Master of Science (MSc)
Faculty of Science
The concept of strict dominance provides a technique that can be used normatively to predict the play of games based only on the assumption of individual rationality. Such predictions, unlike those based on Nash equilibria, do not depend on players’ beliefs about the behaviour of others. One strategy strictly dominates another if and only if the payoff from the first strategy is strictly greater than the payoff from the second, no matter how the opponent(s) plays. It is possible for iterated elimination of strictly dominated strategies to remove all but a single choice for each player, in which case we say that the game is strict-dominance solvable. Analysis of games with continuous strategy spaces reveals necessary and sufficient conditions on the payoff functions for strict-dominance solvability. These conditions will be identified first for symmetric two-player games with quadratic payoff functions, and then extended to higher-order payoff functions and asymmetric games. The conditions discovered can be applied to specific games, producing conclusions that can be compared to other solutions of those games.
Elkington, Andrew Campbell, "Strict-Dominance Solvability of Games on Continuous Strategy Spaces" (2009). Theses and Dissertations (Comprehensive). 907.