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Game theory and dynamic programming in alternate games

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    * Corresponding author 
The first author is supported by the National Council of Science and Technology (CONACyT) and the National University of Mexico (UNAM).
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  • We present an analysis of different classes of alternate games from different perspectives, including game theory, logic, bounded rationality and dynamic programming. In this paper we review some of these approaches providing a methodological framework which combines ideas from all of them, but emphasizing dynamic programming and game theory. In particular we study the relationship between games in discrete and continuous time and state space and how the latter can be understood as the limit of the former. We show how in some cases the Hamilton-Jacobi-Bellman equation for the discrete version of the game leads to a corresponding HJB partial differential equation for the continuous case and how this procedure allow us to obtain useful information about optimal strategies. This analysis yields another way to compute subgame perfect equilibrium.

    Mathematics Subject Classification: Primary: 91A25, 91B06; Secondary: 91B50.

    Citation:

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  • Figure 1.  Full game tree of dominoes

    Figure 2.  Collapsed game tree for dominoes

    Figure 3.  Full game tree for Jehiel's example

    Figure 4.  Collapsed game tree for Jehiel's example

    Figure 5.  Counting paths

    Figure 6.  Two squared grids $5\times5$ and $10\times10$

    Figure 7.  Two rectangular grids $5\times10$ and $10\times5$

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