{"id":"hexagon/2610.00257","pdf":"https://hexagonmath.org/pdf/2610.00257v1","url":"https://hexagonmath.org/abs/2610.00257v1","tags":["math.CA","msc:91A10"],"score":0,"title":"Sequential Games","domain":"math.FA","origin":"ai-generated","source":"hexagon","authors":["Rajesh Dachiraju"],"reviews":0,"subject":"math.FA","summary":"We formulate a time-series game in which each player chooses a hidden Markov model (HMM) as a mixed strategy. The HMM generates a finite, variable-length sequence of probability vectors, and the payoff is assigned to the completed game as the sum of its stage rewards. We prove a conditional Nash-equilibrium existence result for games with a common finite bound on output lengths. The proof applies a fixed-point argument to the best-response correspondence when each player's admissible HMM-density set is nonempty, convex, and compact in $(L^1)$, and the completed-game payoff is bounded and…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-15","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}