A dynamic game of coalition formation under ambiguity

In a previous paper, we generalized to the mixed strategy case the γ model of coalition formation (introduced by Hart and Kurz in Econometrica 51(4):1047–1064, 1983) for situations in which players have ambiguous expectations about the formation of the coalitions in which they are not involved; then we analyzed the corresponding evolutionary games. In this paper, we embody into the model rationality of the players; it follows that allowing for mixed strategies makes it impossible to construct unequivocally a von Neumann–Morgestein expected utility function coherent (in the sense of de Finetti B in Sul Significato Soggettivo della Probabilità, Fundamenta Mathematicae, T, vol XVIII, pp 298–329, 1931) to every strategy profile. We find out that if the multiplicity of coherent beliefs problem is approached by considering “ambiguity loving” players then existence results for classical static equilibria can be obtained in this model. Moreover, we provide conditions for the game to be dynamically playable and we find how the coalition structure beliefs might evolve coherently (according) to the evolution of the strategies.     

Designing the conflict resolution machinery using game theory–based neural network

We consider some general and practical cases of conflicts and design a neural network that is able to solve these basic conflict problems. For the preliminary definition and concepts in game theory, neural network and optimization, such as pay off function, stable solutions, and linear programming see, Fundenberg and Tirole (Game theory, Massachusetts Institute of Technology, Cambridge, 1996), Gass (Linear programming, McGraw Hill, New York, 1958), Hertz et al. (Introduction to the theory of neural computation, Addison Wesley Company, Redwood City, 1991).     

A Comparative Study of Game Theoretic and Evolutionary Models of Bargaining for Software Agents

Most of the existing work in the study of bargaining behavior uses techniques from game theory. Game theoretic models for bargaining assume that players are perfectly rational and that this rationality is common knowledge. However, the perfect rationality assumption does not hold for real-life bargaining scenarios with humans as players, since results from experimental economics show that humans find their way to the best strategy through trial and error, and not typically by means of rational deliberation. Such players are said to be boundedly rational. In playing a game against an opponent with bounded rationality, the most effective strategy of a player is not the equilibrium strategy but the one that is the best reply to the opponents strategy. The evolutionary model provides a means for studying the bargaining behaviour of boundedly rational players. This paper provides a comprehensive comparison of the game theoretic and evolutionary approaches to bargaining by examining their assumptions, goals, and limitations. We then study the implications of these differences from the perspective of the software agent developer.     

A Rough Set Approach to Estimating the Game Value and the Shapley Value from Data

A value of a game v is a function which to each coalition S assigns the value v(S) of this coalition, meaning the expected pay–off for players in that coalition. A classical approach of von Neumann and Morgenstern [6] had set some formal requirements on v which contemporary theories of value adhere to. A Shapley value of the game with a value v [14] is a functional Φ giving for each player p the value Φ_p(v) estimating the expected pay-off of the player p in the game. Game as well as conflict theory have been given recently much attention on the part of rough and fuzzy set communities [11,8,1,4,7,2]. In particular, problems of plausible strategies [1] in conflicts as well as problems related to Shapley's value [3,2] have been addressed.We confront here the problem of estimating a value as well as Shapley's value of a game from a partial data about the game. We apply to this end the rough set ideas of approximations, defining the lower and the upper value of the game and, respectively, the lower and upper Shapley value. We also define a notion of an exact coalition, on which both values coincide giving the true value of the game; we investigate the structure of the family of exact sets showing its closeness on complements, disjoint sums, and intersections of coalitions covering the set of players. This work sets open a new area of rough set applications in mining constructs from data. The construct mined in this case are values as well as Shapley values of games.     

Spatial approaches to broadband jamming in heterogeneous mobile networks: a game-theoretic approach

In this paper, we address the problem of a mobile intruder jamming the communication network in a vehicular formation. In order to understand the spatial aspect of the jamming problem, we consider a jamming model that takes into account the relative distance of the jammer from the vehicles. We formulate the problem as a zero-sum pursuit-evasion game between a jammer and a team of players with players possessing heterogeneous dynamics. We use Isaacs’ approach to arrive at the equations governing the optimal strategies of the team of players. Finally, we obtain the optimal trajectories in the neighborhood of termination by numerically simulating the strategies for some variants of the problem.     

The Reciprocal Influences among Motivation,Personality Traits,and Game Habits for Playing Pokémon GO

This article reports a study exploring motivations of Pokémon Game use, individual differences related to personality traits, and game habits. First, it analyzed Pokémon GO motivations through exploratory factor analysis (EFA) by administering online the Pokémon GO Motivational Scale to a group of Italian gamers (N = 560). Successively, a Confirmatory Factor Analysis (CFA) was conducted testing three factorial models of Pokémon Game motivations on a selected random sample (N = 310). Results showed a three-factor model of Pokémon GO Game motivations (i.e. Personal Needs, Social Needs and Recreation), accounting for 68.9% of total variance plus a general higher order factor that best fits the data. Individual differences in Pokémon GO motivations and personality traits have been explored showing that high involved Pokémon GO players are introverted, low agreeableness, and conscientiousness people, driven by personal social and recreational needs. Reciprocal influences on motivational involvement, personality, and game habits were discussed.     

Distributing game instances in a hybrid client-server/P2P system to support MMORPG playability

MMORPG (Massively Multiplayer Online Role Playing Games) is the most popular genre among network gamers, and now attract millions of users, who play simultaneously in an evolving virtual world. This huge number of concurrent players requires the availability of high performance computation servers. Additionally, gaming aware distribution mechanisms are needed to distribute game instances among servers to avoid load imbalances that affect performance negatively. In this work, we tackle the problem of game distribution and scalability by means of a hybrid Client-Server/P2P architecture that can scale dynamically according to the demand. To manage peak loads that occur during the game, we distribute game computation across the system according to the behavior of MMORPGs. We distinguish between the computation associated with the Main Game, that affects all players, and the computation of Auxiliary Games that affects only a few players and acts in isolation from the execution of the Main Game. Taking this distinction into account, we propose a mechanism that is focused in the distribution of Auxiliary Games, as an entity, across the pool of servers and peers of the underlying hybrid architecture. We evaluate the performance of the balancing mechanism taking the criteria of latency and reliability into account, and we compare the effectiveness of the mechanism with a classic approach that applies load balancing to individually players in a Client-Server system. We show that the balancing mechanism based on the latency criteria provides lower latency than the classical proposal, while in relation to reliability, we obtain a failure probability of under 0.9 % in the worst case, which is amply compensated by the scalability provided by the use of the P2P area.     

What makes good games go viral? The role of technology use,efficacy, emotion and enjoyment in players’ decision to share a prosocial digital game

Serious digital games may be an effective tool for prosocial message dissemination because they offer technology and experiences that encourage players to share them with others, and spread virally. But little is known about the factors that predict players’ willingness to share games with others in their social network. This panel study explores how several factors, including sharing technology use, emotional responses, and game enjoyment, contribute to players’ decision to share the game Darfur is Dying, with others. College students played the game and completed questionnaires that assessed whether they had shared the games at two different time points: during game play and after game play. Positive emotions predicted sharing while students played the game, but negative emotions predicted whether the game was shared after initial game play. Game enjoyment predicted players’ intentions to share the game, but it did not predict actual sharing behavior. Neither players’ general use of sharing technologies nor their satisfaction related to sharing digital content predicted sharing intentions or behavior. These findings have implications for the study of viral social marketing campaigns, and serious game design and theory.     

Overlapping community detection in social networks using coalitional games

Community detection is a significant research problem in various fields such as computer science, sociology and biology. The singular characteristic of communities in social networks is the multimembership of a node resulting in overlapping communities. But dealing with the problem of overlapping community detection is computationally expensive. The evolution of communities in social networks happens due to the self-interest of the nodes. The nodes of the social network acts as self-interested players, who wish to maximize their benefit through interactions in due course of community formation. Game theory provides a systematic framework tox capture the interactions between these selfish players in the form of games. In this paper, we propose a Community Detection Game (CDG) that works under the cooperative game framework. We develop a greedy community detection algorithm that employs Shapley value mechanism and majority voting mechanism in order to disclose the underlying community structure of the given network. Extensive experimental evaluation on synthetic and real-world network datasets demonstrates the effectiveness of CDG algorithm over the state-of-the-art algorithms.     

Network Design with Weighted Players

We consider a model of game-theoretic network design initially studied by Anshelevich et al. (Proceedings of the 45th Annual Symposium on Foundations of Computer Science (FOCS), pp. 295–304, 2004), where selfish players select paths in a network to minimize their cost, which is prescribed by Shapley cost shares. If all players are identical, the cost share incurred by a player for an edge in its path is the fixed cost of the edge divided by the number of players using it. In this special case, Anshelevich et al. (Proceedings of the 45th Annual Symposium on Foundations of Computer Science (FOCS), pp. 295–304, 2004) proved that pure-strategy Nash equilibria always exist and that the price of stability—the ratio between the cost of the best Nash equilibrium and that of an optimal solution—is Θ(log k), where k is the number of players. Little was known about the existence of equilibria or the price of stability in the general weighted version of the game. Here, each player i has a weight w _i ≥1, and its cost share of an edge in its path equals w _i times the edge cost, divided by the total weight of the players using the edge. This paper presents the first general results on weighted Shapley network design games. First, we give a simple example with no pure-strategy Nash equilibrium. This motivates considering the price of stability with respect to α-approximate Nash equilibria—outcomes from which no player can decrease its cost by more than an α multiplicative factor. Our first positive result is that O(log w _max)-approximate Nash equilibria exist in all weighted Shapley network design games, where w _max is the maximum player weight. More generally, we establish the following trade-off between the two objectives of good stability and low cost: for every α=Ω(log w _max), the price of stability with respect to O(α)-approximate Nash equilibria is O((log W)/α), where W is the sum of the players’ weights. In particular, there is always an O(log W)-approximate Nash equilibrium with cost within a constant factor of optimal. Finally, we show that this trade-off curve is nearly optimal: we construct a family of networks without o(log w _max/ log log w _max)-approximate Nash equilibria, and show that for all α=Ω(log w _max/log log w _max), achieving a price of stability of O(log W/α) requires relaxing equilibrium constraints by an Ω(α) factor. Research of H.-L. Chen supported in part by NSF Award 0323766. Research of T. Roughgarden supported in part by ONR grant N00014-04-1-0725, DARPA grant W911NF-04-9-0001, and an NSF CAREER Award.     

The effects of a player’s network centrality on resource accessibility,game enjoyment,and continuance intention: A study on online gaming communities

This study applies social capital theory to investigate how a player’s network centrality in an online gaming community (i.e., a guild) affects his/her attitude and continuance intention toward a Massive Multiplayer Online Game (MMOG). Analysis of 347 usable responses shows that players’ network centrality has a negative impact on their ties to players who belong to other guilds (i.e., non-guild interaction), but a positive effect on players’ access to resources. However, players’ network centrality fails to increase their perceived game enjoyment directly. Players’ resource accessibility and perceived game enjoyment play mediating roles in the relationship between network centrality and attitude toward playing an MMOG, which in turn influences game continuance intention. The results also show that although players’ non-guild interaction is negatively related to their resource accessibility from the networks, it is positively associated with perceived game enjoyment. The article concludes with implications and limitations of the study.     

Bidirectional Optimization from Reasoning and Learning in Games

We reopen the investigation into the formal and conceptual relationship between bidirectional optimality theory (Blutner in J Semant 15(2):115–162, 1998, J Semant 17(3):189–216, 2000) and game theory. Unlike a likeminded previous endeavor by Dekker and van Rooij (J Semant 17:217–242, 2000), we consider signaling games not strategic games, and seek to ground bidirectional optimization once in a model of rational step-by-step reasoning and once in a model of reinforcement learning. We give sufficient conditions for equivalence of bidirectional optimality and the former, and show based on numerical simulations that bidirectional optimization may be thought of as a process of reinforcement learning with lateral inhibition.     

Towards affective camera control in games

Information about interactive virtual environments, such as games, is perceived by users through a virtual camera. While most interactive applications let users control the camera, in complex navigation tasks within 3D environments users often get frustrated with the interaction. In this paper, we propose inclusion of camera control as a vital component of affective adaptive interaction in games. We investigate the impact of camera viewpoints on psychophysiology of players through preference surveys collected from a test game. Data is collected from players of a 3D prey/predator game in which player experience is directly linked to camera settings. Computational models of discrete affective states of fun, challenge, boredom, frustration, excitement, anxiety and relaxation are built on biosignal (heart rate, blood volume pulse and skin conductance) features to predict the pairwise self-reported emotional preferences of the players. For this purpose, automatic feature selection and neuro-evolutionary preference learning are combined providing highly accurate affective models. The performance of the artificial neural network models on unseen data reveals accuracies of above 80% for the majority of discrete affective states examined. The generality of the obtained models is tested in different test-bed game environments and the use of the generated models for creating adaptive affect-driven camera control in games is discussed.     

Game-theoretic axioms for local rationality and bounded knowledge

We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like rationality at a node and knowledge at a node. We distinguish between the game theorist's and the players' own theory of the game. The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the game theorist's theory of the game is not and need not be axiomatized, the players' theory must be an axiomatic one, since we model players as analogous to automatic theorem provers that play the game by inferring (or computing) a sequence of moves. We provide the players with an axiomatic theory sufficient to infer a solution for the game (in our case, the backwards induction equilibrium), and prove its consistency. We then inquire what happens when the theory of the game is augmented with information that a move outside the inferred solution has occurred. We show that a theory that is sufficient for the players to infer a solution and still remains consistent in the face of deviations must be modular. By this we mean that players have distributed knowledge of it. Finally, we show that whenever the theory of the game is group-knowledge (or common knowledge) among the players (i.e., it is the same at each node), a deviation from the solution gives rise to inconsistencies and therefore forces a revision of the theory at later nodes. On the contrary, whenever a theory of the game is modular, a deviation from equilibrium play does not induce a revision of the theory.A former version of this paper was presented at the Center for Rationality and Interactive Decision Theory at the Hebrew University of Jerusalem. A subsequent version has been presented at the Nobel Symposium on Game Theory held in Björkborn, Sweden, in June 1993. We would like to thank Martin Dufwenberg, Itzhak Gilboa, Sergiu Hart, Bart Lipman, Dov Samet, Shmuel Zamir and especially Robert Aumann for many useful comments.     

How Well Do People Play a Quantum Prisoner’s Dilemma?

Game theory suggests quantum information processing technologies could provide useful new economic mechanisms. For example, using shared entangled quantum states can alter incentives so as to reduce the free-rider problem inherent in economic contexts such as public goods provisioning. However, game theory assumes players understand fully the consequences of manipulating quantum states and are rational. Its predictions do not always describe human behavior accurately. To evaluate the potential practicality of quantum economic mechanisms, we experimentally tested how people play the quantum version of the prisoner’s dilemma game in a laboratory setting using a simulated version of the underlying quantum physics. Even without formal training in quantum mechanics, people nearly achieve the payoffs theory predicts, but do not use mixed-strategy Nash equilibria predicted by game theory. Moreover, this correspondence with game theory for the quantum game is closer than that of the classical game.     

When Can Limited Randomness Be Used in Repeated Games?

The central result of classical game theory states that every finite normal form game has a Nash equilibrium, provided that players are allowed to use randomized (mixed) strategies. However, in practice, humans are known to be bad at generating random-like sequences, and true random bits may be unavailable. Even if the players have access to enough random bits for a single instance of the game their randomness might be insufficient if the game is played many times. In this work, we ask whether randomness is necessary for equilibria to exist in finitely repeated games. We show that for a large class of games containing arbitrary two-player zero-sum games, approximate Nash equilibria of the n-stage repeated version of the game exist if and only if both players have Ω(n) random bits. In contrast, we show that there exists a class of games for which no equilibrium exists in pure strategies, yet the n-stage repeated version of the game has an exact Nash equilibrium in which each player uses only a constant number of random bits. When the players are assumed to be computationally bounded, if cryptographic pseudorandom generators (or, equivalently, one-way functions) exist, then the players can base their strategies on “random-like” sequences derived from only a small number of truly random bits. We show that, in contrast, in repeated two-player zero-sum games, if pseudorandom generators do not exist, then Ω(n) random bits remain necessary for equilibria to exist.     

Constructing infinite models represented by tree automata

We propose a method to use finite model builders in order to construct infinite models of first-order formulae. The constructed models are Herbrand interpretations, in which the interpretation of the predicate symbols is specified by tree tuple automata (Comon et al. 1997). Our approach is based on formula transformation: a formula ϕ is transformed into a formula Δ(ϕ) s.t. ϕ has a model representable by a term tuple automaton iff Δ(ϕ) has a finite model. This paper is an extended version of Peltier (2008).     

Guessing Bank PINs by Winning a Mastermind Game

In this paper we formally prove that the problem of cracking, i.e., correctly guessing, bank PINs used for accessing Automated Teller Machines and the problem of solving the Generalized Mastermind Game are strictly related. The Generalized Mastermind Game with N colors and k pegs is an extension of the well known Mastermind game, played with 6 colors and 4 pegs. The rules are the same, one player has to conceal a sequence of k colored pegs behind a screen and another player has to guess the exact position and colors of the pegs using the minimal number of moves. We first introduce a general game, called the Extended Mastermind Game (EMG), and we then formally prove it includes both the Generalized Mastermind Game and the PIN cracking Problem. We then present some experimental results that we have devised using a computer program that optimizes a well known technique presented by Knuth in 1976 for the standard Mastermind game. We finally show that the program improves the as state-of-the-art Mastermind solvers as it is able to compute strategies for cases which were not yet covered. More interestingly, the same solving strategy is adapted also for the solution of the PIN cracking problem.     

Ambidextrous Innovation and Game Market Fit Performance: Feedback from Game Testers

ABSTRACT

The dynamics of the market pose a challenge for the digital game industry. Game development firms must develop innovative games to satisfy game players’ ever-changing needs and sustain a suitable product/market fit. To realize such innovation, developers tend to adopt an ambidextrous approach that includes exploratory and exploitative activities to develop games. In addition, game development teams must rely on feedback from game testers to enhance development and meet game players’ needs. However, the effect of feedback on innovation is subject to debate. Some studies have proposed that feedback has potentially negative effects on creativity. Given the prevalence of ambidextrous innovation and the utilization of feedback from game testers, no study to date has investigated the effects of feedback on game development quality. A survey of 119 paired game producers and developers revealed that “feedback timing” from game testers positively enhances the relationship between ambidextrous innovation and a game’s final development performance, whereas “feedback specificity” impairs the effectiveness of ambidextrous innovation. This paper discusses the implications of this study.     

An old game,new experience: exploring the effect of players’ personal gameplay history on game experience

This experimental study explores how game experience differs between players with different gameplay histories within the same game universe. We are interested in how prolonged engagement with a game series affects the gameplay experience in relation to the most recent game version in the series. A total of 54 participants were divided into four groups depending on their gaming experience, namely non-gamers, new-gamers, old-gamers and core-gamers. They played the mobile version of Super Mario Run, and questionnaire data was collected after the gameplay session. The results of the study showed that not only the players’ personal gameplay history but also the length of experience or degree of familiarity with the game universe affected the experience of playing a new game in the same game universe. Additionally, familiarity with the game universe had a positive impact on the feeling of competence, immersion, emotions and flow.