We rely on simple sequential games with two strategies and two movers. As most of the employed games have prisoner dilemma structures, we label the two strategies as ‘cooperate’ and ‘defect’. In all games, the first-mover makes a decision to cooperate or defect, followed by the second-mover to make the same choice. For the second-movers we utilise the strategy method to elicit decisions, only focusing on behaviour after the first-mover has ‘cooperated’. Previous research has shown that unconditional cooperation (cooperate after defection) is very rare and it is not relevant for the estimation of our distributional preference parameters. The payoffs that can be achieved vary across games, where ‘cooperate-cooperate’ (CC) yields payoffs of (R,R), ‘cooperate-defect’ (CD) yields (S,T) and ‘defect-cooperate’ (DC) as well as ‘defect-defect’ (DD) yields (P,P). In our design we hold R (500 Tokens) constant, and vary P, T and S along 4 values, resulting in 4x4x4 = 64 games in total. The table below presents details on the specific values for P, T and S.
P T S
100 400 20
200 600 40
300 800 90
400 1000 180
Using the decisions from the second-mover, we then estimate three social preference models following the Charness-Rabin (2002) framework. We consider the second-movers choice to ‘cooperate’ to be a result of their social preferences as well as the ‘level of kindness’ by the first-mover. We measure ‘kindness’ along two dimensions, first we define R-P as the amount the first-mover has given to the second-mover and P-S as the risk of the first-mover that is associate with the decision to ‘cooperate’.
The three models we estimate then account for
1. Social preferences + noise
2. Social preferences + first-mover giving to second mover (R-P) + noise
3. Social preferences + first-mover risk to ‘cooperate’ (P-S) + noise
Using logit regressions, we estimate individual distributional preferences and sensitivity to the kindness of the first-mover in the three models described above. Most importantly, the estimated models also include a rationality parameter that captures noisy decisions, thereby allowing us to separate social preferences from noisy decision making.
For the data collection we assign subjects to either the role of the first- or second-mover for the entire experiment. In the beginning of the experiment, we group one first-mover with one second-mover. This match stays the same for the duration of the experiment and each group faces the same 64 game decisions in the identical random order. We always implement ‘defection’ after ‘defection’ for the second-mover and thus use the strategy method to elicit second-mover willingness to ‘cooperate’ after the first-mover’s decision to ‘cooperate’. Thus, both players in our set-up make a binary decision between cooperating and defecting (C, D) in each game. Choices are incentivised by selecting one random game for a group and pay a bonus according to the decisions made.
In addition, we also elicit incentivised beliefs of each player after each game, where the player reports the probability of the other player to choose ‘cooperate’. We incentivise these using a binary scoring mechanism, where honest reporting yields a higher chance to win a fixed bonus than misreporting the probability.
Charness, G., & Rabin, M. (2002). Understanding social preferences with simple tests. The Quarterly Journal of Economics, 117(3), 817-869.
Giamattei, M., Yahosseini, K. S., Gächter, S., & Molleman, L. (2020). LIONESS Lab: a free web-based platform for conducting interactive experiments online. Journal of the Economic Science Association, 6(1), 95-111.