Modeling Precomputation In Games Played Under Computational Constraints
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Understanding the properties of games played under computational constraints remains challenging. For example, how do we expect rational (but computationally bounded) players to play games with a prohibitively large number of states, such as chess? This paper presents a novel model for the precomputation (preparing moves in advance) aspect of computationally constrained games. A fundamental trade-off is shown between randomness of play, and susceptibility to precomputation, suggesting that randomization is necessary in games with computational constraints. We present efficient algorithms for computing how susceptible a strategy is to precomputation, and computing an ϵ-Nash equilibrium of our model. Numerical experiments measuring the trade-off between randomness and precomputation are provided for Stockfish (a well-known chess playing algorithm).
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