General Game Research Articles

Strategic Teaching and Learning in Games

It is known that there are uncoupled learning heuristics leading to Nash equilibrium in all finite games. Why should players use such learning heuristics and where could they come from? We show that there is no uncoupled learning heuristic leading to Nash equilibrium in all finite games that a player has an incentive to adopt, that would be evolutionary stable or that could learn itself. Rather, a player has an incentive to teach such a learning opponent in order secure at least the Stackelberg leader payoff. The impossibility result remains intact when restricted to the classes of generic games, two-player games, potential games, games with strategic complements or 2 x 2 games, in which learning is known to be nice. More generally, it also applies to uncoupled learning heuristics leading to correlated equilibria, rationalizable outcomes, iterated admissible outcomes, or minimal curb sets. A possibility result restricted to strategically trivial games fails if some generic games outside this class are considered as well.

Understanding hermaphrodite species through game theory.

We investigate the existence and stability of sexual strategies (sequential hermaphrodite, successive hermaphrodite or gonochore) at a proximate level. To accomplish this, we constructed and analyzed a general dynamical game model structured by size and sex. Our main objective is to study how costs of changing sex and of sexual competition should shape the sexual behavior of a hermaphrodite. We prove that, at the proximate level, size alone is insufficient to explain the tendency for a pair of prospective copulants to elect the male sexual role by virtue of the disparity in the energetic costs of eggs and sperm. In fact, we show that the stability of sequential vs. simultaneous hermaphrodite depends on sex change costs, while the stability of protandrous vs. protogynous strategies depends on competition cost.

Lifting Model Sampling for General Game Playing to Incomplete-Information Models

General Game Playing is the design of AI systems able to understand the rules of new games and to use such descriptions to play those games effectively. Games with incomplete information have recently been added as anew challenge for general game-playing systems. The only published solutions to this challenge are based on sampling complete information models. In doing so they ground all of the unknown information, thereby making information gathering moves of no value; a well-known criticism of such sampling based systems. We present and analyse a method for escalating reasoning from complete information models to incomplete information models and show how this enables a general game player to correctly value information in incomplete information games. Experimental results demonstrate the success of this technique over standard model sampling.

Only the carrot, not the stick: incorporating trust into the enforcement of regulation.

New enforcement strategies allow agents to gain the regulator’s trust and consequently face a lower audit probability. Prior research suggests that, in order to prevent lower compliance, a reduction in the audit probability (the “carrot”) must be compensated with the introduction of a higher penalty for non-compliance (the “stick”). However, such carrot-and-stick strategies reflect neither the concept of trust nor the strategies observed in practice. In response to this, we define trust-based regulation as a strategy that incorporates rules that allow trust to develop, and using a generic (non-cooperative) game of tax compliance, we examine whether trust-based regulation is feasible (i.e., whether, in equilibrium, a reduction in the audit probability, without ever increasing the penalty for non-compliance, does not lead to reduced compliance). The model shows that trust-based regulation is feasible when the agent sufficiently values the future. In line with the concept of trust, this strategy is feasible when the regulator is uncertain about the agent’s intentions. Moreover, the model shows that (i) introducing higher penalties makes trust-based regulation less feasible, and (ii) combining trust and forgiveness can lead to a lower audit probability for both trusted and distrusted agents. Policy recommendations often point toward increasing deterrence. This model shows that the opposite can be optimal.

Adaptive topographies and equilibrium selection in an evolutionary game.

It has long been known in the field of population genetics that adaptive topographies, in which population equilibria maximise mean population fitness for a trait regardless of its genetic bases, do not exist. Whether one chooses to model selection acting on a single locus or multiple loci does matter. In evolutionary game theory, analysis of a simple and general game involving distinct roles for the two players has shown that whether strategies are modelled using a single ‘locus’ or one ‘locus’ for each role, the stable population equilibria are unchanged and correspond to the fitness-maximising evolutionary stable strategies of the game. This is curious given the aforementioned population genetical results on the importance of the genetic bases of traits. Here we present a dynamical systems analysis of the game with roles detailing how, while the stable equilibria in this game are unchanged by the number of ‘loci’ modelled, equilibrium selection may differ under the two modelling approaches.

Common agency with informed principals: Menus and signals

This paper considers general games in which multiple informed principals simultaneously compete to influence the decisions of a common agent. It shows that we can characterize all outcomes of any game in which principals delegate the final decisions to the agent using arbitrary mechanisms, by studying a simpler game in which they can offer only menus of decisions and send cheap-talk signals to the agent. For games in which the principals instead participate in making final decisions, we can characterize all their outcomes by studying a simpler game in which principals can again send cheap-talk signals but can offer only menus of direct mechanisms, to which they report their information truthfully.

Evaluating Player Task Engagement and Arousal Using Electroencephalography

Advances in affective computing technologies have made it possible for researchers to investigate brain function while users interact in virtual environments. Progress in sensors and algorithms for off-the-shelf EEG systems has made it possible for gaming researchers to perform real-time estimation of human cognitive and affective states using EEG. In this study our aim was to coordinate “Task Engagement” data with “Arousal-Valence” data. The resulting coordinate was designed for application to expressive transformations to video game play in real time by tuning different performance parameters in an Engagement-Arousal rule system. Results revealed that the engagement index (Beta / (Alpha + Theta)) was capable of differentiating high intensity game events (Player Death) from general game play. Given that higher levels of engagement during death events may reflect increase in autonomic response, we also measured arousal by using (BetaF3 + BetaF4) / (AlphaF3 + AlphaF4) and valence using (AlphaF4 / BetaF4) - (AlphaF3 / BetaF3). Results revealed that arousal increases and valence decreases during high intensity game events (Player Death) when compared to lower intensity game events (General Game Play). Given our desire to establish “Task Engagement” data with “Arousal-Valence” coordinates for a flow model, we divided the data into quartiles, which allowed us to establish upper and lower thresholds to indicate when the player has left a state of flow. Our aim was to use an off-the-shelf EEG system to establish “Task Engagement” and “Arousal-Valence” coordinates during video game play that can be used for a flow model. It is believed that this model will allow for future use of the Emotiv for assessing the cognitive and emotional processing of the player.

Recent Advances in General Game Playing

The goal of General Game Playing (GGP) has been to develop computer programs that can perform well across various game types. It is natural for human game players to transfer knowledge from games they already know how to play to other similar games. GGP research attempts to design systems that work well across different game types, including unknown new games. In this review, we present a survey of recent advances (2011 to 2014) in GGP for both traditional games and video games. It is notable that research on GGP has been expanding into modern video games. Monte-Carlo Tree Search and its enhancements have been the most influential techniques in GGP for both research domains. Additionally, international competitions have become important events that promote and increase GGP research. Recently, a video GGP competition was launched. In this survey, we review recent progress in the most challenging research areas of Artificial Intelligence (AI) related to universal game playing.

The Axiom General Purpose Game Playing System

A general game playing system, Axiom, was developed to overcome the limitations inherent in an existing commercial general purpose game playing system which incorporates a generic AI. Axiom extends the range of possible games via an extensible language, thereby allowing for a high degree of game-specific customization within the AI as well as in defining complex game behaviors. This paper provides an overview of the Axiom system and discusses some important aspects of the customizable AI. It also answers the question “Can a powerful game definition language be developed to enhance a popular general game platform?”

BERGE–ZHUKOVSKII EQUILIBRIA: EXISTENCE AND CHARACTERIZATION

In this paper, we investigate the existence of Berge–Zhukovskii equilibrium in general normal form games. We characterize its existence via the existence of a symmetric Nash equilibrium of some n-person subgame derived of the initial game. The significance of the obtained results is illustrated by two applications. One in economy with environmental externalities and the other in oligopoly markets.

EvoMCTS: A Scalable Approach for General Game Learning

In this paper, we present the application of genetic programming as a generic game learning approach to zero-sum, deterministic, full-knowledge board games by evolving board-state evaluation functions to be used in conjunction with Monte Carlo tree search (MCTS). Our method involves evolving board-evaluation functions that are then used to guide the MCTS playout strategy. We examine several variants of Reversi, Dodgem, and Hex using strongly typed genetic programming, explicitly defined introns, and a selective directional crossover method. Our results show a proficiency that surpasses that of baseline handcrafted players using equal and in some cases greater amounts of search, with little domain knowledge and no expert domain knowledge. Moreover, our results exhibit scalability.

Self-Adaptation of Playing Strategies in General Game Playing

The term general game playing (GGP) refers to a subfield of AI which aims at developing agents able to effectively play many games from a particular class (finite, deterministic). It is also the name of the annual competition proposed by Stanford Logic Group at Stanford University (Stanford, CA, USA), which provides a framework for testing and evaluating GGP agents. In this paper, we present our GGP player which managed to win four out of seven games in the 2012 preliminary round and advanced to the final phase. Our system (named MINI-Player) relies on a pool of playing strategies and autonomously picks the ones which seem to be best suited to a given game. The chosen strategies are combined with one another and incorporated into the upper confidence bounds applied to trees (UCT) algorithm. The effectiveness of our player is evaluated on a set of games from the 2012 GGP Competition as well as a few other, single-player games. The paper discusses the efficacy of proposed playing strategies and evaluates the mechanism of their switching. The proposed idea of dynamically assigning search strategies during play is both novel and promising.

Decaying Simulation Strategies

The aim of general game playing (GGP) is to create programs capable of playing a wide range of different games at an expert level, given only the rules of the game. The most successful GGP programs currently employ simulation-based Monte Carlo tree search (MCTS). The performance of MCTS depends heavily on the simulation strategy used. In this paper, we investigate the application of a decay factor for two domain-independent simulation strategies: the N-gram selection technique (NST) and the move-average sampling technique (MAST). Three decay factor methods, called move decay, batch decay, and simulation decay, are applied. Furthermore, a combination of move decay and simulation decay is also tested. The decay variants are implemented in the GGP program CadiaPlayer. Four types of games are used: turn taking, simultaneous move, one player, and multiplayer. Except for one-player games, experiments show that decaying can significantly improve the performance of both NST and MAST simulation strategies.

The Game Description Language Is Turing Complete

In this short paper, we show that the game description language (GDL) is Turing complete. In particular, we show how to simulate a Turing machine (TM) as a single-player game described in GDL. Positions in the game correspond to configurations of the machine, and the TM accepts its input exactly when the agent has a winning strategy from the initial position. As direct consequences of the Turing completeness of GDL, we show that well formedness as well as some other properties of a GDL description are undecidable. We propose to strengthen the recursion restriction of the original GDL specification into a general recursion restriction. The restricted language is not Turing complete, and the aforementioned properties become decidable. Checking whether a game description satisfies the suggested restriction is as easy as checking that the game is syntactically correct. Finally, we argue that practical expressivity is not affected as all syntactically correct games in a collection of more than 500 games having appeared in previous general game playing (GGP) competitions belong to the proposed GDL fragment.

Efficiency of GDL Reasoners

The variety of open-source game description language (GDL) reasoners available to newcomers to general game playing (GGP) lowers the technical barrier of entering the field. This variety, however, also makes it more complicated to decide on a fitting reasoner for a given GGP project, considering the project's objectives, ambitions, and technical constraints. This paper gives an overview of available GDL reasoners, discusses their main pros and cons, and, most importantly, quantifies their relative reasoning performance on a number of games (in terms of nodes searched per second), showing two orders of magnitude difference in some cases. We similarly quantify the performance difference between game playing systems specifically designed for playing a single game on the one hand, and GGP systems on the other hand, witnessing up to several orders of magnitude difference.

FSM 기반의 게임 NPC 인공 지능 평가

게임 NPC(Non Player Character)는 게임 플레이어와 대전 또는 협력함으로써 게임의 재미를 증가시키는 중요한 요소이다. 대부분 기존 게임에서 제공되는 NPC 인공지능은 FSM(Finite State Machine)으로 제작되어 행동 패턴이 정해져 있고 능력이 동일한 특징을 갖고 있다. 따라서 이러한 특징을 갖는 NPC들과 대전하는 플레이어는 창조적인 게임 플레이를 진행하는 것이 어려울 수 있다. 본 논문은 이 문제점을 개선하기 위하여 실제 생활에서 늑대들이 먹이를 사냥하는 행동 모델을 게임 NPC의 행동 모델로 제작하고 이를 평가하기 위한 것이다. 이를 위하여 첫째, 실세계에서 늑대들이 먹이를 포획하기 위한 행동 상태들을 조사 연구한다. 둘째, 이 행동 상태들을 Unity3D 엔진을 이용하여 구현한다. 셋째, 구현된 NPC들의 상태 전이 비율과 실세계의 NPC들의 상태 전이 비율, 일반적인 게임 NPC의 상태 전이 비율을 비교한다. 비교 결과, 구현된 NPC들의 상태 전이 비율은 실세계의 상태 전이 비율과 비슷함을 보인다. 이는 구현된 NPC들의 행동 패턴이 실세계의 늑대 사냥 행동 패턴과 유사함을 의미하는데, 이렇게 함으로써 플레이어에게 보다 증가된 사용자 경험을 제공할 수 있다.

Representing and Reasoning about Game Strategies

As a contribution to the challenge of building game-playing AI systems, we develop and analyse a formal language for representing and reasoning about strategies. Our logical language builds on the existing general Game Description Language (GDL) and extends it by a standard modality for linear time along with two dual connectives to express preferences when combining strategies. The semantics of the language is provided by a standard state-transition model. As such, problems that require reasoning about games can be solved by the standard methods for reasoning about actions and change. We also endow the language with a specific semantics by which strategy formulas are understood as move recommendations for a player. To illustrate how our formalism supports automated reasoning about strategies, we demonstrate two example methods of implementation: first, we formalise the semantic interpretation of our language in conjunction with game rules and strategy rules in the Situation Calculus; second, we show how the reasoning problem can be solved with Answer Set Programming.

Solving the Problem of UAV Air Combat Game Based on Differential Variational Inequality and D-Gap Function

The strategy of unmanned aerial vehicle air combat can be described as a differential game problem. The analytical solutions for the general differential game problem are usually difficult to obtain. In most cases, we can only get its numerical solutions. In this paper, a Nash differential game problem is converted to the corresponding differential variational inequality problem, and then converted into optimal control problem via D-gap function. The nonlinear continuous optimal control problem is obtained, which is easy to get numerical solutions. Compared with other conversion methods, the specific solving process of this method is more simple, so it has certain validity and feasibility.

Fast interpreter for logical reasoning in general game playing

Fast interpreter for logical reasoning in general game playing

Repeated games with incomplete information and discounting

We analyze discounted repeated games with incomplete information, such that the players' payoffs depend only on their own type (known-own payoff case). We describe an algorithm for finding all equilibrium payoffs in games for which there exists an open set of belief-free equilibria of Hörner and Lovo (2009). This includes generic games with one-sided incomplete information and a large and important class of games with multisided incomplete information. When players become sufficiently patient, all Bayesian Nash equilibrium payoffs can be approximated by payoffs in sequential equilibria in which information is revealed finitely many times. The set of equilibrium payoffs is typically larger than the set of equilibrium payoffs in repeated games without discounting and is larger than the set of payoffs obtained in belief-free equilibria. The results are illustrated in bargaining and oligopoly examples.