Evaluation Functions in General Game Playing

While in traditional computer game playing agents were designed solely for the purpose of playing one single game, General Game Playing is concerned with agents capable of playing classes of games. Given the game's rules and a few minutes time, the agent is supposed to play any game of the class and eventually win it. Since the game is unknown beforehand, previously optimized data structures or human-provided features are not applicable. Instead, the agent must derive a strategy on its own. One approach to obtain such a strategy is to analyze the game rules and create a state evaluation function that can be subsequently used to direct the agent to promising states in the match. In this thesis we will discuss existing methods and present a general approach on how to construct such an evaluation function. Each topic is discussed in a modular fashion and evaluated along the lines of quality and efficiency, resulting in a strong agent.:Introduction Game Playing Evaluation Functions I - Aggregation Evaluation Functions II - Features General Evaluation Related Work Discussio

Automated Theorem Proving for General Game Playing

While automated game playing systems like Deep Blue perform excellent within their domain, handling a different game or even a slight change of rules is impossible without intervention of the programmer. Considered a great challenge for Artificial Intelligence, General Game Playing is concerned with the development of techniques that enable computer programs to play arbitrary, possibly unknown n-player games given nothing but the game rules in a tailor-made description language. A key to success in this endeavour is the ability to reliably extract hidden game-specific features from a given game description automatically. An informed general game player can efficiently play a game by exploiting structural game properties to choose the currently most appropriate algorithm, to construct a suited heuristic, or to apply techniques that reduce the search space. In addition, an automated method for property extraction can provide valuable assistance for the discovery of specification bugs during game design by providing information about the mechanics of the currently specified game description. The recent extension of the description language to games with incomplete information and elements of chance further induces the need for the detection of game properties involving player knowledge in several stages of the game. In this thesis, we develop a formal proof method for the automatic acquisition of rich game-specific invariance properties. To this end, we first introduce a simple yet expressive property description language to address knowledge-free game properties which may involve arbitrary finite sequences of successive game states. We specify a semantic based on state transition systems over the Game Description Language, and develop a provably correct formal theory which allows to show the validity of game properties with respect to their semantic across all reachable game states. Our proof theory does not require to visit every single reachable state. Instead, it applies an induction principle on the game rules based on the generation of answer set programs, allowing to apply any off-the-shelf answer set solver to practically verify invariance properties even in complex games whose state space cannot totally be explored. To account for the recent extension of the description language to games with incomplete information and elements of chance, we correctly extend our induction method to properties involving player knowledge. With an extensive evaluation we show its practical applicability even in complex games

Empirical Game-Theoretic Methods for Strategy Design and Analysis in Complex Games.

Complex multi-agent systems often are not amenable to standard game-theoretic analysis. I study methods for strategic reasoning that scale to more complex interactions, drawing on computational and empirical techniques. Several recent studies have applied simulation to estimate game models, using a methodology known as empirical game-theoretic analysis. I report a successful application of this methodology to the Trading Agent Competition Supply Chain Management game. Game theory has previously played little—if any—role in analyzing this scenario, or others like it. In the rest of the thesis, I perform broader evaluations of empirical game analysis methods using a novel experimental framework. I introduce meta-games to model situations where players make strategy choices based on estimated game models. Each player chooses a meta-strategy, which is a general method for strategy selection that can be applied to a class of games. These meta-strategies can be used to select strategies based on empirical models, such as an estimated payoff matrix. I investigate candidate meta-strategies experimentally, testing them across different classes of games and observation models to identify general performance patterns. For example, I show that the strategy choices made using a naive equilibrium model quickly degrade in quality as observation noise is introduced. I analyze three families of meta-strategies that predict distributions of play, each interpolating between uninformed and naive equilibrium predictions using a single parameter. These strategy spaces improve on the naive method, capturing (to some degree) the effects of observation uncertainty. Of these candidates, I identify logit equilibrium as the champion, supported by considerable evidence that its predictions generalize across many contexts. I also evaluate exploration policies for directing game simulations on two tasks: equilibrium confirmation and strategy selection. Policies based on computing best responses are able to exploit a variety of structural properties to confirm equilibria with limited payoff evidence. A novel policy I propose—subgame best-response dynamics—improves previous methods for this task by confirming mixed equilibria in addition to pure equilibria. I apply meta-strategy analysis to show that these exploration policies can improve the strategy selections of logit equilibrium.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/61590/1/ckiekint_1.pd