Decision Making In Prisoner’s Dilemma

11.3 Variables

The independent variable is the presence of cheap talk (condition X vs. condition Y).

The depended variables are willingness to cooperate stated by the subject (variables “49”, “50”, “51”, “56”, “57”, “58”), and the willingness to cooperate on the opponent’s part expected by the subject (variables “52”, “53”, “54”, “59”, “60”, “61”).
The exact measures of variables compared:
Variable “49”: The willingness to cooperate (the amount of C choices) stated by the subject in moves 1-10 (in condition X)
Variable “50”: The willingness to cooperate (the amount of C choices) stated by the subject in moves 11-20 (in condition X)
Variable “51”: The willingness to cooperate (the amount of C choices) stated by the subject in moves 21-30 (in condition X)
Variable “52”: The willingness to cooperate (the amount of C choices) on the opponent’s part expected by the subject in moves 1-10 (in condition X)
Variable “53”: The willingness to cooperate (the amount of C choices) on the opponent’s part expected by the subject in moves 11-20 (in condition X)
Variable “54”: The willingness to cooperate (the amount of C choices) on the opponent’s part expected by the subject in moves 21-30 (in condition X)
Variable “55”: The willingness to cooperate (the amount of C choices) stated by the opponent
Variable “56”: The willingness to cooperate (the amount of C choices) stated by the subject in moves 1-10 (in condition Y)
Variable “57”: The willingness to cooperate (the amount of C choices) stated by the subject in moves 11-20 (in condition Y)
Variable “58”: The willingness to cooperate (the amount of C choices) stated by the subject in moves 21-30 (in condition Y)
Variable “59”: The willingness to cooperate (the amount of C choices) on the opponent’s part expected by the subject in moves 1-10 (in condition Y)
Variable “60”: The willingness to cooperate (the amount of C choices) on the opponent’s part expected by the subject in moves 11-20 (in condition Y)
Variable “61”: The willingness to cooperate (the amount of C choices) on the opponent’s part expected by the subject in moves 21-30 (in condition Y)

11.4 Hypotheses

█ (H13) The willingness to cooperate (the amount of C choices) stated by subjects in condition with cheap talk (condition Y) will increase in comparison with the willingness to cooperate stated by subjects in condition without cheap talk (condition X).

Null hypothesis is rejected and H13 is supported if:
“56” > “49”,

“57” > “50”,

“58” > “51”.

█ (H14) The willingness to cooperate (the amount of C choices) on the opponent’s part expected by subjects in condition with cheap talk (condition Y) will increase in comparison with the willingness to cooperate on the opponent’s part expected by subjects in condition without cheap talk (condition X).

Null hypothesis is rejected and H14 is supported if:
“59” > “52”,

“60” > “53”,

“61” > “54”.

11.5 Results

Ad H13
With dependent t-test for repeated measures we confirmed that “56” > “49”, p < 0,01, “57” > “50”, p < 0,01, and “58” > “51”, p < 0,01. (for more details see Tables 11.3, 11.4, and 11.5 and Graphs 11.1, 11.2, and 11.3 below). That means we proved an increase in subjects’ willingness to cooperate due to cheap talk (H13).
Graph 11.1: Variables “49” and “56”

(Graph 11.1: □ = mean, box = mean ± SD, whiskers = mean ± 1,96 SD; y axis shows number of subject’s own expected C choices)

Table 11.3: Comparing variables “49” and “56”

Variables	Dependent t-test for repeated measures
	Mean	SD	N	t	df	p
“49”	7,24	1,00
“56”	7,76	1,05	45	-3,241	44	0,002

* * * * * *

Graph 11.2: Variables “50” and “57”

(Graph 11.2: □ = mean, box = mean ± SD, whiskers = mean ± 1,96 SD; y axis shows number of subject’s own expected C choices)

Table 11.4: Comparing variables “50” and “57”

Variables	Dependent t-test for repeated measures
	Mean	SD	N	t	df	p
“50”	7,00	1,21
“57”	7,40	1,03	45	-3,108	44	0,003

* * * * * *

Graph 11.3: Variables “51” and “58”

(Graph 11.3: □ = mean, box = mean ± SD, whiskers = mean ± 1,96 SD; y axis shows number of subject’s own expected C choices)

Table 11.5: Comparing variables “51” and “58”

Variables	Dependent t-test for repeated measures
	Mean	SD	N	t	df	p
“51”	6,58	1,34
“58”	6,89	1,21	45	-2,976	44	0,005

Ad H14
With dependent t-test for repeated measures we confirmed that “59” > “52”, p < 0,001, “60” > “53”, p < 0,001, and “61” > “54”, p < 0,01 (for details see Tables 11.6, 11.7, 11.8 and Graphs 11.4, 11.5, and 11.6). Hypothesis H14 was supported. We confirmed that in the condition with cheap talk subjects expected their opponents to be more willing to cooperate.

Graph 11.4: Variables “52” and “59”

(Graph 11.4: □ = mean, box = mean ± SD, whiskers = mean ± 1,96 SD; y axis shows number of C choices expected by subject on his opponent’s part)

Table 11.6: Comparing variables “52” and “59”

Variables	Dependent t-test for repeated measures
	Mean	SD	N	t	df	p
“52”	6,76	0,83
“59”	7,67	0,71	45	-9,652	44	0,000

* * * * * *

Graph 11.5: Variables “53” and “60”

(Graph 11.5: □ = mean, box = mean ± SD, whiskers = mean ± 1,96 SD; y axis shows number of C choices expected by subject on his opponent’s part)

Table 11.7: Comparing variables “53” and “60”

Variables	Dependent t-test for repeated measures
	Mean	SD	N	t	df	p
“53”	6,67	0,95
“60”	7,47	0,79	45	-5,686	44	0,000

* * * * * *

Graph 11.6: Variables “54” and “61”

(Graph 11.6: □ = mean, box = mean ± SD, whiskers = mean ± 1,96 SD; y axis shows number of C choices expected by subject on his opponent’s part)

Table 11.8: Comparing variables “54” and “61”

Variables	Dependent t-test for repeated measures
	Mean	SD	N	t	df	p
“54”	6,36	1,11
“61”	6,89	0,83	45	-3,254	44	0,002