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毕业设计(论文)外文翻译

2020 年 2 月 23 日

On the modeling and agent-based simulation of a cooperative group anagram game

ABSTRACT：

Anagram games (i.e., word construction games in which players use letters to form words) have been researched for some 60 years. Games with individual players are the subject of over 20 published investigations. Moreover, there are many popular commercial anagram games such as Scrabble. Recently, cooperative team play of anagram games has been studied experimentally. With all of this experimental work and the popularity of such games, it is somewhat surprising that very little modeling of anagram games has been done to predict player behavior/actions in them. We devise a cooperative group anagram game and develop an agent-based modeling and simulation framework to capture player interactions of sharing letters and forming words. Our primary goals are to understand, quantitatively predict, and explain aggregate group behavior, through simulations, to inform the design of a group anagram game experimental platform.

1 INTRODUCTION

1.1 Background and Motivation

Anagram games, or word construction games, consist of players forming words from a provided group of letters. Research on anagram games—individual anagram games—has a long history that dates back at least to 1958, and encompasses more than 20 works that study a variety of issues. Moreover, there are many popular anagram games that are typically played by competing individuals, such as Scrabble, Bananagram, and Upwords. Recently, Charness et al. (2014) introduced a group anagram game (GrAG), where players cooperate to form words. See Section 2 for details.

Considering the substantial use of anagram games, it is surprising that almost no work has been done in modeling and simulating these games. In particular, we are interested in modeling GrAGs, notably player interactions and inter-dependence, and the implications of these interactions. There are several general

reasons to prefer computational modeling over (laboratory) experiments, e.g., the ability of a validated model to perform computational experiments much faster and with lesser cost. Beyond general motivations, there are several reasons that are expressly related to anagram games, including: (i) modeling GrAGs can be a precursor to modeling other phenomena such as team unity (Charness et al. 2014); and (ii) GrAGs have much in common with other situations in which individuals may share resources in order to mutually benefit (e.g., how to cope during crises, such as hurricanes and forest fires, along with others who remain behind (Yang et al. 2019)). Finally, a primary motivation for our modeling and simulation work is to predict and understand group performance (e.g., aggregate temporal changes in numbers of words formed, letters requested, and letter replies) in this game in order to provide insights for designing a GrAG software platform in which to conduct GrAG experiments.

1.2 Our Group Anagram Game (GrAG)

An overview of the GrAG is given here; details are provided in Section 3. The GrAG is a game played among several players that work cooperatively to form words. They share letters with their immediate neighbors (players are arranged in a network) who use them to form more words than they could form using only their own allotment of letters. Figure 1 shows an illustrative conceptual view of the pair-wise interactions among four players over three time steps. The stated goal of the game is for the team to form as many words as possible. This is because the teamrsquo;s earnings in the game are directly proportional to the number of words that the team forms in total. All players split the earnings evenly, regardless of their performance in the game (e.g., regardless of how many words a particular player forms). This is done to motivate the players to cooperate. Hence, forming the greatest number of words is equivalent to players trying to maximize their earnings.

Figure 1: Illustration of the group anagram game (GrAG) setup, and interactions among the four networked players over three time steps. Gray thick lines represent communication channels over which players can request letters from their distance-1 neighbors, and receive them if/when they are sent. Each player has a box of a sequence Liih of letters in-hand (i.e., letters that they can use) to form words. Owned letters (i.e., those initially assigned to a player) are in black and received letters from neighbors are in brown. For example, at time (t 1), v2 has Liih = (b;g;s;u); u is a received letter. Player actions (in blue) are form words, request letters from neighbors, reply to neighbor letter requests, and think (think not shown; it is a no-op). Motivations are in purple, e.g., at time t, v2 gets the idea to form bug, and so requests u. A letter received from another player vanishes once it is used (see Section 3 for details).

We emphasize that our work is not modeling cognitive processes within agents that determine agent actions. Rather, we model differences among playersrsquo; actions by changing their probabilities of taking actions. As will be explained later, greater probabilities result in more actions by players.

1.3 Novel

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