1. Introduction

1.1 MDA Framework, Existing Theory

MDA Framework is an existing theory, which connects game design, analysis, and research by grasping the game as a structure of the following three layers [1].

(1) Mechanics
Mechanism of data / algorithm level. Shuffle and deal of cards, ammunition and resurrection of FPS, etc.

(2) Dynamics
Dynamism caused by players' actions. That earning more money is easier by a player who earned money at Monopoly, and that a fierce battle is spread at the appearance point of ammunition recovery item at FPS, etc.

(3) Aesthetics
Desirable feelings of the player. Fun to overcome obstacles, and fun to explore unfamiliar territories, etc.

1.1.1 Usefulness of MDA Framework

By analyzing games using this framework, it is possible to verify comprehensibility and integrity of the structure of the game. The usefulness of this framework is widely accepted, so since 2001 the workshops have been held every year until 2017, at GDC, the world's largest game developer conference.

1.1.2 Problems of MDA Framework

Aesthetics, which is one of the three-layer structure of this framework, is classified by the following eight types.

(1) Sensation
Fun of visual, auditory, tactual, and phisical feelings. To be evoked emotions by the game.

(2) Fantasy
Fun of virtual worlds. To immerse in the world expressed by the game.

(3) Narrative
Fun of stories. To weave a story through the player's own actions.

(4) Challenge
Fun of overcoming obstacles. To play over and over and acquire skills and knowledge.

(5) Fellowship
Fun of social frameworks. To form communities among players.

(6) Discovery
Fun of exploring unfamiliar areas. To explore the vast world with purpose with the player's own will.

(7) Expression
Fun of self discovery. To demonstrate the creativity of the player using editors and others.

(8) Submission
Fun of killing time. To submit to work that does not use the player's head.

This classification is not exhaustive (as the authors themselves also mention). Also, since the mechanism by which each fun occurs is unknown, in order to make it a guideline on game design, the part which must rely on personal sensitivity is quite large.

1.2 Agential Structure Model, Overcoming the Problems

In order to overcome the problems of MDA Framework, I propose "Agential Structure Model". This is a theory to classify fun into 8 comprehensive types according to the mechanism of the game generating fun.

2. Previous Research

2.1 Rules and Fiction

According to Juul [2], meaning expressed in videogames has the following two aspects.

(1) Rules
Challenges given to the players and mechanisms to change the game state.

(2) Fiction
The fictional world the game expresses. Character, places such as town and jungle, etc.

Although this theory is not intended to classify the fun, according to this framework, it can be considered to classify as the fun occurring from the aspect of rules and that from the aspect of fiction.

2.2 Agon, Alea, Mimicry, and Ilinx

According to Caillois [3], play can be divided into the following four categories.

(1) Agon
Play of competition, given equal opportunity. Sports competitions, chess, quizzes, etc.

(2) Alea
Play of chance, which stands on independent decision exceeding players' power. Lotteries, rock–paper–scissors, etc.

(3) Mimicry
Play of mimesis, which on the premise of accepting the fictional world. Mimicing, pretend play, etc.

(4) Ilinx
Play of vertigo, which destroys perception's stability and falls into a panic condition. Swings, roller coasters, etc.

This theory categorizes play, not games, but at least from the daily usage the concept of games mostly overlaps that of play. Therefore, there is a high possibility that the above four categories can also be used for classification of fun of games.

3. Agential Fun and Game

3.1 Agential Fun

Fun occurring from games can also occurs from activities other than games, such as labor and learning. For example, taking a scholastic test may sometimes be fun for examinees, and this fun is usually similar to that when playing quiz games.

Among the fun occurring from various entertainment activities (watching movies, listening music, and so on), it is characterized in that in a typical game or play it occurs from actions (behaviors with objectives) and feedback. Such fun is called "Agential Fun". It can occurs also from labor or learning.

3.2 Game

A typical game is an artificially designed system intended to allow players to enjoy the maximum Agential Fun with minimal effort and time. Specifically, by providing the players with the following elements, it generates fun.

(1) Objectives
Includes the final goal (checkmating the opponent's king, reaching the specific place earlier than the opponent and so on) and small objectives (winning one round, defeating one enemy and so on). There are cases where the game directly presents clear objectives, and cases where the game urges the player to set objectives voluntarily by providing (2) and (3).

(2) Means for Input
The player achieves the objectives using this means. In videogames this corresponds to the user interface.

(3) Feedback
The game state changes based on the input and the game mechanics, then the information is output.

4. Classification of Fun 

4.1 Rewardal Fun

The fun occurring from the objectives is called "Rewardal Fun". Specifically, the following fun is included.

(1) Fun of Improve
Fun to improve influence on the game state. Level ups in RPGs, unlocking new actions in action games, etc.
Especially, improving the process to get the next improvement, which also be called a positive feedback loop generates big fun.

 (2) Fun of Solution
Fun to solve the presented mystery. Puzzles, detective adventure games, etc.

(3) Fun of Pride
Fun to feel proud of the player's own abilities and achievements. Social games, PvP, leaderboards, etc.

(4) Fun of Benefit
Fun to obtain property, knowledge, and skills that are useful for real life. Gambling, brain training, etc.

4.2 Interactional Fun

The fun occurring from input and feedback is called "Interactional Fun". This can be classified into "Operational Fun", "Social Fun" and "Considerational Fun" depending on the object of interaction.

4.2.1 Operational Fun

The fun occurring from the direct interaction with the actual game state is called "Operational Fun". Specifically, the following fun is included.

(1) Fun of Manipulation
Fun to manipulate things as the player oneself imagines. Platform games, racing games, etc.

(2) Fun of Destruction
Fun to overthrow and destroy things. Shoot'em ups, hack and slash action games, etc.

(3) Fun of Cleanup
Fun to arrange or complement the messy state. Tile-matching puzzles, collecting items in RPGs, etc.

(4) Fun of Chain
Fun that things which the player operated influences other things. Physics puzzles, miniscapes, etc.

4.2.2 Social Fun 

The fun to influence the game state through interaction with other players is called "Social Fun". Specifically, the following fun is included.

(1) Fun of Conflict
Fun to compete with other players. Fighting games, board games, etc.

(2) Fun of Deception
Fun to deceive and spy on other players. Poker, werewolf, etc.

(3) Fun of Cooperation
Fun to cooperate with other players. MOBAs, multiplayer FPSs, etc.

 4.2.3 Considerational Fun

Fun to influence the game state through the player's own thinking is called "Considerational Fun". Specifically, the following fun is included.

(1) Fun of Strategy
Fun to build the optimal strategy to achieve given objectives. Strategy games, Sokoban-type puzzles, etc.

(2) Fun of Expression
Fun to design the process to achieve the game state that the player contrived. Miniscapes, TCGs, etc.

4.3 Fictional Fun 

Interactional Fun and Rewardal Fun occur primarily from the aspect of rules (so these types constitute the supertype "Mechanical Fun"). A state change in the aspect of rules causes that in the aspect of fiction. The fun occurring from such state changes in the aspect of fiction is called "Fictional Fun". Specifically, the following fun is included.

(1) Fun of Immersion
Fun when the player's actions are strongly linked to state changes in the aspect of fiction. FPS campaigns, action adventure games, etc.

(2) Fun of Unfolding
Fun to unfold the story by actions of the player. Visual novels, RPGs, etc.

(3) Fun of Favor
Fun to influence the player's favorite things or to let things do the player's favorite action in the aspect of fiction. Sports games, games using popular characters, etc.

4.4 Fun other than Agential Fun 

4.4.1 External Fun

Agential Fun is attributed directly to things inside the game, so it is positioned as the supertype "Internal Fun". On the other hand, "External Fun" includes the following fun.

Fun of Chat
Fun to chat with other players carefreely about subjects that do not directly contribute to achieving the objectives of the game. Online user communities, party games, etc.

4.4.2 Objectual Fun 

Among Internal Fun, Agential Fun occurs by having the consciousness that the player oneself is a party to the game state changes, so it is positioned as the supertype "Participational Fun". On the other hand, "Objectual Fun" includes the following fun.

Fun of Appreciation
Fun to objectively appreciate the beauty of images, music, literature and so on. Cut scene, BGM etc.

4.4.3 Passival Fun

Among Participational Fun, fun other than Agential Fun is called as "Passival Fun", which includes the following fun.

(1) Fun of Intoxication
Fun to mix self-consciousness into the environment. Music games, merry-go-rounds, etc.

(2) Fun of Thrill
Fun to feel fear and tension. Horror games, roller coasters, etc.

5. Comparison with Categories by Caillois 

5.1 Agon

The fun that is clearly close to Agon is Social Fun, such as Go and soccer. Play mainly with Considerational Fun such as puzzles and chess problems also is positioned as Agon as competitive games.

Regarding play mainly based on Operational Fun such as kite flying and yo-yo, the categories of Agon / Alea / Mimicry / Ilinx has not been clarified. By extending Agon to Interactional Fun (Operational Fun + Social Fun + Considerational Fun), the above play can be clearly categorized into Agon.

5.2 Alea

The main cause of the fun of typical Alea such as lotteries and horse races is expectations for rewards. With pure Alea not accompanied by rewards, for example, in simple dice play that does not have occasions to demonstrate players' ability, there is no such fun that the players immerse for a long time in general. Chance is merely a means for reducing the effort to enjoy expectations for rewards and enhancing replayability. In other words, Alea is very close to Rewardal Fun, but the latter is more fundamental as a classification criterion for fun.

5.3 Mimicry

Mimicry is almost equivalent to Fictional Fun.

5.4 Ilinx

Ilinx is almost equivalent to Passival Fun.

As mentioned above, adding together the range of extended and modified Agon, Alea, Mimicry, and Ilinx corresponds to Participational Fun.

6. Representation of Structure of Fun

The mechanism that generates fun can be represented by the structure of the objectives. A relationship between objectives are called integration.

6.1 Objectives

Objectives are divided into the following two types.

(1) Clear Objective
An Objective whose actions towards achievement have clear starting and ending.  

(2) Unclear Objective
An objective whose actions towards achievement do not have clear starting and ending.  

The former includes the following type.

(3) Main Objective
An objective that the player considers for the longest time, whose achievement or failure tend to be a break of playing.  

6.2 Integration

Integration can be classified by two axes.

6.2.1 Vertical / Horizontal Integration

(1) Vertical Integration
It is a relationship between an Upper Objective and Lower Objectives. In order to achieve the Upper objective, it is necessary to achieve multiple Lower Objectives.  

(2) Horizontal Integration
It is a relationship between a Former Objective and a Latter Objective. In order to achieve the Latter Objective, it is necessary to achieve one Former Objective.  

6.2.2 Progressive / Emergent Integration

(1) Progressive Integration
- Achieving the certain Lower Objective does not influence the other Lower Objectives.
- Achieving the Former Objective does not influence Lower Objectives under the Latter Objective.
- It allows immediate feedback of clear evaluation against the player input, so that it supports Rewardal Fun.  

(2) Emergent Integration
- Achieving the certain Lower Objective greatly influences the other Lower Objectives.
- Achieving the Former Objective greatly influence Lower Objectives under the Latter Objective.
- It increases the influence of the player's action on the game state or other players, so that it supports Interactional Fun.  

6.3 Fun

Fun can be linked to the objectives or integration. However, Interactional Fun must be linked to integration. And, Rewardal Fun must be linked to objectives.
* Fun other than Agential Fun is not directly attributable to objectives and integration, but it can be represented as being linked to them.

From the objective that generates Fun of Improve, the link to the integration which is improved can be drawn.

6.4 Analysis Example

6.4.1 Legend of Zelda: Ocarina of Time

6.4.2 Pokémon

6.4.3 Guitar Hero

7. Conclusion

7.1 Summary

Agential Structure Model classifies fun of games into eight types based on its occurrence mechanism: Operational Fun, Social Fun, Considerational Fun, Rewardal Fun, Fictional Fun, Passival Fun, Objectual Fun, and External Fun.

By this model, Agon, Alea, Mimicry, and Ilinx can be extended and modified to more fundamental categories, and play whose category is not clear can be reduced. Fun included in Participational Fun (fun other than Objectual Fun and External Fun) corresponds to these categories without omission or duplication.

Based on this model, it is possible to graphically represent the structure of the objectives and the fun of a whole game. It enables you to find game design defects and improve them. You also can accurately convey the fun of the game at the planning stage to others by this method.

7.2 Future Work

7.2.1 Gamification

Agential Structure Model can be the theoretical foundation for gamification. In present general gamification, there are many mechanisms that mainly focus on Rewardal Fun, such as points, badges and leaderboards. By introducing a mechanism that generates Interactional Fun, it can be expected to further enhance fun and replayability.

7.2.2 Automatic Game Design

Agential Structure Model can also be the theoretical foundation for automatic game design. Quantification of fun is an important subject for automatic game design, but its difficulty depends on the type of fun. Considerational Fun and Social Fun are relatively easy to quantify, but Fictional Fun and Passival Fun are hard to quantify.

References

[1] Hunicke, R., LeBlanc, M., and Zubek, R. (2004). MDA: A formal approach to game design and game research. Proceedings of Games AI Workshop, Nineteenth National Conference of Artificial Intelligence.

[2] Juul, J. (2005). Half-Real: Video Games between Real Rules and Fictional Worlds. MIT Press.

[3] Caillois, R. (1961). Man, Play and Games. Translated by Barash, M. University of Illinois Press.