Fuzzy utility and equilibria

A decision maker is frequently confronted with fuzzy constraints, fuzzy utility maximization, and fuzziness about the state of competitors. In this paper we present a framework for fuzzy decision-making, using techniques from fuzzy logic, game theory, and micro-economics. In the first part, we study the rationality of fuzzy choice. We introduce fuzzy constraints, and show that this can easily be combined with maximizing a fuzzy utility. The second part of the paper analyzes games with uncertainty about the state of the competitors. We implement fuzzy Cournot adjustment, define equilibria, and study their stability. Finally, we show how a play progresses where the players have uncertainty about the state of the other players, and about their utility. For a likely procedure of utility maximization, the equilibria are the same as for the game without utility maximization.     

Fuzzy restrictions and an application to cooperative games with restricted cooperation

The concept of restriction, which is an extension of that of interior operator, was introduced to model limited cooperation in cooperative game theory. In this paper, a fuzzy version of restrictions is presented. We show that these new operators, called fuzzy restrictions, can be characterized by the transitivity of the fuzzy dependence relations that they induce. As an application, we introduce cooperative games with fuzzy restriction, which are used to model cooperative situations in which each player in a coalition has a level of cooperation within the coalition. A value for these games is defined and characterized.     

Extending Answer Sets for Logic Programming Agents

We present systems of logic programming agents (LPAS) to model the interactions between decision-makers while evolving to a conclusion. Such a system consists of a number of agents connected by means of unidirectional communication channels. Agents communicate with each other by passing answer sets obtained by updating the information received from connected agents with their own private information. We introduce a credulous answer set semantics for logic programming agents. As an application, we show how extensive games with perfect information can be conveniently represented as logic programming agent systems, where each agent embodies the reasoning of a game player, such that the equilibria of the game correspond with the semantics agreed upon by the agents in the LPAS.     

Access network synthesis game in next generation networks

In next generation communication networks, multiple access networks will coexist on a common service platform. In cases where network resource planning indicates that individual access network resources are insufficient to meet service demands, these networks can cooperate and combine their resources to form a unified network that satisfies these demands. We introduce and study the Network Synthesis game, in which individual access networks with insufficient resources form coalitions in order to satisfy service demands. The formation of stable coalitions in the core of the game is investigated, in both cases where payoffs are transferable or are attributed in proportion to the contribution of each member of the coalition. We also consider an alternative payoff allocation approach, according to the value of the well-known Shapley–Shubik, Banzhaf and Holler–Packel power indices, which represent the relative power each player has in the formation of coalitions. Using the knowledge attained from the coalition game analysis, we propose a new power index, called Popularity Power Index, which is based on the number of stable coalitions an access network would participate in if payoffs were assigned in a fair manner.     

Influence of head-up displays’ characteristics on user experience in video games

Head-up displays (HUD) are important parts of visual interfaces of virtual environments such as video games. However, few studies have investigated their role in player–video game interactions. Two experiments were designed to investigate the influence of HUDs on player experience according to player expertise and game genre. Experiment 1 used eye-tracking and interviews to understand how and to what extent players use and experience HUDs in two types of commercial games: first-person shooter and real-time strategy games. Results showed that displaying a permanent HUD within the visual interface may improve the understanding of this environment by players. They also revealed that two HUD characteristics, namely composition and spatial organization, have particular influence on player experience. These critical characteristics were manipulated in experiment 2 to study more precisely the influence of HUD design choices on player experience. Results showed that manipulation of design of these HUD characteristics influences player experience in different ways according to player expertise and game genre. For games with HUDs that are perceived as very useful, the higher player expertise is, the more player experience is influenced. Recommendations for video game design based on these results are proposed.     

MMORPG Player actions: Network performance, session patterns and latency requirements analysis

Providing Massively Multiplayer Online Role-Playing Games (MMORPGs) is a big challenge for future mobile, IP-based networks. Understanding how the players’ actions affect the network parameters, the game platform, and the overall perceived quality is highly relevant for the purposes of game design, as well as for the networking infrastructure and network support for games. We break player actions down into discrete categories, and show that each category is distinct in terms of several key metrics. We discuss which categories of actions could be supported on current mobile devices, and present evidence in form of a user survey demonstrating the demand for such services. The starting points into the discussion include the networking, session and latency requirements for particular player actions on one side, and the players’ interest on the other. The Blizzard Entertainment’s World of Warcraft (WoW) is used as a case study.     

Price of Stability in Survivable Network Design

We study the survivable version of the game theoretic network formation model known as the Connection Game, originally introduced in Anshelevich et al. (Proc. 35th ACM Symposium on Theory of Computing, 2003). In this model, players attempt to connect to a common source node in a network by purchasing edges, and sharing their costs with other players. We introduce the survivable version of this game, where each player desires 2 edge-disjoint connections between her pair of nodes instead of just a single connecting path, and analyze the quality of exact and approximate Nash equilibria. This version is significantly different from the original Connection Game and have more complications than the existing literature on arbitrary cost-sharing games since we consider the formation of networks that involve many cycles.     

A modular timed graph transformation language for simulation-based design

We introduce the MoTif (Modular Timed graph transformation) language, which allows one to elegantly model complex control structures for programmed graph transformation. These include modular construction, parallel composition, and a temporal dimension in addition to the usual transformation control structures. The first part of this contribution formally introduces MoTif and its semantics is based on the Discrete EVent system Specification (DEVS) formalism which allows for highly modular, hierarchical modelling of timed, reactive systems. In MoTif, graphs are embedded in events and individual transformation rules are embedded in atomic DEVS models. A side effect of the use of DEVS is the introduction of an explicit notion of time. This allows one to model a time-advance for every rule as well as to interrupt (pre-empt) rule execution. In the second part, we design a case study to show how the explicit notion of time allows for the simulation-based design of reactive systems such as modern computer games. We use the well-known game of PacMan as an example and model its dynamics in MoTif. This also allows the modelling of player behaviour, incorporating data about human players’ behaviour, and reaction times. Thus, a model of both player and game is obtained which can be used to evaluate, through simulation, the playability of a game design. We propose a playability performance measure and change the value of some parameters of the PacMan game. For each variant of the game thus obtained, simulation yields a value for the quality of the game. This allows us to choose an “optimal” (from a playability point of view) game configuration. The user model is subsequently replaced by a visual interface to a real player, and the game model is executed using a real-time DEVS simulator.     

Fuzzy logic and related methods as a screening tool for detecting gene regulatory networks

The analysis of gene expression microarrays plays an important role in elucidating the functionality of genes, including the discovery of genetic interactions that regulate gene expression. Several methods for modeling such gene regulatory networks exist, including a variety of continuous and discrete models. Methods based on fuzzy logic provide an interesting alternative. However, the guidelines for modeling gene expression with fuzzy logic are fairly open, and the need arises to investigate how adjustments in the modeling scheme will affect the results. In this work, we modify an existing fuzzy logic algorithm to involve an arbitrary number of classification states, and investigate the limiting behavior as the number of states tends to infinity. We also propose a probabilistic model as an alternative to the fuzzy logic model. We investigate the behavior of both models using yeast cell-cycle data and the simulated data of Werhli et al. [A.V. Werhli, M. Grzegorczyk, D. Husmeier, Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical Gaussian models, and Bayesian networks, Bioinformatics 22 (2006) 2523–2531]. We found that altering the number of classification states in both the fuzzy logic and probability models can influence which networks are predicted by both models. As the number of states tends to infinity, the predictions made by both models converge to those of a regression model. Models with a small to moderate number of classification states produced better results from a biological standpoint, compared to models with higher numbers of states. In simulated data, models with differing numbers of classification states produced similar overall results. Thus, increasing the complexity of the models has no apparent benefit, and models with smaller numbers of classification states are therefore preferred based on their ease of linguistic interpretation. The software used in this paper is freely available for non-commercial use at http://louisville.edu/~g0broc01.     

Interpersonal influence on online game choices

Several theories stress the importance of interpersonal influence on an individual’s adoption of a product or service. However, there has been little research that empirically examined how online friends influence an individual’s online product choices. This study examines the effect of a game player’s online friends who adopted a game earlier than the player on the likelihood that the player adopts the game. Two main factors considered in this study are: (1) the number of online friends who adopted a game earlier and (2) the strength of ties between the player and the player’s online friends who adopted the game earlier. Using a hazard model with data on 1,668 game players’ gaming activities and relational connections, we find (1) the likelihood that a player adopts a particular game increases the more her online friends adopted the game earlier, and (2) the influence of the prior adopter friends on the likelihood that a player adopts the game varies with the strength of ties between the player and her prior adopter friends. But the p-values of the coefficients for the corresponding independent variables are larger than the conventional cutoff point, 0.05. Possible causes for this statistical insignificance are discussed in the text.     

GLEAM: a graph clustering framework based on potential game optimization for large-scale social networks

With the growing explosion of online social networks, the study of large-scale graph clustering has attracted considerable interest. Most of traditional methods view the graph clustering problem as an optimization problem based on a given objective function; however, there are few methodical theories for the emergence of clusters over real-life networks. In this paper, each actor in online social networks is viewed as a selfish player in a non-cooperative game. The strategy associated with each node is defined as the cluster membership vector, and each one’s incentive is to maximize its own social identity by adopting the most suitable strategy. The definition of utility function in our game model is inspired by the conformity psychology, which is defined as the weighted average of one’s social identity by participating different clusters. With this setting, the proposed game can well match a potential game. So that the cluster could be shaped by the actions of those closely interactive users who adopt the same strategy in a Nash equilibrium. To this end, we propose a novel Graph cLustering framework based on potEntial gAme optiMization (GLEAM) for parallel graph clustering. It first utilize the cosine similarity to weight each edge in the original network. Then, an initial partition, including a number of clusters dominated by those potential “leader nodes”, is created by a fast heuristic process. Third, a potential game-based weighted Modularity optimization is used to improve the initial partition. Finally, we introduce the notion of potentially attractive cluster, and then discover the overlapping partition of the graph using a simple double-threshold procedure. Three phases in GLEAM are carefully designed for parallel execution. Experiments on real-world networks analyze the convergence inside GLEAM, and demonstrate the high performance of GLEAM by comparing it with the state-of-the-art community detection approaches in the literature.     

Neural fuzzy logic programming

A foundational development of propositional fuzzy logic programs is presented. Fuzzy logic programs are structured knowledge bases including uncertainties in rules and facts. The precise specifications of uncertainties have a great influence on the performance of the knowledge base. It is shown how fuzzy logic programs can be transformed to neural networks, where adaptations of uncertainties in the knowledge base increase the reliability of the program and are carried out automatically.     

A game attention model for efficient bit rate allocation in cloud gaming

The widespread availability of broadband internet access and the growth in server-based processing have provided an opportunity to run games away from the player into the cloud and offer a new promising service known as cloud gaming. The concept of cloud gaming is to render a game in the cloud and stream the resulting game scenes to the player as a video sequence over a broadband connection. To meet the stringent network bandwidth requirements of cloud gaming and support more players, efficient bit rate reduction techniques are needed. In this paper, we introduce the concept of game attention model (GAM), which is basically a game context-based visual attention model, as a means for reducing the bit rate of the streaming video more efficiently. GAM estimates the importance of each macro-block in a game frame from the player’s perspective and allows encoding the less important macro-blocks with lower bit rate. We have evaluated nine game video sequences, covering a wide range of game genre and a spectrum of scene content in terms of details, motion and brightness. Our subjective assessment shows that by integrating this model into the cloud gaming framework, it is possible to decrease the required bit rate by nearly 25 % on average, while maintaining a relatively high user quality of experience. This clearly enables players with limited communication resources to benefit from cloud gaming with acceptable quality.     

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.     

Equilibria problems on games: Complexity versus succinctness

We study the computational complexity of problems involving equilibria in strategic games and in perfect information extensive games when the number of players is large. We consider, among others, the problems of deciding the existence of a pure Nash equilibrium in strategic games or deciding the existence of a pure Nash or a subgame perfect Nash equilibrium with a given payoff in finite perfect information extensive games. We address the fundamental question of how can we represent a game with a large number of players? We propose three ways of representing a game with different degrees of succinctness for the components of the game. For perfect information extensive games we show that when the number of moves of each player is large and the input game is represented succinctly these problems are PSPACE-complete. In contraposition, when the game is described explicitly by means of its associated tree all these problems are decidable in polynomial time. For strategic games we show that the complexity of deciding the existence of a pure Nash equilibrium depends on the succinctness of the game representation and then on the size of the action sets. In particular we show that it is NP-complete, when the number of players is large and the number of actions for each player is constant, and that the problem is -complete when the number of players is a constant and the size of the action sets is exponential in the size of the game representation. Again when the game is described explicitly the problem is decidable in polynomial time.     

Iterative inversion of fuzzified neural networks

The inversion of a neural network is a process of computing inputs that produce a given target when fed into the neural network. The inversion algorithm of crisp neural networks is based on the gradient descent search in which a candidate inverse is iteratively refined to decrease the error between its output and the target. In this paper. we derive an inversion algorithm of fuzzified neural networks from that of crisp neural networks. First, we present a framework of learning algorithms of fuzzified neural networks and introduce the idea of adjusting schemes for fuzzy variables. Next, we derive the inversion algorithm of fuzzified neural networks by applying the adjusting scheme for fuzzy variables to total inputs in the input layer. Finally, we make three experiments on the parity-three problem, examine the effect of the size of training sets on the inversion, and investigate how the fuzziness of inputs and targets of training sets affects the inversion     

ON THE THEORY OF BAGS

We introduce the bag structure as a set-like object in which repeated elements are significant. We discuss operations on bags such as intersection, union and addition. We introduce the operation of selecting elements from a bag based upon their membership in a set. We show the usefulness of the bag structure in relational data bases. We provide a definition for fuzzy bags. In these fuzzy bags the count of the number of elements itself becomes a crisp bags. We investigate a calculus for fuzzy bags.