Dynamic Programming for Pure-Strategy Subgame Perfection in an Arbitrary Game
Peter Streufert
Papers from arXiv.org
Abstract:
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.
Date: 2023-02, Revised 2023-03
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http://arxiv.org/pdf/2302.03855 Latest version (application/pdf)
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Working Paper: Dynamic Programming for Pure-Strategy Subgame Perfection in an Arbitrary Game (2023)
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