direction, we show that the skeleton of every dynamically stable set (i.e. the set of pure profiles it contains) must also be preferentially stable, that is, it must be closed under profitable deviations. We then ask the converse question: when do preferences determine the long-run behavior of the players' learning dynamics? We begin by showing that preferences characterize asymptotic stability in the case of subgames -- i.e. subsets of pure profiles obtained by restricting players' action sets. Beyond this case however, the equivalence between dynamic and preferential stability collapses: concretely, we construct a three-player game with a preferentially stable set whose span is dynamically unstable, showing in this way that preferences do not suffice as a criterion of dynamic stability. We then bridge this gap via the notion of resilience under aggregate deviations, an easy-to-check payoff-based condition that guarantees asymptotic stability of arbitrary spans of pure strategies.
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