Comparison of Two Process Tracing
Methods in Iterated Prisoner’s Dilemma
Game
Mariya Popova
Supervisor:
Assoc. Prof. Maurice Grinberg, Ph. D.
Consultant:
Evgenia Hristova, Ph. D.
Prisoner’s Dilemma game
Social dilemma
Two strategies - cooperation (C), defection (D)
Player II
Player II
C
C
D
3, 3
1, 4
Player I
C
D
C Rs, Rc Ss, Tc
Player I
D
4, 1
2, 2
D Ts, Sc Ps, Pc
Prisoner’s Dilemma game
The payoffs PD must satisfy the following inequalities:
T>R>P>S
2R>T+S
Player II
C
D
C Rs, Rc Ss, Tc
Player I
D Ts, Sc Ps, Pc
Prisoner’s Dilemma game
Cooperation index (Rapoport and Chammah 1965)
CI = (R-P)/(T-S)
Player II
Player II
C
C
D
C 56, 56
0, 60
D
2, 2
Player I
0, 60
CI = 0,9
D
C 56, 56
0, 60
D
50, 50
Player I
0, 60
CI = 0,1
Basic assumptions of Game Theory
• Rationality assumption - players always
choose strategies that maximize their
payoff.
• Complete information
– all factors of the game are common
knowledge
– rationality also is common knowledge
Bounded rationality
• Limited computational abilities
• Limitations of the cognitive effort and time
that are devoted to a decision
(trade-off between the benefit of searching
the information and the cost of this search)
• Limited access to information
Information acquisition in decision
making
• Study how decision strategies are linked to
the specificity of information acquisition
• Process tracing methods provide detailed
data about the patterns of information
acquisition
• It is important to investigate the
applicability and reliability of such methods
and how/if they influence game playing
Process tracing methods
• Content of the information which subjects
attend to
• Sequence of acquisition
• Amount of information acquired
• Time needed to examine the information
Experiments: goals (cont’d)
• Study the type and amount of information acquired
• Study how the information acquisitions patterns are
linked with player’s strategies
• Study heterogeneity among players in relation to:
– information acquisition patterns
– strategies used
– map the two types of groups:
• Are subjects from a information acquisition
group belonging to the same strategy group and
vice versa?
Experiments: goals
• To investigate whether process tracing
methods influence the decision making
• Compare the results of two such methods:
eye-tracking (ET) and computerised
process tracing (CPT) (mouse click based
method)
Experiment 1 - eye-tracking study
Experimental design and procedure
• Participants 40 (17 males, 23 females) - 4
groups of 10
• Four conditions that differed in the positioning of
information on the display
• Each participant played 100 PD games (20
training)
• Computer opponent - probabilistic version of the
tit-for-tat strategy that takes into account the two
previous moves of the player and plays the
same move with probability 0.8.
Experimental design and procedure
• A set of 100 PD different payoff matrices,
containing an equal number of games with
CI equal to 0.1, 0.3, 0.5, 0.7, and 0.9
• Payoff matrices were randomly generated
• The games were presented randomly with
respect to their CI
Experimental design and procedure
• The game was presented in a formal and
a neutral formulation
• No cooperation or defection was
mentioned in the instructions or in the
interface
• Moves were labelled as ‘1’ and ‘2’
• Participants were instructed to try to
maximize their payoffs and not to compete
with the computer
Four interfaces
Group1
Computer
C
Group2
Computer
D
D
C
D Ps, Pc Ts, Sc
C Rs, Rc Ss, Tc
Player
Player
C Ss, Tc Rs, Rc
D Ts, Sc Ps, Pc
Group3
Group4
Player
C
Player
D
D
C
D Pc, Ps Tc, Ss
C Rc, Rs Sc, Ts
Computer
Computer
D Tc, Ss Pc, Ps
C Sc, Ts Rc, Rs
Areas of interest (AOI)
Areas of interest (AOI)
• Four AOIs containing the participant’s
possible payoffs Ts, Rs, Ps, and Ss.
• Four AOIs containing the computer’s
possible payoffs Tc, Rc, Pc, and Sc
• Six AOIs containing the game outcome:
S Move, C Move, S Points, C Points, Tot
Points, Money
Dependent variables
• The number of cooperative choices for
each CI was used as a dependent variable
characterizing the participants playing.
• The number of fixations in each AOI per
game.
1,2
1,0
Group 1
Group 2
0,8
Group 3
Group 4
0,6
0,4
0,2
oi
nt
s
To
tp
on
ey
M
po
in
ts
C
po
in
ts
S
ov
e
m
C
ov
e
S
m
Sc
Pc
Rc
Tc
Ss
Ps
Rs
0,0
Ts
Mean Number of Zone Attendances
per Game
Attention to different zones
AOI
Mean number of fixations per game in all 14 areas of interest for
the four experimental groups.
Cooperation in 4 experimental
conditions
Mean Cooperation (%)
35
30
25
Group1
20
Group2
15
Group3
Group4
10
5
0
0,1
0,3
0,5
0,7
0,9
CI
Mean cooperation for PD games with different CI for the four experimental
conditions.
Mean Number of Zone Attendances
per Game
Attention to different zones
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0,0
Ts
Rs
Ps
Ss
Tc
Rc
Pc
Sc
S
C
move move
AOI
Mean number of fixations per game in 10 areas of interest - zones
containing participant’s possible payoffs, computer’s possible
payoffs, participant’s move, and computer’s move.
Mean Number of Transitions per Game
Transitions between different
zones
0,4
0,3
Group1
Group2
0,2
Group3
Group4
0,1
0,0
T↔R
T↔P
T↔S
R↔P
R↔S
P↔S
Mean number of transitions per game between zones containing
participant’s possible payoffs.
Mean Number of Transitions per
Game
Transitions between different
zones
0,30
0,25
0,20
0,15
0,10
0,05
0,00
T↔R
T↔P
T↔S
R↔P
R↔S
P↔S
Mean number of transitions per game between zones containing
participant’s possible payoffs – averaged data.
Types of players with respect to their IA
patterns – 3 clusters
Mean Number of Zone
Attendances per Game
1,6
1,4
1,2
1,0
Type 1
0,8
Type 2
0,6
Type3
0,4
0,2
_m
ov
e
C
ov
e
S_
m
Sc
Pc
c
R
Tc
Ss
Ps
s
R
Ts
0,0
AOI
Mean number of fixations per game in different AOIs for three
different types of players.
Types of players with respect to their IA
patterns – 3 clusters
Mean Cooperation (%)
40
35
30
25
Type 1
20
Type 2
15
Type 3
10
5
0
0,1
0,3
0,5
0,7
0,9
CI
Mean cooperation for PD games with different CI for the three types of
players with different IA patterns: type 1 (bold line), type 2 (solid line), type
3 (dotted line).
Mean Number of Transitions per
Game
Types of players with respect to their IA
patterns – 3 clusters
1,2
1,0
0,8
Type 1
0,6
Type 2
Type 3
0,4
0,2
0,0
T↔R
T↔P
T↔S
R↔P
R↔S
P↔S
Mean number of transitions per game for PD games with different CI for
the three types of players with different IA patterns: type 1 (black bars),
type 2 (grey bars), type 3 (white bars).
Types of players with respect to their
cooperation patterns – 2 clusters
Mean Cooperation (%)
50
40
30
CI-based
20
Non-CI-based
10
0
0,1
0,3
0,5
0,7
0,9
CI
Mean cooperation for PD games with different CI: CI-based group (dotted
line), non-CI-based group (solid line).
Types of players with respect to their
cooperation patterns – 2 clusters
CI-based
1,2
Non CI-based
1,0
0,8
0,6
0,4
0,2
e
ov
_m
C
S_
m
ov
e
Sc
Pc
c
R
Tc
S
P
R
0,0
T
Mean Number of Zone
Attendances per Game
1,4
AOI
Mean number of fixations per game in different AOIs for CI-based (dark
grey bars).and non-CI-based players (light grey bars).
Mean Number of Transitions per Game
Types of players with respect to their
cooperation patterns – 2 clusters
0,5
CI-based
Non CI-based
0,4
0,3
0,2
0,1
0,0
T↔R
T↔P
T↔S
R↔P
R↔S
P↔S
Mean number of transitions per game in different AOIs for CI-based and
non-CI-based players.
Summary
• Participants do not pay equal attention to all
possible payoffs.
• Difference in mean number of zone attendances
in different zones between the 4 experimental
conditions.
• No differences in transitions between zones
containing participant’s payoffs in 4 experimental
conditions.
• No difference in cooperation between the 4
experimental conditions.
– in the mean level of cooperation
– in cooperation pattern with respect to CI
Summary
Three types of players on the basis of their IA
pattern
• Type 1 - pay attention to their bigger payoffs R,T
– non influenced of CI
– less transitions except T R
• Type 2 - pay attention to all payoffs
– influenced of CI
– the most transitions
• Type 3 - pay little attention to information
– non influenced on CI
– much less transitions
Summary
Two types of players on the basis of their
cooperation pattern
• CI-based – influenced of CI
– attention to all information
– more transitions
• Non-CI-based – non influenced of CI
– less attention to all information
– less transition
Types of players - summary
TYPE1
attention to own
payoffs
TYPE2
attention to all
information
TYPE3
little attention to
information
TOTAL
NON CI BASED
CI BASED
TOTAL
7
4
11
9
7
16
12
1
13
28
12
40
Experiment 2 – computerized process
tracing tool (CPT)
Experimental design and procedure
• Process tracing tool
• Participants – 80 participants divided into
four groups of 20
• Four experimental conditions which
differed in the position of the information
on the display
• Hidden information
1,0
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0,0
Group 1
Group 2
Group 3
po
in
ts
C
po
in
ts
M
on
To e y
tp
oi
nt
s
S
ov
e
m
C
ov
e
S
m
Sc
Pc
Rc
Tc
Ss
Ps
Rs
Group 4
Ts
Mean Number of Zone Attendances
per Game
Attention to different zones
AOI
Mean number of zone attendances per game in all 14 areas of interest for
the four experimental groups.
Cooperation in 4 experimental
conditions
Mean Cooperation (%)
45
40
35
30
Group 1
25
Group 2
20
Group 3
15
Group 4
10
5
0
0,1
0,3
0,5
0,7
0,9
CI
Mean cooperation for PD games with different CI for the four experimental
conditions.
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
m
ov
e
C
ov
e
S
m
Sc
Pc
c
R
Tc
Ss
Ps
R
s
0,0
Ts
Mean Number of Zone Attendances per
Game
Attention to different zones
AOI
Mean number of fixations per game in zones containing participant’s
possible payoffs, computer’s possible payoffs, participant’s move, and
computer’s move.
Mean Number of Transitions per Game
Transitions between different
zones
0,7
0,6
0,5
Group 1
Group 2
0,4
Group 3
0,3
Group 4
0,2
0,1
0,0
T↔R
T↔P
T↔S
R↔P
R↔S
P↔S
Mean number of transitions per game between zones containing
participant’s possible payoffs.
Mean Number of Transitions per
Game
Transitions between different
zones
0,40
0,35
0,30
0,25
0,20
0,15
0,10
0,05
0,00
T↔R
T↔P
T↔S
R↔P
R↔S
P↔S
Mean number of transitions per game between zones containing
participant’s possible payoffs – averaged data.
1,4
1,2
1,0
Type1
0,8
Type2
0,6
Type3
0,4
0,2
ov
e
m
c_
s_
m
ov
e
Sc
Pc
c
R
Tc
S
P
R
0,0
T
Mean Number of Zone Attendances
per Game
Types of players with respect to their
IA patterns – 3 clusters
AOI
Mean number of fixations per game in different AOIs for three different types of
players.
Types of players with respect to
their IA patterns – 3 clusters
Mean Cooperation (%)
40
35
30
25
Type1
20
Type2
15
Type3
10
5
0
0,1
0,3
0,5
0,7
0,9
CI
Mean cooperation for PD games with different CI for the three types of players with
different IA patterns: type 1 (bold line), type 2 (solid line), type 3 (dotted line).
Mena Number of Transitions per Game
Types of players with respect to
their IA patterns – 3 clusters
0,9
0,8
0,7
0,6
Type1
0,5
Type2
0,4
Type3
0,3
0,2
0,1
0,0
T↔R
T↔P
T↔S
R↔P
R↔S
P↔S
Mean number of transitions per game for PD games with different CI for the three
types of players with different IA patterns: type 1 (black bars), type 2 (grey bars),
type 3 (white bars).
Types of players with respect to their
cooperation patterns – 2 clusters
Mean Cooperation (%)
70
60
50
40
CI-based
30
Non CI-based
20
10
0
0,1
0,3
0,5
0,7
0,9
CI
Mean cooperation for PD games with different CI: CI-based group (dotted line),
non-CI-based group (solid line).
1,6
CI-based
1,4
Non CI-based
1,2
1,0
0,8
0,6
0,4
0,2
ov
m
C
S
m
ov
e
e
Sc
Pc
c
R
Tc
Ss
Ps
R
s
0,0
Ts
Mean Number of Zone Attendances
per Game
Types of players with respect to their
cooperation patterns – 2 clusters
AOI
Mean number of zone attendances per game in different AOIs for CI-based and
non-CI-based players.
Mean Number of Transitions per Game
Types of players with respect to their
cooperation patterns – 2 clusters
0,8
CI-based
0,7
Non CI-based
0,6
0,5
0,4
0,3
0,2
0,1
0
T↔R
T↔P
T↔S
R↔P
R↔S
P↔S
Mean number of transitions per game in different AOIs for CI-based and non-CIbased players.
Summary
• Participants do not pay equal attention to all
possible payoffs.
• No difference in mean number of zone
attendances in different zones between the 4
experimental conditions.
• Differences in the transitions between zones
containing participant’s payoffs – TP, RS.
• No difference in cooperation between the 4
experimental conditions.
– in the mean level of cooperation
– in cooperation pattern with respect to CI
Summary
Three types of players on the basis of their IA
pattern
• Type 1 - pay attention to their own payoffs
– influenced of CI
– the most transitions
• Type 2 - pay attention to all payoffs
– influenced of CI
– less transitions
• Type 3 - pay little attention to information
– non influenced on CI
– much less transitions
Summary
Two types of players on the basis of their
cooperation pattern
• CI-based – influenced of CI
– attention to all information
– more transitions
• Non-CI-based – non influenced of CI
– less attention to all information
– less transition
Types of players - summary
TYPE1
attention to own
payoffs
TYPE2
attention to all
information
TYPE3
little attention to
information
TOTAL
NON CI BASED
CI BASED
TOTAL
22
9
31
14
6
20
27
2
29
63
17
80
Comparison between Eye tracking
and CPT system
AOI
ov
e
ov
e
m
m
Sc
po
in
ts
C
po
in
ts
M
on
ey
To
tp
oi
nt
s
S
C
S
1,0
Pc
1,2
Rc
ov
e
ov
e
m
m
Sc
po
in
ts
C
po
in
ts
M
on
To e y
tp
oi
nt
s
S
C
S
Pc
Rc
1,0
Tc
Ss
Ps
Rs
Ts
Mean Number of Fixations per Game
1,2
Tc
Ss
Ps
Rs
Ts
Mean Number of Zone Attendances
per Game
Attention to different AOI
Eye- tracker
0,8
Group 1
Group 2
Group 3
Group 4
0,6
0,4
0,2
0,0
AOI
CPT system
0,8
Group 1
Group 2
Group 3
Group 4
0,6
0,4
0,2
0,0
Attention to different AOI
0,9
ET
0,8
0,7
BOX
0,6
0,5
0,4
0,3
0,2
0,1
AOI
ov
e
c_
m
ov
e
s_
m
Sc
Pc
Rc
Tc
Ss
Ps
Rs
0,0
Ts
Mean Numbr of Zone Attendancess
per Game
Comparison between both experiments - mean number of zone attendances
per game in zones containing participant’s possible payoffs, computer’s
possible payoffs, participant’s move, and computer’s move.
Cooperation
Mean Cooperation (%)
40
35
30
25
ET
20
BOX
15
10
5
0
0,1
0,3
0,5
0,7
0,9
CI
Mean cooperation for PD games with different CI for the two methods of
information acquisition (bold line - eye-tracking, dotted line – CPT system)
Transitions between different zones
Mean Number of Transitions per Game
Mean Number of Transitions per Game
Mean number of transitions per game between zones containing participant’s
possible payoffs
0,7
Eye- tracker
0,6
0,5
Group1
Group2
0,4
Group3
0,3
Group4
0,2
0,1
0,0
T↔R
T↔P
T↔S
R↔P
R↔S
P↔S
0,7
CPT system
0,6
0,5
Group 1
Group 2
0,4
Group 3
0,3
Group 4
0,2
0,1
0,0
T↔R
T↔P
T↔S
R↔P
R↔S
P↔S
0,30
Eye- tracker
0,25
0,20
0,15
0,10
0,05
0,00
Mean Number of Transitions per
Game
Mean Number of Transitions per
Game
Transitions between different zones
T↔R
T↔P
T↔S
R↔P
R↔S
P↔S
0,40
CPT system
0,35
0,30
0,25
0,20
0,15
0,10
0,05
0,00
T↔R
T↔P
T↔S
R↔P
R↔S
P↔S
Summary
• Method of recording IA has influence on the
pattern of information search in relation to the
presentation of the game (4 interfaces).
– ET – interface*zone interaction
– CPT – interface*transitions interaction
• Method of recording IA do not influence on
playing behaviour – no differences in the mean
level of cooperation and in cooperation in
respect to CI.
Summary
• Players do not look all information about the
game.
• Different types of players exist
– different playing behaviour
– different looking behaviour
• These types partially overlap – week relationship
between playing strategy and information
acquisition behaviour.