Predicting Dominance Rankings for Score-Based Games

Game competitions may involve different player roles and be score-based rather than win/loss based. This raises the issue of how best to draw opponents for matches in ongoing competitions, and how best to rank the players in each role. An example is the Ms Pac-Man versus Ghosts Competition which requires competitors to develop software controllers to take charge of the game's protagonists: participants may develop software controllers for either or both Ms Pac-Man and the team of four ghosts. In this paper, we compare two ranking schemes for win-loss games, Bayes Elo and Glicko. We convert the game into one of win-loss ("dominance") by matching controllers of identical type against the same opponent in a series of pair-wise comparisons. This implicitly creates a "solution concept" as to what a constitutes a good player. We analyze how many games are needed under two popular ranking algorithms, Glicko and Bayes Elo, before one can infer the strength of the players, according to our proposed solution concept, without performing an exhaustive evaluation. We show that Glicko should be the method of choice for online score-based game competitions.