Heuristics, Optimization, and Equilibrium Analysis for Automated Wargames
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In this thesis, we transform a paper-based wargame into a computer-based one using Matlab programming and its graphical user interface (GUI). Since such wargames usually consist of at most thirty-two turns, the number of stages is "finite,'' and thus we provide an algorithm to solve the gaming using backward induction. However, due to the complexity of the wargaming structure, the backward induction algorithm may not be sufficiently efficient in solving some complicated wargames involving large number of players, player options, system states, mission types, and uncertainties of operation/campaign results. Therefore, instead of solving the wargame completely, we develop and analyze heuristics, which are used to an existing six-player wargame and a simplified version of two-player wargame. For each wargame, we define the game rules, design 2–4 heuristics for each of the players, develop interfaces with user inputs and automation, and run the simulation 1,000 times for each possible combinations of different players' heuristics. In particular, first, for the two-player wargame, we design three heuristics for Player 1 (prioritization based on location, population types, and randomized mission types), and two heuristics for Player 2 (prioritization based on location, and population types). We use the simulation results (winning frequencies for each of the players) as payoffs to calculate the players' best-response functions and the (mixed-strategy) equilibrium solutions. Second, for the six-player wargame, we use human player's experiences to improve Player 1's heuristics. In particular, Player 1 not only maximizes his short-term payoffs by assigning faction to population cards, but also preventing other players from winning by destroying their resources, especially when the other players are close to their victory conditions. Our simulation results show that the improved heuristics would: (a) increase Player 1's equilibrium winning frequencies from 25% to 90%; (b) increase Player 1's average period payoffs from about 60 to 70; and (c) decrease the average game periods before the game ends, leading Player 1 to win the game faster. Our research provides some novel insights for advancing automated wargaming.