Game Balancing using Koopman-based Learning

This paper addresses the analysis of how the outcome of a zero-sum two-player game is affected by the value of numerical parameters that are part of the game rules and/or winning criterion. This analysis aims at selecting numerical values for such parameters that lead to games that are “fair” or “balanced” in spite of the fact that the two players may have distinct attributes/capabilities. Motivated by applications of game balancing for the commercial gaming industry, our effort is focused on complex multi-agent games for which low-dimensional models in the form of differential or difference equations are not possible or not available. To overcome this challenge, we use a parameter-dependent Koopman operator to model the game evolution, which we train using an ensemble of simulation traces of the actual game. This model is subsequently used to determine values for the game parameters that optimize the appropriate game balancing criterion. The approach proposed here is illustrated and validated on a minigame derived from the StarCraft II real-time strategy game from Blizzard Entertainment.

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