2023/02/08 by Peter A. Streufert, Streufert, Peter A.
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #90C39 #91A18 #Computer Science and Game Theory (cs.GT) #Economic theories and models #Experimental Behavioral Economics Studies #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Game Theory and Applications #Optimization and Control (math.OC) #Theoretical Economics (econ.TH)
paper · pdf · doi:10.48550/arxiv.2302.03855
openalex publication_date 2023/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper uses value functions to characterize the pure-strategy subgame-perfect equilibria of an arbitrary, possibly infinite-horizon game. It specifies the game's extensive form as a pentaform (Streufert 2023p, arXiv:2107.10801v4), which is a set of quintuples formalizing the abstract relationships between nodes, actions, players, and situations (situations generalize information sets). Because a pentaform is a set, this paper can explicitly partition the game form into piece forms, each of which starts at a (Selten) subroot and contains all subsequent nodes except those that follow a subsequent subroot. Then the set of subroots becomes the domain of a value function, and the piece-form partition becomes the framework for a value recursion which generalizes the Bellman equation from dynamic programming. The main results connect the value recursion with the subgame-perfect equilibria of the original game, under the assumptions of upper- and lower-convergence. Finally, a corollary characterizes subgame perfection as the absence of an improving one-piece deviation.