Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/297766 
Year of Publication: 
2023
Series/Report no.: 
Research Report No. 2023-3
Publisher: 
The University of Western Ontario, Department of Economics, London (Ontario)
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.
Subjects: 
Bellman equation
value function
upper-convergence
lower-convergence
pentaform
JEL: 
C61
C73
Document Type: 
Working Paper

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