Comparison of Two Process Tracing Methods in Iterated Prisoner’s Dilemma Game

1. 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.

2. Prisoner’s Dilemma game Social dilemma Two strategies - cooperation (C), defection (D)

3. Prisoner’s Dilemma game The payoffs PD must satisfy the following inequalities: T>R>P>S 2R>T+S

4. Prisoner’s Dilemma game Cooperation index (Rapoport and Chammah 1965) CI = (R-P)/(T-S) CI = 0,9 CI = 0,1

5. Basic assumptions of Game Theory • Rationality assumption - playersalways choose strategies that maximize their payoff. • Complete information • all factors of the game are common knowledge • rationality also is common knowledge

6. 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

7. 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

8. Process tracing methods • Content of the information which subjects attend to • Sequence of acquisition • Amount of information acquired • Time needed to examine the information

9. 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?

10. 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)

11. Experiment 1 - eye-tracking study

12. 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.

13. 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

14. 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

15. Four interfaces

16. Areas of interest (AOI)

17. 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

18. 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.

19. Attention to different zones Mean number of fixations per game in all 14 areas of interest for the four experimental groups.

20. Cooperation in 4 experimental conditions Mean cooperation for PD games with different CI for the four experimental conditions.

21. Attention to different zones 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.

22. Transitions between different zones Mean number of transitions per game between zones containing participant’s possible payoffs.

23. Transitions between different zones Mean number of transitions per game between zones containing participant’s possible payoffs – averaged data.

24. Types of players with respect to their IA patterns – 3 clusters Mean number of fixations per game in different AOIs for three different types of players.

25. Types of players with respect to their IA patterns – 3 clusters 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).

26. Types of players with respect to their IA patterns – 3 clusters 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).

27. Types of players with respect to their cooperation patterns – 2 clusters Mean cooperation for PD games with different CI: CI-based group (dotted line), non-CI-based group (solid line).

28. Types of players with respect to their cooperation patterns – 2 clusters Mean number of fixations per game in different AOIs for CI-based (dark grey bars).and non-CI-based players (light grey bars).

29. Types of players with respect to their cooperation patterns – 2 clusters Mean number of transitions per game in different AOIs for CI-based and non-CI-based players.

30. 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

31. 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 allpayoffs • influenced of CI • the most transitions • Type 3 - pay little attention to information • non influenced on CI • much less transitions

32. 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

33. Types of players - summary

34. Experiment 2 – computerized process tracing tool (CPT)

35. 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

36. Attention to different zones Mean number of zone attendances per game in all 14 areas of interest for the four experimental groups.

37. Cooperation in 4 experimental conditions Mean cooperation for PD games with different CI for the four experimental conditions.

38. Attention to different zones Mean number of fixations per game in zones containing participant’s possible payoffs, computer’s possible payoffs, participant’s move, and computer’s move.

39. Transitions between different zones Mean number of transitions per game between zones containing participant’s possible payoffs.

40. Transitions between different zones Mean number of transitions per game between zones containing participant’s possible payoffs – averaged data.

41. Types of players with respect to their IA patterns – 3 clusters Mean number of fixations per game in different AOIs for three different types of players.

42. Types of players with respect to their IA patterns – 3 clusters 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).

43. Types of players with respect to their IA patterns – 3 clusters 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).

44. Types of players with respect to theircooperation patterns – 2 clusters Mean cooperation for PD games with different CI: CI-based group (dotted line), non-CI-based group (solid line).

45. Types of players with respect to theircooperation patterns – 2 clusters Mean number of zone attendances per game in different AOIs for CI-based and non-CI-based players.

46. Types of players with respect to theircooperation patterns – 2 clusters Mean number of transitions per game in different AOIs for CI-based and non-CI-based players.

47. 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

48. Summary Three types of players on the basis of their IA pattern • Type 1 - pay attention to their ownpayoffs • influenced of CI • the most transitions • Type 2 - pay attention to allpayoffs • influenced of CI • less transitions • Type 3 - pay little attention to information • non influenced on CI • much less transitions

49. 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

50. Types of players - summary