General Game Research Articles

General Equilibrium vs. General Nash Equilibrium

We generalize the concept of Nash equilibrium to the concept of general Nash equilibrium such that it becomes applicable to more general games. We also generalize the concept of general equilibrium in general equilibrium theory to a more general concept of general equilibrium such that it becomes applicable to any game. To illustrate the usefulness of these generalized concepts, we apply them to industrial organizations and general equilibrium theory.

The 2016 Two-Player GVGAI Competition

This paper showcases the setting and results of the first Two-Player General Video Game AI Competition, which ran in 2016 at the IEEE World Congress on Computational Intelligence and the IEEE Conference on Computational Intelligence and Games. The challenges for the general game AI agents are expanded in this track from the single-player version, looking at direct player interaction in both competitive and cooperative environments of various types and degrees of difficulty. The focus is on the agents not only handling multiple problems, but also having to account for another intelligent entity in the game, who is expected to work toward their own goals (winning the game). This other player will possibly interact with first agent in a more engaging way than the environment or any nonplaying character may do. The top competition entries are analyzed in detail and the performance of all agents is compared across the four sets of games. The results validate the competition system in assessing generality, as well as showing Monte Carlo tree search continuing to dominate by winning the overall championship. However, this approach is closely followed by rolling horizon evolutionary algorithms, employed by the winner of the second leg of the contest.

Gamification Science, Its History and Future: Definitions and a Research Agenda

Background. Definitions of gamification tend to vary by person, both in industry and within academia. One particularly popular lay interpretation, introduced and popularized by Ian Bogost, and reiterated by Jan Klabbers, is that gamification is “bullshit” and “exploitationware.” They describe gamification as a marketing term or business practice invented to sell products rather than to represent a real and unique phenomenon relevant to a nascent game science. However, this view is an oversimplification, one which ignores a growing body of theory development and empirical research on gamification within a post-positivist epistemology. In fact, because gamification is so much more outcome-focused than general game design, current gamification research in many ways has a stronger footing in modern social science than much games research does.Aim. In this article, to address common misunderstandings like these, we describe the philosophical underpinnings of modern gamification research, define the relationship between games and gamification, define and situate gamification science as a subdiscipline of game science, and explicate a six-element framework of major concerns within gamification science: predictor constructs, criterion constructs, mediator constructs, moderator constructs, design processes, and research methods. This framework is also presented diagrammatically as a causal path model.Conclusion. Gamification science refers to the development of theories of gamification design and their empirical evaluation within a post-positivist epistemology. The goal of gamification scientist-practitioners should be to understand how to best meet organizational goals through the design of gamification interventions, drawing upon insights derived from both gamification science and games research more broadly.

Material selection in a sustainable manufacturing practice of a badminton racket frame using Elimination and Choice Expressing Reality (ELECTRE) Method

Badminton is one of the leading sports in the world. It has its own set of rules on the equipments used and general game play. One of the main equipment used is the badminton racket. Each sections of a badminton racket have its own design requirements and one of it is the racket’s material selection. Therefore, material selection is very important to improve the usage of a badminton racket. This study describes the use of the Elimination and Choice Expressing Reality (ELECTRE) method in the material selection of a badminton racket frame with reference to the sustainable manufacturing practice of the frame. By categorizing the materials of the badminton racket frame according to mechanical, physical, chemical and environmental properties, and further detailed sub criteria were set according to the usage of these frames, the ELECTRE I method was used to determine the dominant material. Out of the six materials usually used in the manufacturing of a badminton racket frame, carbon fibre was the dominant material selected from three out of the four properties which are the mechanical, chemical and most importantly the environmental properties, as to comply with the sustainable manufacturing practice of these frames.

Ethnography of Afar Koeso in Depth Study and Documentation

Games are none formalized and formalized expressions of playing which allow people to go beyond immediate imagination and direct physical activity. Generally they will classify in two major groups like, low organized and minor (cultural) games and major games. Games have a power to capture the ideas and behaviors of people `imagination at one period of time and carry that through time to their descendants. Objectives of the study: - To assessing, organizing and documenting of Afar Koeso traditional sport games. Method: - descriptive method has been implemented on this study because of the study nature is inventory, the major sampling techniques was non-probability such assnow ball (networking) (for different groups) and purposive techniques (for different offices). The data collecting materials are in-depth interview, field observation, close and open ended questionnaires, oral information. The main data sources were clan leaders, elders, former and current Afar Koeso players, and different offices. Findings:- the major findings of this research are:- Afar Koeso; (History, types, Nature, Rules and Regulations, Necessary materials, Facilities, Equipment, Socio-cultural values, Team Classifications positions, Risks and benefits, Officials, faults and punishments, etc have been assessed. Conclusion:- According to in depth interview, different sources and practical observation of different Afar Koeso games, there is no clear bench mark about Afar Koeso when, how and who began it but it has long relation with Afar Community. Right now Afar Koeso game is not practicing more compared with previous time. In general Afar Koeso game is famous and has great social impact in the community according to social interaction, recreational activities, leisure time, physical strength etc.

The core of a strategic game

AbstractIn this paper, I introduce and study the $\gamma$-core of a general strategic game. I first show that the $\gamma$-core of an arbitrary strategic game is smaller than the conventional $\alpha$- and $\beta$- cores. I then consider the partition function form of a general strategic game and show that a prominent class of partition function games admit nonempty $\gamma$-cores. Finally, I show that each $\gamma$-core payoff vector (a cooperative solution) can be supported as an equilibrium outcome of an intuitive non-cooperative game and the grand coalition is the unique equilibrium outcome if and only if the $\gamma$-core is non-empty.

The Nash Equilibrium Point of Dynamic Games Using Evolutionary Algorithms in Linear Dynamics and Quadratic System

In this paper, examining some games, we show that classical techniques are not always effective for games with not many stages and players and it can’t be claimed that these techniques of solution always obtain the optimal and actual Nash equilibrium point. For solving these problems, two evolutionary algorithms are then presented based on the population to solve general dynamic games. The first algorithm is based on the genetic algorithm and we use genetic algorithms to model the players' learning process in several models and evaluate them in terms of their convergence to the Nash Equilibrium. in the second algorithm, a Particle Swarm Intelligence Optimization (PSO) technique is presented to accelerate solutions’ convergence. It is claimed that both techniques can find the actual Nash equilibrium point of the game keeping the problem’s generality and without imposing any limitation on it and without being caught by the local Nash equilibrium point. The results clearly show the benefits of the proposed approach in terms of both the quality of solutions and efficiency.

Receiver’s dilemma

In a sender–receiver game, the sender’s concern for his credibility as a source of truthful information will boost his incentive to report truthfully. However, because his preferences over the outcomes differ from the receivers’, he still has an incentive to manipulate information in his favor. While the receivers comprehend this incentive, we nevertheless show that they do not ignore his message and play according to his preferences, which leads to his (not their) favorite outcome. This is the dilemma that the receivers are faced with. We identify a generic game that shows this receiver’s dilemma.

Co-action equilibrium fails to predict choices in mixed-strategy settings

Social projection is the tendency to project one’s own characteristics onto others. This phenomenon can potentially explain cooperation in prisoner’s dilemma experiments and other social dilemmas. The social projection hypothesis has recently been formalized for symmetric games as co-action equilibrium and for general games as consistent evidential equilibrium. These concepts have been proposed to predict choice behavior in experimental one-shot games. We test the predictions of the co-action equilibrium concept in a simple binary minimizer game experiment. We find no evidence of social projection.

Strategic Complements in Two Stage, 2x2 Games

Strategic complements are well understood for normal form games, but less so for extensive form games. There is some evidence that extensive form games with strategic complementarities are a very restrictive class of games (Echenique (2004)). We study necessary and sufficient conditions for strategic complements (defined as increasing best responses) in two stage, 2x2 games. We find that the restrictiveness imposed by quasisupermodularity and single crossing property is particularly severe, in the sense that the set of games in which payoffs satisfy these conditions has measure zero. Payoffs with these conditions require the player to be indifferent between their actions in two of the four subgames in stage two, eliminating any strategic role for their actions in these two subgames. In contrast, the set of games that exhibit strategic complements (increasing best responses) has infinite measure. This enlarges the scope of strategic complements in two stage, 2x2 games (and provides a basis for possibly greater scope in more general games). The set of subgame perfect Nash equilibria in the larger class of games continues to remain a nonempty, complete lattice. The results are easy to apply, and are robust to including dual payoff conditions and adding a third player. Examples with several motivations are included.

Compositional strategy synthesis for stochastic games with multiple objectives

Design of autonomous systems is facilitated by automatic synthesis of controllers from formal models and specifications. We focus on stochastic games, which can model interaction with an adverse environment, as well as probabilistic behaviour arising from uncertainties. Our contribution is twofold. First, we study long-run specifications expressed as quantitative multi-dimensional mean-payoff and ratio objectives. We then develop an algorithm to synthesise ε-optimal strategies for conjunctions of almost sure satisfaction for mean payoffs and ratio rewards (in general games) and Boolean combinations of expected mean-payoffs (in controllable multi-chain games). Second, we propose a compositional framework, together with assume-guarantee rules, which enables winning strategies synthesised for individual components to be composed to a winning strategy for the composed game. The framework applies to a broad class of properties, which also include expected total rewards, and has been implemented in the software tool PRISM-games.

On Hobbes’s state of nature and game theory

Hobbes’s state of nature is often analyzed in two-person two-action non-cooperative games. By definition, this literature only focuses on duels. Yet, if we consider general games, i.e., with more than two agents, analyzing Hobbes’s state of nature in terms of duel is not completely satisfactory, since it is a very specific interpretation of the war of all against all. Therefore, we propose a definition of the state of nature for games with an arbitrary number of players. We show that this definition coincides with the strategy profile considered as the state of nature in two-person games. Furthermore, we study what we call rational states of nature (that is, strategy profiles which are both states of nature and Nash equilibria). We show that in rational states of nature, the utility level of any agent is equal to his maximin payoff. We also show that rational states of nature always exist in inessential games. Finally, we prove the existence of states of nature in a class of (not necessarily inessential) symmetric games.

Group Testing Game

Group testing offers a cost/time-beneficial method to identify all, but few, infected individuals (defective items in general) among a large set of individuals (items). In a group testing scheme, a series of tests are performed on groups of individuals rather than single individuals. A test on a group determines whether the group contains at least one infected individual. This paper investigates the classical group testing problem from a game-theoretic perspective, where every individual, once called for a test, decides to comply with or defy the call. In this framework, an individual’s decision is driven by his knowledge of his well-being, that is healthy or infected. This leads to the so-called group testing game which is formulated in this work. Some simplified versions of the general game as a team game is then presented and analyzed, that result in some novel, generalized group testing problems to be addressed in future work.

On the Geometry of Perfect Recall

This paper investigates the relationship between the existence of equilibria in behavioral strategies, perfect recall, and notions of convexity in extensive form games. The central result is that players possess perfect recall if and only if their sets of behavioral strategies are behavioral convex, a novel generalized convexity condition. This result implies that perfect recall is the weakest restriction on players’ information partitions under which standard fixed point arguments ensure the existence of equilibria in behavioral strategies in finite games. The equivalence between convexity and perfect recall motivates the adoption of mixed behavioral strategies in games with imperfect recall. By randomizing ex-ante over behavioral strategies, players can generate distributions over outcomes and equilibria that cannot be achieved using mixed or behavioral strategies alone. Since equilibria in mixed behavioral strategies exist in any finite extensive form game, it follows that they are the most natural class of strategies for general extensive form games.

A Game Theoretical Approach to Hacktivism: Is Attack Likelihood a Product of Risks and Payoffs?

The current study examines hacktivism (i.e., hacking to convey a moral, ethical, or social justice message) through a general game theoretic framework-that is, as a product of costs and benefits. Given the inherent risk of carrying out a hacktivist attack (e.g., legal action, imprisonment), it would be rational for the user to weigh these risks against perceived benefits of carrying out the attack. As such, we examined computer science students' estimations of risks, payoffs, and attack likelihood through a game theoretic design. Furthermore, this study aims at constructing a descriptive profile of potential hacktivists, exploring two predicted covariates of attack decision making, namely, peer prevalence of hacking and sex differences. Contrary to expectations, results suggest that participants' estimations of attack likelihood stemmed solely from expected payoffs, rather than subjective risks. Peer prevalence significantly predicted increased payoffs and attack likelihood, suggesting an underlying descriptive norm in social networks. Notably, we observed no sex differences in the decision to attack, nor in the factors predicting attack likelihood. Implications for policymakers and the understanding and prevention of hacktivism are discussed, as are the possible ramifications of widely communicated payoffs over potential risks in hacking communities.

The coopetition game in international liner shipping

ABSTRACTIn maritime freight transportation, carriers build collaborative relationships with other carriers while competing with each other to optimize their own profits. In such a scenario, a game of coopetition is formed. We formulate a nonlinear mixed-integer problem to determine the optimal levels of coopetition for a single company and embed the resulting problem into a general game theoretic framework. A diagonalization algorithm that incorporates an ascent direction search technique is developed to effectively evaluate the game. The numerical results show that carriers choose similar coopetition levels to maximize their profits, and the coopetition game can reach equilibrium under general conditions.

Scarce-resource capacity sharing in cognitive radio environments: a new game theoretical model

The paper proposes a general game theoretical model, called capacity demand game, for treating simultaneous capacity requests in scarce-resource cognitive radio (CR) environments. The approach is that of non-cooperative games describing CR interactions in terms of radio resource access. Experiments reveal stable states (equilibria) that favour an equitable usage of radio resources to the benefit of all participants. Several equilibria are detected and discussed: Nash (NE), Pareto, joint Nash–Pareto, and Lorenz equilibrium.

The Efficiency of the HyperPlay Technique Over Random Sampling

We show that the HyperPlay technique, which maintains a bag of updatable models for sampling an imperfect-information game, is more efficient than taking random samples of play sequences. Also, we demonstrate that random sampling may become impossible under the practical constraints of a game. We show the HyperPlay sample can become biased and not uniformly distributed across an information set and present a remedy for this bias, showing the impact on game results for biased and unbiased samples. We extrapolate the use of the technique beyond General Game Playing and in particular for enhanced security games with in-game percepts to facilitate a flexible defense response.

A Survey of Learning Classifier Systems in Games [Review Article

Games are becoming increasingly indispensable, not only for fun but also to support tasks that are more serious, such as education, strategic planning, and understanding of complex phenomena. Computational intelligence-based methods are contributing significantly to this development. Learning Classifier Systems (LCS) is a pioneering computational intelligence approach that combines machine learning methods with evolutionary computation, to learn problem solutions in the form of interpretable rules. These systems offer several advantages for game applications, including a powerful and flexible agent architecture built on a knowledge-based symbolic modeling engine; modeling flexibility that allows integrating domain knowledge and different machine learning mechanisms under a single computational framework; an ability to adapt to diverse game requirements; and an ability to learn and generate creative agent behaviors in real-time dynamic environments. We present a comprehensive and dedicated survey of LCS in computer games. The survey highlights the versatility and advantages of these systems by reviewing their application in a variety of games. The survey is organized according to a general game classification and provides an opportunity to bring this important research direction into the public eye. We discuss the strengths and weaknesses of the existing approaches and provide insights into important future research directions.

Piecewise closed-loop equilibria in differential games with regime switching strategies

We propose a new methodology exploring piecewise closed-loop equilibrium strategies in differential games with regime switching actions. We develop a general game with two players. Players choose an action that influences the evolution of a state variable, and decide on the switching time from one regime to another. Compared to the optimal control problem with regime switching, necessary optimality conditions are modified for the first player to switch. When choosing her optimal switching strategy, this player considers the impact of her choice on the other player’s actions and consequently on her own payoffs. In order to determine the equilibrium timing of regime changes, we derive conditions that help eliminate candidate equilibrium strategies that do not survive deviations in switching strategies. We then apply this new methodology to an exhaustible resource extraction game.