In this paper, we give several applications of the discrete game approach to partial differential equations (PDEs). We first present a rigorous game-theoretic proof of fattening phenomenon for motion by curvature with figure-eight–shaped initial curves without using parabolic PDE theory. The proof is based on a comparison between the game value and its inverse. Accompanied by the example of fig...

In this paper, we give several applications of the discrete game approach to partial differential equations. We first present a rigorous game-theoretic proof of fattening phenomenon for motion by curvature with figure-eight shaped initial curves without using parabolic PDE theory. The proof is based on a comparison between the game value and its inverse one. Accompanied with the example of figu...

a {em roman dominating function} on a graph $g = (v ,e)$ is a function $f : vlongrightarrow {0, 1, 2}$ satisfying the condition that every vertex $v$ for which $f (v) = 0$ is adjacent to at least one vertex $u$ for which $f (u) = 2$. the {em weight} of a roman dominating function is the value $w(f)=sum_{vin v}f(v)$. the roman domination number of a graph $g$, denoted by $gamma_r(g)$, equals the...

Drama in games is created by the interplay of the narrative structure of story and the ludic structure of challenges. In this paper, we combine Csikszentmihalyi’s model of engagement and flow with Freytag’s pyramid, a model of narrative structure. Using this combination, we explore the dramatic structure of Halo: Combat Evolved, comparing ludic and narrative structures at each stage of the game...

We introduce the path player game, a noncooperative network game with a continuum of mutually dependent set of strategies. This game models network flows from the point of view of competing network operators. The players are represented by paths in the network. They have to decide how much flow shall be routed along their paths. The competitive nature of the game is due to the following two asp...

Flow theory has been widely applied in the context of information technology and is useful in understanding users’ behavior; however, few studies empirically examine what factors influence players’ flow, and what the facets and consequences of flow are in the context of electronic games (e-games). In this study, the author reviews previous flow-related literature to develop the proposed model t...

With the rapid development of mobile games and the roaring growth of market size, mobile game addiction is becoming a public concern. Hence, understanding the reasons behind mobile game addiction is worthwhile. Based on previous studies and two salient features of mobile games (e.g., hedonic and sociality), a research model is developed to examine the antecedents of mobile game addiction. Our p...

An experiment (N = 74) was conducted to investigate the impact of game difficulty and player performance on game enjoyment. Participants played a First Person Shooter game with systematically varied levels of difficulty. Satisfaction with performance and game enjoyment were assessed after playing. Results are not fully in line with predictions derived from flow and attribution theory and sugges...

This paper describes an alternate approach to the modeling of game systems and game flow with Petri nets. Modeling languages usually used in this area are of limited efficiency when it comes to validating the underlying game systems. We provide a case study to show that Petri Nets can be used with advantages over other modeling languages. Their graphical notation is simple, yet it can be used t...

This paper describes an alternate approach to the modeling of game systems and game flow with Petri nets. Modeling languages usually used in this area are of limited efficiency when it comes to validating the underlying game systems. We provide a case study to show that Petri Nets can be used with advantages over other modeling languages. Their graphical notation is simple, yet it can be used t...