The document proposes using game theory to refactor object-oriented software by modeling the refactoring problem as a non-cooperative game between players who each extract one class from a "blob" class. The goal of each player is to maximize the cohesion of their extracted class while maintaining low coupling. An example 2-player game is presented and analyzed. An empirical study found the game theory approach improved class metrics like LCOM by over 70% compared to baseline refactoring techniques and received higher qualitative ratings than the baselines from student evaluators.

1. In Medio Stat Virtus: Extract
Class Refactoring through
Nash Equilibria
Gabriele Bavota, Rocco Oliveto, Andrea De Lucia,
Andrian Marcus, Yann-Gael Guéhéneuc, Giuliano Antoniol

2. GameTheory Refactoring
Approach
Empirical
Study

3. GameTheory

4. Game
Theory
A game consits of:
a set of players
a set of moves available to those players
payoffs for each combination of moves
A branch of mathematics, capture
behavior in strategic situations, in
which an individual’s success in
making choices depends on the
choices of others

5. Game
Theory
A game consits of:
a set of players
a set of moves available to those players
payoffs for each combination of moves
A branch of mathematics, capture
behavior in strategic situations, in
which an individual’s success in
making choices depends on the
choices of others

6. Game
Theory
A game consits of:
a set of players
a set of moves available to those players
payoffs for each combination of moves
A branch of mathematics, capture
behavior in strategic situations, in
which an individual’s success in
making choices depends on the
choices of others

7. Game
Theory
A game consits of:
a set of players
a set of moves available to those players
payoffs for each combination of moves
A branch of mathematics, capture
behavior in strategic situations, in
which an individual’s success in
making choices depends on the
choices of others

8. The prisoner’s dilemma

9. TOMSALLY
The prisoner’s dilemma

10. TOM
SALLY
The prisoner’s dilemma

11. CONFESS NOT CONFESS
TOM
SALLY
CONFESS
NOT CONFESS
The prisoner’s dilemma

12. CONFESS NOT CONFESS
TOM
SALLY
CONFESS
NOT CONFESS
5,5 0,7
7,0 4,4
The prisoner’s dilemma

13. CONFESS NOT CONFESS
TOM
SALLY
CONFESS
NOT CONFESS
5,5 0,7
7,0 4,4
The prisoner’s dilemma
0,7
7,0 4,4

14. CONFESS NOT CONFESS
TOM
SALLY
CONFESS
NOT CONFESS
5,5 0,7
7,0 4,4
The prisoner’s dilemma
0,7
7,0

15. CONFESS NOT CONFESS
TOM
SALLY
CONFESS
NOT CONFESS
5,5 0,7
7,0 4,4
The prisoner’s dilemma

16. CONFESS NOT CONFESS
TOM
SALLY
CONFESS
NOT CONFESS
5,5 0,7
7,0 4,4
The prisoner’s dilemma
5,5

17. Contrasting
Goals

18. Contrasting
Goals
Pursuing high cohesion and low
coupling in object oriented
systems

19. Contrasting
Goals
Pursuing high cohesion and low
coupling in object oriented
systems
Bug triageing,
Test Case generation, ...

20. Contrasting
Goals
Pursuing high cohesion and low
coupling in object oriented
systems
Bug triageing,
Test Case generation, ...
Software engineering is the art of
compromise...

21. Software
Refactoring

22. Extract Class
Refactoring
Splitting a class with many
responsibilities into different classes
Input
Class C
BLOB
Class C1
Output
Class C2

24. A non-cooperative game
between n players

25. A non-cooperative game
between n players
Each player is in charge of
extracting one class from
the Blob

26. A non-cooperative game
between n players
Each player is in charge of
extracting one class from
the Blob
Each player seeks to
maximize its cohesion while
maintaining its coupling as
low as possible

27. 2-players game
TOM
SALLY
m5
m1
m2 m3 m4 N
m2
m3
m4
N
-1.00, -1.00
-0.49, -0.24
-0.70, -0.80
-0.20, 0.00
0.49, 0.22
-1.00, -1.00
-0.21, -0.58
0.29, 0.22
0.70, 0.80
0.21, 0.58
-1.00, -1.00
0.50, -0.80
0.70, 0.50
0.21, 0.28
0.00, -0.30
-1.00, -1.00

28. 2-players game
TOM
SALLY
m5
m1
m2 m3 m4 N
m2
m3
m4
N
-1.00, -1.00
-0.49, -0.24
-0.70, -0.80
-0.20, 0.00
0.49, 0.22
-1.00, -1.00
-0.21, -0.58
0.29, 0.22
0.70, 0.80
0.21, 0.58
-1.00, -1.00
0.50, -0.80
0.70, 0.50
0.21, 0.28
0.00, -0.30
-1.00, -1.00

29. 2-players game
TOM
SALLY
m5
m1
m2 m3 m4 N
m2
m3
m4
N
-1.00, -1.00
-0.49, -0.24
-0.70, -0.80
-0.20, 0.00
0.49, 0.22
-1.00, -1.00
-0.21, -0.58
0.29, 0.22
0.70, 0.80
0.21, 0.58
-1.00, -1.00
0.50, -0.80
0.70, 0.50
0.21, 0.28
0.00, -0.30
-1.00, -1.00

30. 2-players game
TOM
SALLY
m5
m1
m2 m3 m4 N
m2
m3
m4
N
-1.00, -1.00
-0.49, -0.24
-0.70, -0.80
-0.20, 0.00
0.49, 0.22
-1.00, -1.00
-0.21, -0.58
0.29, 0.22
0.70, 0.80
0.21, 0.58
-1.00, -1.00
0.50, -0.80
0.70, 0.50
0.21, 0.28
0.00, -0.30
-1.00, -1.00
0.70 = sim(m1, m2) - sim(m1, m4)

31. 2-players game
TOM
SALLY
m5
m1
m2 m3 m4 N
m2
m3
m4
N
-1.00, -1.00
-0.49, -0.24
-0.70, -0.80
-0.20, 0.00
0.49, 0.22
-1.00, -1.00
-0.21, -0.58
0.29, 0.22
0.70, 0.80
0.21, 0.58
-1.00, -1.00
0.50, -0.80
0.70, 0.50
0.21, 0.28
0.00, -0.30
-1.00, -1.00
0.70 = sim(m1, m2) - sim(m1, m4)
COHESION

32. 2-players game
TOM
SALLY
m5
m1
m2 m3 m4 N
m2
m3
m4
N
-1.00, -1.00
-0.49, -0.24
-0.70, -0.80
-0.20, 0.00
0.49, 0.22
-1.00, -1.00
-0.21, -0.58
0.29, 0.22
0.70, 0.80
0.21, 0.58
-1.00, -1.00
0.50, -0.80
0.70, 0.50
0.21, 0.28
0.00, -0.30
-1.00, -1.00
0.70 = sim(m1, m2) - sim(m1, m4)
COHESION COUPLING

33. 2-players game
TOM
SALLY
m5
m1
m2 m3 m4 N
m2
m3
m4
N
-1.00, -1.00
-0.49, -0.24
-0.70, -0.80
-0.20, 0.00
0.49, 0.22
-1.00, -1.00
-0.21, -0.58
0.29, 0.22
0.70, 0.80
0.21, 0.58
-1.00, -1.00
0.50, -0.80
0.70, 0.50
0.21, 0.28
0.00, -0.30
-1.00, -1.00

34. 2-players game
TOM
SALLY
m5
m1
m2 m3 m4 N
m2
m3
m4
N
-1.00, -1.00
-0.49, -0.24
-0.70, -0.80
-0.20, 0.00
0.49, 0.22
-1.00, -1.00
-0.21, -0.58
0.29, 0.22
0.70, 0.80
0.21, 0.58
-1.00, -1.00
0.50, -0.80
0.70, 0.50
0.21, 0.28
0.00, -0.30
-1.00, -1.00

35. 2-players game
TOM
SALLY
m5
m1
m2 m3
m4
N
m2
m3
m4
N
-1.00, -1.00
-0.49, -0.24
-0.70, -0.80
-0.20, 0.00
0.49, 0.22
-1.00, -1.00
-0.21, -0.58
0.29, 0.22
0.70, 0.80
0.21, 0.58
-1.00, -1.00
0.50, -0.80
0.70, 0.50
0.21, 0.28
0.00, -0.30
-1.00, -1.00

36. 2-players game
TOM
SALLY
m5
m1
m3 N
m2
m3
m4
N
-1.00, -1.00
0.39, 0.32
0.19, 0.25
-1.00, -1.00
m2
-1.00, -1.00
-0.49, -0.24
-0.70, -0.80
-0.20, 0.00
m4
0.21, 0.58
-1.00, -1.00
0.50, -0.80
0.49, 0.22
-0.21, -0.58
0.70, 0.50
0.00, -0.30
m2
m4
0.70, 0.80

37. 2-players game
TOM
SALLY
m5
m1
m3 N
m2
m3
m4
N
-1.00, -1.00
0.39, 0.32
0.19, 0.25
-1.00, -1.00
m2
-1.00, -1.00
-0.49, -0.24
-0.70, -0.80
-0.20, 0.00
m4
0.21, 0.58
-1.00, -1.00
0.50, -0.80
0.49, 0.22
-0.21, -0.58
0.70, 0.50
0.00, -0.30
m2
m4
0.70, 0.80

38. 2-players game
TOM
SALLY
m5
m1
m3
N
m2
m3
m4
N
-1.00, -1.00
0.39, 0.32
0.19, 0.25
-1.00, -1.00
m2
-1.00, -1.00
-0.49, -0.24
-0.70, -0.80
-0.20, 0.00
m4
0.21, 0.58
-1.00, -1.00
0.50, -0.80
0.49, 0.22
-0.21, -0.58
0.70, 0.50
0.00, -0.30
m2
m4
0.70, 0.80

39. 2-players game
TOM
SALLY
m5
m1m2
m3m4

40. Study
Design

41. Metric-based
Evaluation

43. LCOM
+72%

44. LCOM C3
+72% +118%

45. LCOM C3 MPC
+72% +118% +1%

46. Qualitative
Evaluation

47. Subjects
2 PhD and 6 Master students
Objects
The 7 Blobs of the metric evaluation
What we asked
Agreement to the claim: “The proposed refactoring results in an
appropriate division of responsibilities”
Five point Likert scale: “1: Strongly disagree; 2: Disagree; 3:
Neutral; 4: Agree; 5: Fully agree”
Baselines
We refactored the 7 Blobs using: our approach, k-means, and a
random splitting.

48. 5
4
3
2
1
Game Theory k-means Random

49. Conclusion

60. ?