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Sequential Games

A mix of human-written and AI-generated textHuman understanding: some partsmath.FA — Functional Analysismath.CA — Classical Analysis and ODEs

Contributed by Rajesh Dachiraju ↗

Version 2 / Oct 15, 2026 / CC BY 4.0

Abstract

We formulate sequential games in which HMMs generate finite sequences of probability vectors, and players may randomize over HMMs. Payoffs are assumed to be BV for these games. For a fixed finite state space and horizon, compact symbol-emission density families with a common BV bound generate compact sets of sequence densities; arbitrary HMM mixtures make the strategy-density sets compact and convex.Kakutani's theorem yields a Nash equilibrium.

Provenance statement

ChatGPT was used to prepare this document.

References

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  7. Shapley, Lloyd S. Stochastic Games. Proceedings of the National Academy of Sciences, vol. 39, no. 10, pp. 1095–1100. 1953DOI

Version history

  1. v1Submitted by Rajesh DachirajuInitial depositSupersededOct 15, 2026
  2. v2Submitted by Rajesh DachirajuSubmitted as a new versionCurrentOct 25, 2026