Decision Making In Prisoner’s Dilemma
Yüklə 2,24 Mb.
|
- Bu səhifədəki naviqasiya:
- 10.4 Hypothesis
- 10.5 Results
10.2 ProcedureWe will use the data obtained in the fifteen 30-moves games played with our subjects, as described in section 8.44. 10.3 VariablesThe independent variable is, essentially, whether the subject meets with the given strategy for the first, second, or third time – or how much opportunity he had to learn how to play against such a strategy. Each subject plays three games against each strategy. The order of encounters is balanced among subjects. The depended variable is successfulness, or the number of points obtained. The pay-off matrix is T = 5, R = 3, P = 1, S = 0. The exact measures of successfulness that will be compared to test the hypothesis about the effect of learning are listed below. We compare the results (success) in moves 1-25 only, to eliminate the influence of end-effect. Variable “1”: Subject’s gain in his first encounter with Tit for Tat in moves 1-25 Variable “2”: Subject’s gain in his second encounter with Tit for Tat in moves 1-25 Variable “3”: Subject’s gain in his third encounter with Tit for Tat in moves 1-25 Variable “4”: Subject’s gain in his first encounter with Random in moves 1-25 Variable “5”: Subject’s gain in his second encounter with Random in moves 1-25 Variable “6”: Subject’s gain in his third encounter with Random in moves 1-25 Variable “7”: Subject’s gain in his first encounter with Benevolent in moves 1-25 Variable “8”: Subject’s gain in his second encounter with Benevolent in moves 1-25 Variable “9”: Subject’s gain in his third encounter with Benevolent in moves 1-25 Variable “10”: Subject’s gain in his first encounter with Deterrent in moves 1-25 Variable “11”: Subject’s gain in his second encounter with Deterrent in moves 1-25 Variable “12”: Subject’s gain in his third encounter with Deterrent in moves 1-25 Variable “13”: Subject’s gain in his first encounter with Bully in moves 1-25 Variable “14”: Subject’s gain in his second encounter with Bully in moves 1-25 Variable “15”: Subject’s gain in his third encounter with Bully in moves 1-25 Variable “16”: Subject’s summary gain in his first encounter with all of the five strategies in moves 1-25 Variable “17”: Subject’s summary gain in his second encounter with all of the five strategies in moves 1-25 Variable “18”: Subject’s summary gain in his third encounter with all of the five strategies in moves 1-25 10.4 Hypothesis█ (H12) In repeated encounters with a particular strategy (or set of strategies) subjects have higher gains than in previous encounters with that strategy (or set). We assume that supporting this hypothesis is tantamount to supporting the existence of an effect of learning in the Prisoner’s Dilemma game. Null hypothesis is rejected and H12 is supported if: (“18” > “16”, and/or “18” > “17”, and/or “17” > “16”), and/or
“3” > “2”, and/or “2” > “1”), and/or
“6” > “5”, and/or “5” > “4”), and/or
“9” > “8”, and/or “8” > “7”), and/or
“12” > “11”, and/or “11” > “10”), and/or
“15” > “14”, and/or “14” > “13”).
With dependent t-test for repeated measures we confirmed that “18” > “16”, p < 0,001, that “18” > “17”, p < 0,05, and that “17” > “16”, p < 0,001 (for more details see Tables 10.1, 10.2, 10.3 and Graph 10.1). Graph 10.1: Variables “16”, “17”, “18” 
(Graph 10.1: □ = median, box = 25%-75%, whiskers = values without outliers, * and ○ = outliers; y axis shows gains) Table 10.1: Comparing variables “18” and “16”
Table 10.2: Comparing variables “18” and “17”
Table 10.3: Comparing variables “17” and “16”
That means hypothesis H12 is partially confirmed: we found effect of learning when all third encounters with all strategies taken together were compared with all first, as well as with all second encounters with all strategies taken together. We also found effect of learning when all second encounters with all strategies taken together were compared with all first encounters with all strategies taken together. When effect of learning for particular strategies was tested individually (see below), the results were as follows: we found effect of learning in encounters with Tit for Tat, Deterrent, and Bully, we did not find effect of learning in encounters with Benevolent and Random. Tit for Tat: With dependent t-test for repeated measures we confirmed that “3” > “1”, p < 0,001, that “3” > “2”, p < 0,01, and that “2” > “1”, p < 0,01 (see Tables 10.4, 10.5, 10.6). Table 10.4: Comparing variables “3” and “1”
Table 10.5: Comparing variables “3” and “2”
Table 10.6: Comparing variables “2” and “1”
That means hypothesis H12 is partially confirmed: we found effect of learning when all third encounters with Tit for Tat were compared with all first, as well as with all second encounters with Tit for Tat. We also found effect of learning when all second encounters with Tit for Tat were compared with all first encounters with this strategy. * * * * * * Random: With dependent t-test for repeated measures we did not find statistically significant differences between successfulness in the third (“6”) and the first (“4”), the third (“6”) and second (“5”), or the second (“5”) and the first (“4”) encounters with Random strategy (see Tables 10.7, 10.8, 10.9 and Graph 10.2 below). That means we found no evidence for an effect of learning when this particular strategy was encountered. Graph 10.2: Variables “4”, “5”, “6” 
(Graph 10.2: □ = median, box = 25%-75%, whiskers = values without outliers, ○ = outliers; y axis shows gains) Table 10.7: Comparing variables “6” and “4”
Table 10.8: Comparing variables “6” and “5”
Table 10.9: Comparing variables “5” and “4”
* * * * * * Benevolent: With dependent t-test for repeated measures we did not find statistically significant differences between successfulness in the third (“9”) and the first (“7”), the third (“9”) and second (“8”), or the second (“8”) and the first (“7”) encounters with Benevolent strategy (see Tables 10.10, 10.11, 10.12 and Graph 10.3). That means we found no evidence for an effect of learning when Benevolent was encountered. Graph 10.3: Variables “7”, “8”, “9” 
(Graph 10.3: □ = median, box = 25%-75%, whiskers = values without outliers; y axis shows gains) Table 10.10: Comparing variables “9” and “7”
Table 10.11: Comparing variables “9” and “8”
Table 10.12: Comparing variables “8” and “7”
* * * * * * Deterrent: With dependent t-test for repeated measures we found out that “12” > “10”, p < 0,001, and that “11” > “10”, p < 0,05. We found no difference between “12” and “11” (i. e. between subjects’ gain in the third and in the second encounter with this strategy). For more details see Tables 10.13, 10.14, 10.15 and Graph 10.4. Hypothesis H12 was partially confirmed. Graph 10.4: Variables “10”, “11”, “12” 
(Graph 10.4: □ = median, box = 25%-75%, whiskers = values without outliers, * and ○ = outliers; y axis shows gains) Table 10.13: Comparing variables “12” and “10”
Table 10.14: Comparing variables “12” and “11”
Table 10.15: Comparing variables “11” and “10”
* * * * * * Bully: With dependent t-test for repeated measures we confirmed that “15” > “13”, p < 0,001, “15” > “14”, p < 0,001, and “14” > “13”, p < 0,05 (see Tables 10.16, 10.17, and 10.18 and Graph 10.5). Hypothesis H12 was again partially confirmed: we found effect of learning when all third encounters with Bully were compared with all first, as well as with all second encounters with Bully. We also found effect of learning when all second encounters with Bully were compared with all first encounters with this strategy. Graph 10.5: Variables “13”, “14”, “15” 
(Graph 10.4: □ = median, box = 25%-75%, whiskers = values without outliers, ○ = outliers; y axis shows gains) Table 10.16: Comparing variables “15” and “13”
Table 10.17: Comparing variables “15” and “14”
Table 10.18: Comparing variables “14” and “13”
Yüklə 2,24 Mb. Dostları ilə paylaş:
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||