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