Game Theory Analysis of The Settlers of Catan: The Optimal Solver Through Theoretical Model

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Jefray Ding, Mark Ma, Thienkingkeaw Porpun

May 20, 2024

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Game Theory has seen increasing applications in economics, social and behavioral sciences, and, more recently, artificial intelligence. To explore how AI combined with Game Theory can model and enhance the strategies of colonists during the Partition of Africa, which was driven by new imperialism, we ran simulations using the framework of the board game ”The Settlers of Catan.” This non-deterministic, multi-player game involves numerous branching options that satisfy trading, ports, settlements, and roads, analogous to the strategic considerations in Africa at the turn of the 20th century. To determine the optimal course of action, we utilized the MiniMax algorithm as the primary decision-making structure, supplemented by Alpha-Beta Pruning to analyze multiple moves ahead (search depth) and identify actions leading to the most advantageous board state (closest to victory). We assigned assumed values for various board conditions to construct payouts for each board layout (value functions) and adjusted them based on win rates during benchmarks. We developed a Catan game in Java featuring two types of play-testing players: the Complete Random player and the Weighted Random player. Based on our solver, our results show that the player achieved a 84% win rate in 2000 games against a weighted random player using a normal distribution. Expanding the scope of data-driven value functions in different contexts, particularly with multiple agents instead of just two, will further enhance our understanding of colonial economics and expansion strategies.

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