# Towards Adaptive Gamification: A Method Using Dynamic Player Profile and a Case Study
## 3 Runtime Method for Adaptive Gamification
### Previous Definitions
#### 3.1.2 Game Element  
Based on the correlation analysis of the HEXAD player types with 52 game design elements performed by [PERSON] et al. [24], we selected a subset of 14 game elements (see Table 1) covering the whole spectrum of player types (see Figure 1). The 52 game design elements were grouped by player types using the correlation value of each player type'smean score and the corresponding design elements' mean score per user. In our study, considering the fact that all game elements are equally motivating for one player type, we selected at least two of those: one related to its nature itself (for example, the Easter Egg game element is specific to the free spirit players and not others), and another considered complementary or additional for another type of player, if it exists (for example, the social status is specific to the socializer but is also an additional game element for player types such as disruptor or player). It should be noted that in the analysis carried out by [24], they did not find game elements correlated to the philanthropist player type. Then, we opted to include two of the philanthropist game mechanics suggested by [20] (knowledge sharing and gifting). There are no game elements associated to non-player type. Moreover, the educational context of our application further helped us either select or discard the game elements for each player type. For example, a development tools mechanism can be implemented as a prize that allows disruptors to change the system, e.g., change the design of badges. Nevertheless the anarchic gameplay mechanism of disruptors is not adequate for a massive online open course because its implementation can go against the learning objectives. Game elements are defined as  
\[GE=(ge_{1},ge_{2},\ \ldots,\ ge_{14}) \tag{3}\]  
The game elements, \(ge_{i}\), are briefly explained below:  
1. Development tool: allows the player user to create certain gamification mechanics such as badges, challenges and unlockables. 2. Challenge: the player must overcome a challenge, such as reaching a certain level and solving a problem in a certain time;
3. Easter egg: the mechanism consists of an image which, when pressed five consecutive times, allows access to a mini-game;
4. Unlockable: when a player overcomes a certain challenge, a hidden content is unlocked, which can be a message, a mini-game, etc. ;
5. Badge: awarded to the player when they manage to complete a difficult task;
6. Level: shows the user's progress in completing a task, subdivided into levels;
7. Point: the player gains score, experience, virtual money, etc. ;
8. Leaderboard: displays a ranking of scores;
9. Gift Opener: the player opens gifts they have received;
10. Lottery: game of chance (roulette) that allows players to increase their scores;
11. Social network: a small social network that allows players to create a profile, add friends and view their profiles;
12. Social status: collection of rankings of players based on their scores, especially those related to social interactions, such as the number of followers, visitors, etc. ;
13. Share knowledge: the player sends help messages to everyone in a group;
14. Gift: the player sends gifts to other users. It is worth mentioning that each game element does not target only one type of player but can motivate different types of players. Thus, the \(i\)-th game element, \(ge_{i}\), has associated a vector of motivation indexes \(GM_{i}\), where each component, \(m_{j}\), is the percentage of motivation it can cause in one of the seven types of players, \(p_{j}\). For example, the fifth game element \"Badge\" (see Figure 1) can motivate users with both achiever (\(pt_{3}\)) and player (\(pt_{4}\)) player types, then the \(GM_{5}=(0,0.5,0.5,0,0,0)\):  
\[GM_{i}=(m_{1},m_{2},\ldots,m_{7})\ \ \forall i=1\ldots 14 \tag{4}\]  
Therefore, we define the matrix, \(M\) as  
\[M=(GM_{i})_{1\leq i\leq 14}=(m_{ij})_{1\leq i\leq 14,\ 1\leq j\leq 7} \tag{5}\]where the rows of this matrix are indexed by the game elements, and the columns by the player types.