The Benefits and Costs of Expected-Norm Consis-

In this part we look at whether it is profitable to be expected norm consis- tent when playing against different opponents.

We first summarise the payoff data from the experiment. Consistent trustors send significantly more than inconsistent trustors (£1.91 vs. £0.77, p-valuefor a Fligner-Policello robust rank order test is less than 0.0001). Meanwhile, consistent trustees return significantly more in total for all pos- sible amounts sent than inconsistent trustees: £7.74 (excluding all subjects who send £0 as trustors, because these are not asked for their beliefs; £6.64 if including those) vs. £4.60; p-value for a Fligner-Policello robust rank order test is less than 0.0001.

Based on the basic characterisation, there is a substantial number of inconsistent subjects. When the proportion of inconsistent subjects is rel- atively big, subjects risk their payoffs by being consistent, because the in- consistent subjects send less as trustors and return less as trustees than the consistent subjects. We analyse this by first looking as the real payoff data and then the simulation results.

30_{Fisher’s exact test result show that the hypothesis for equal proportion of EPS sub-}

54

TABLE3.5: Simulated result for payoffs

(between consistent/inconsistent trustors and trustees)

trustee

Con Incon

trustor Con 3.24, 3.57 2.54, 4.27 Incon 3.03, 1.51 2.75, 1.79

TABLE 3.6: Simulated payoffs for different combinations of expected norm consistency at subject level

Combinations Consistent in Trust YES YES NO NO

Consistent in Trustworthiness YES NO YES NO Payoffs

as trustor 3.63 2.39 2.95 2.80

as trustee 3.38 4.24 0.96 2.41

Total 7.01 6.63 3.91 5.21

Through out all the sessions and treatments (after random pairing and random selection of the pairing) , consistent trustors earn on average £2.80, while inconsistent trustors earn slightly more at an average of £2.86.31 Consistent trustees earn on average £2.66 which is significantly (p = 0.0081 for a Fligner-Policello robust rank order test) less than the £3.22 earned by the inconsistent trustees.

It is worth finding out what is the earning for the pair when they are both consistent in two roles comparing with those who are both inconsis- tent in both roles. Consistent pairs earn on average £1.25 more than incon- sistent pairs (£5.50 vs. £6.75). Given that the trust consistent subjects send more than trust inconsistent subjects, it is key to have a larger pie to divide between both players.

Next, we analyse the payoff based on a large simulated sample in or- der to see how being consistent pays. We randomly draw (with immediate

31_{The difference is not significant with p-value of a Fligner-Policello robust rank order}

test equals to 0.7265. The difference when they play against consistent or inconsistent trustees is not big with the highest average of £3, when inconsistent trustors play against consistent trustees, and lowest at £2.62, when consistent trustors play against inconsistent trustees.

replacement) 10,000 subjects’ play as trustors and trustees from the consis- tent and inconsistent categories and match them to calculate each subject’s payoff in each role.

First of all, the best scenario for trustors (with average payoff of £3.24) is to be consistent as trustor and play against inconsistent trustee. On the other hand, for trustees, they get the highest payoff (£4.27) when they are inconsistent as a trustee, but their opponents are consistent as trustor. The lowest payoff in each role is achieved by being consistent and playing against inconsistent opponent.32

In Table 3.6, we report the simulated payoffs when all players are of the same kind and they play among themselves.33 Interpreting along the line of Kant’s “categorical imperative” , it means that a player’s expected norm consistency principle is adopted as a maxim by the population, but in relative terms, that is each player in the population treat other people according to one’s own expected norm.

We randomly draw 30 subjects from certain consistent categories and divide them into three groups. Subjects from each group play the game once in each role against one of the other two groups. The payoff of a sub- ject is the sum of payoffs in playing both roles. Payoffs of 10 subjects from one of the three groups are recorded as 10 observations. This procedure is repeated 1000 times to generate 10,000 observations. Comparing the av- erage of these 10,000 observations from different consistency categories gives the following results.

The trustor-consistent and trustee-consistent population comes first, they could earn on average £7.01 for playing the two roles. Next comes the trustor-consistent and trustee-inconsistent subjects, their average earning is

32_{Analysis from a subject level confirms the above results. When we look at a subjects’}

consistency in both roles as a whole when they play the two roles, the highest earning subjects are consistent as trustor but inconsistent as trustee while their opponent are con- sistent as both trustor and trustee. They could expect to earn on average £8.23. Subject who are consistent in trustor and trustee get the lowest payoff when they face opponents who are inconsistent as trustor and consistent as trustee. They earn on average £3.45.

33_{In Table 3.5, the consistent trustor is not necessarily trustworthiness consis-}

tent(inconsistent), while in Table 3.6, subjects are characterised according to both trust and trustworthiness consistency. This means that the pools from which the strategies are randomly drawn is different.

56 £6.63, which is not significantly lower than the top population.The both in- consistent subjects population comes the third with the average earning of £5.21; it is significantly lower than the top two populations. The worst situ- ation as we have mentioned is when the subjects are all trustor-inconsistent and trustee-consistent. They earn on average only £3.91.

Subjects who send more are more likely to be consistent as trustor, thus creating a bigger pie between the pair. Inconsistent trustees generally return less thus keeping more for themselves. The general welfare of the population largely depends on the amount sent by the trustors, which is why trust is considered as a social capital. Trustworthiness is important in determining the distribution of the total welfare. When the environment is kind, that is when subjects are consistent as trustor and trustee, their payoffs are the highest.