Decision Making In Prisoner’s Dilemma

10.6 Discussion

Hypothesis H12 was 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.
We can conclude that the occurrence of an effect of learning depends on the particular strategy or mix of strategies encountered. We can say that subjects did not improve their performance against Benevolent, since it was already relatively easy to interact successfully with this particular strategy during the initial encounter with it. We can hypothesize that in a different mix of strategies optimal strategy against Random (which is ALL D) would be easier to follow – in our mix, subjects could find it psychologically difficult to act uncooperatively even against Random, because, generally, cooperative behavior was more successful.
Former research:
We did not come across any research that employed repeated exposure to particular strategies in the Prisoner’s Dilemma game to study the existence of inter-game effect of learning.
Helbing et al. (2005) found effect of learning in their experiments with The Route Choice Game. Subjects who previously discovered that oscillatory cooperation with opponents brought them highest gains, were able to apply this rule quickly to new games (the transfer studied by authors was from a 2-person Route Choice to a 4-person Route Choice).
Silverstein et al. (1998) found no significant transfer (in terms of cooperativeness) from an initial iterated Prisoner’s Dilemma game against certain strategy (ALL C, or ALL D, or Random, or Tit for Tat) to a new round of iterated games against real subjects (who previously also played against one of the strategies mentioned above and also showed no transfer).
Sheldon, 1999 successfully “trained cooperation” in his subjects by making them play a 15-rounds iterated Prisoner’s Dilemma against Tit for Tat: subjects cooperated in 61,4% in the first five trials and in 70% in the last five trials (so no end-effect was observed), the result was statistically significant (p < 0,01). One of Sheldon’s hypotheses was that this initial training would yield higher rates of cooperation during his subjects’ second game of iterated Prisoner’s Dilemma organized a month later: subjects were, then, randomly paired and played another 15-rounds game. The average rate of cooperation increased from 66,73% in the first sequence to 72,73% in the second game a month later (the result was statistically significant, p < 0,05). The obvious problem, though, is that the two sequences are not exactly comparable, since in the first game subjects played against a predetermined strategy, and a month later they played against another subject.
Adaptive learning in strategic games is currently studied in computer-simulated experiments. Although this approach has marked practical advantages, it may account for the relative lack of experimentation on human subjects, which is rather unfortunate. One of the early stochastic models (using positive and negative reinforcement and attenuation of cooperative propensities of the simulated agents) is Macy (1991). Examples of recent research in this area are Airiau et al., 2007; Banerjee & Sen, 2007.

11. Cheap-talk

11.1 Task

The task of this experiment is to study the influence of “cheap talk” on preliminary willingness to cooperate on part of the subjects and on the amount of cooperation subjects expect from their opponent.

Cheap talk is usually studied in form of a short discussion in a group that is to play Prisoner’s Dilemma. It was found previously that it enhances cooperation in the game (see section 6.3 paragraph (8) of the theoretical part):
The discussion had different forms in different studies, sometimes it was related only to the group itself, sometimes the upcoming game was discussed. We speak of cheap talk, because no one can bindingly commit to cooperation, and no one can enforce any such promises. There are at least three explanations why “cheap talk” might work: a) group identity and solidarity is developed, b) “cheap” but public promises and commitments are made, c) cooperative norms are primed. It is difficult to disentangle these three effects in empirical studies.
We will operationalize cheap talk as opponent’s statement of his preliminary willingness to cooperate (expressed as number of expected C choices – 9 C in 10 moves, in our case). The opponent will be represented by the experimenter.

11.2 Procedure

The present procedure does not employ actual playing of the game. Subjects will state their willingness to cooperate (expressed as the amount of C choices), and how much willingness to cooperate (expressed, again, as the amount of C choices) they expect on their opponent’s part. Subjects will give these statements and expectations for moves 1-10, 11-20, and 21-30 of a potential Prisoner’s Dilemma. We will then compare, whether the expectations differed in the condition with (condition Y) and without (condition X) cheap talk. Cheap talk, as noted above, is operationalized as opponent’s statement of his preliminary willingness to cooperate (in our case 9 C choices in 10 moves). Subjects are asked to fill in Table 11.1, and after completing it, they are administered Table 11.2 to fill it in as well.

Table 11.1: Subjects’ own expected willingness to cooperate and expected willingness to cooperate on the opponent’s part without cheap talk

	Moves
	1-10	11-20	21-30
Your preliminary willingness to cooperate (the amount of C choices)
Your opponent’s preliminary willingness to cooperate (the amount of C choices) you expect

Table 11.2: Subjects’ own expected willingness to cooperate and expected willingness to cooperate on the opponent’s part with cheap talk

	Moves
	1-10	11-20	21-30
Preliminary willingness to cooperate stated by your opponent	9 C	9 C	9 C
Your preliminary willingness to cooperate (the amount of C choices)
Your opponent’s preliminary willingness to cooperate (the amount of C choices) you actually expect