# The Circulation of Worthless Tokens Aids Cooperation: An Experiment Inspired by the Kula

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. The Kula: the Bond between Objects and People

#### 1.2. Related Experimental Literature

## 2. Results

#### Summary Statistics

#### Regression Analysis

^{2}of 0.17, we estimate a required sample size of 64, which is well below the number of participants (138).

^{2}of 0.033, we estimate a required sample size of 377, which is a number above the total number of participants in our studies (198). The low R

^{2}is the clear source of the lack of power. To tackle this problem, we augment regression (2) with a new regressor that we know from earlier analysis plays an important role in explaining period t contributions, i.e., the total amount contributed to the public good by all players −i in round t − 1. This regressor was already used in regression 1. This new regression features a much higher R

^{2}of 0.15 and the sample size required now is 85, which is well below our number of participants. The new regressor is significant, and the magnitude is identical to the one estimated in regression 1. The new estimates are: ${\widehat{\gamma}}_{1}$ = 0.715, S.E. (${\widehat{\gamma}}_{1})=0.334$, p < 0.05, ${\widehat{\gamma}}_{2}$ = 0.68, S.E. (${\widehat{\gamma}}_{2})=0.363$, p < 0.1, ${\widehat{\gamma}}_{3}$ = 0.14, S.E. (${\widehat{\gamma}}_{3})=0.24$, statistically insignificant, ${\widehat{\gamma}}_{4}$ = −0.24, S.E. (${\widehat{\mathsf{\gamma}}}_{4})=0.16,\mathrm{also}\mathrm{statistically}\mathrm{insignificant}$. The signs of the newly estimated cofficients are the same and the p-values are comparable. The magnitudes of the treatment effects are, however, smaller in the new regression.

#### Robustness Checks

- “Do you think the cardboard pieces were valuable?” 42% of participants answered yes.
- “Do you think the cardboard pieces were useful?” 32% of participants answered yes.
- “Why do you think that some players might have chosen NOT to send the cardboard piece in some rounds?

- “They thought that, at the end of the experiment, the cardboards could be exchanged for money.” In total, 44% of the participants chose this option.
- “They kept the cardboards to use them later” (8%).
- “They kept the cardboards because they liked them” (11%).
- “They thought that sending the cardboard was useless and therefore they did not send them” (14%).
- “They had no cardboard available and, therefore, they could not send any” (20%).

## 3. Discussion

## 4. Materials and Methods

**Hypothesis**

**1.**

**Hypothesis**

**2.**

**Hypothesis**

**3.**

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix

#### Instructions for the Bracelet Study

- How many EMU you spent in good 2 in this round.
- How much all members of your group have spent on good 2 in this round.
- Your earnings from good 2. As already explained, this value (which we have called above g) is obtained by summing the EMU spent in good 2 by all the members of your group, multiplied by 0.4.
- Your total profit in the current round calculated as the sum of x plus g.
- How many EMU you accumulated in total until the current round.
- Please remain silent for the entire duration of the experiment.

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1 | Cf. e.g., Feil ([2]), conducting work in Papua New Guinea and documenting objects such as animals and trees serving this function. |

2 | |

3 | There is a rich literature in economics on signaling as a way to convey information about one’s “type,” information that is otherwise unobservable by the counterpart. Cf. [9] (p. 385) for a presentation of these models. Cf. also [10], showing that signals may, under some parameter choices, spread and be an evolutionary-stable strategy. |

4 | Cf. [6] (p. 287) quoting an islander from the island of Gava saying that “When you are given a Kula shell, your name is spoken; people come to know your name. You climb (ku-mwena).” Also, [11] (p. 166) discussing the “name spreading function” of the Kula in a society that featured no writing and, hence, no possibility of a written record of someone’s ranking in society. |

5 | Although Malinowski reported that the ceremonial aspect of the exchange (Kula) and barter (gimwali) did not “mix”, later scholarship has found that the possessors could use Kula tokens to leverage their position in gimwali barters (i.e., to secure yams, land, and women, cf. [12] (p. 204). |

6 | Cf. on the question of the “value” of the Kula objects [13], (pp. 242–243). |

7 | [14] find evidence in the lab that gifts are given in a three-player (two “producers”, one “customer”) experimental game, and these gifts create obligations to repay. Customers typically favor the producer who gives the gift and discriminate against producers who do not give gifts. |

8 | In William Blackstone’s famous words, ownership is “that sole and despotic dominion which one man claims and exercises over the external things of the world, in total exclusion of the right of any other individual in the universe ([16], Vol. II, p. 3). |

9 | Cf. [11] (p. 166): “the public good in question in the Kula Ring is law and order.” |

10 | Cf. also [25], where recipients have the possibility to send emoticons to their “dictators”. They find that the emoticons are often used and effective in discouraging selfish behavior. |

11 | [8] (p. 71) noticed that the vaygu’a were “at once wealth, tokens of wealth, means of exchange and payment, and things to be given away or destroyed”, and hence should be put in the same “genus” as money (p. 94). He noticed that in Germanic languages the words token and Zeichen both designate money. He criticised Malinowski ([1], p. 528) for objecting to the use of the term "money" for the Kula tokens. According to Mauss, Malinowski adopted a "narrow" notion of money, as storage of value backed by an external institution, which is only applicable to modern societies (p. 94). |

12 | All statistical analyses were conducted using STATA ^{®} 15. |

13 | Across all studies, the distribution of the contribution to the public good is asymmetric, with a spike at 0. A Shapiro-Wilk’s test rejects the null hypothesis of normality for all studies. |

14 | Performing the same test using only period 1 contributions (72 observations for the controls, 162 observations for the treatments) yields equivalent results. Also performing the same test using the median contribution for each group of participants in the first period as the unit (10 observations for the controls and 23 for the treatments) yields equivalent results. While restricting attention to the first period alleviates the problem of the lack of independence of contributions of the individuals across time, it is obviously a wasteful empirical strategy. Considering the longitudinal nature of our dataset, panel data estimators are the natural choice of estimators. |

15 | The result is the same if one restricts attention to period 1 only. |

16 | The period-1 pairwise comparisons of contributions in the control with delay study and each of the treatments, as well as the pairwise comparisons between the treatments, all yield insignificant results. |

17 | Restricting the analysis to period 1 only (24 observations), the mean of contPG is 4.29 and the standard deviation 3.44. The mean of payoff is 16 and the standard deviation 3.71. |

18 | Period 1 only (36 observations): the mean of contPG is 3.44, the standard deviation 2.93. The mean of payoff is 14.82 and the standard deviation 3.14. |

19 | Period 1 only (54 observations): the mean of contPG is 4.46 and the standard deviation 2.71. The mean of payoff is 16.25 and the standard deviation 2.81. The mean of tokensent is 0.76 and the standard deviation 0.43. |

20 | In three cases, we failed to record whether the token was sent or not. |

21 | Period 1 only (54 observations): the mean of contPG is 4.76 and the standard deviation 3.4. The mean of payoff is 16.66 and the standard deviation 3.7. The mean of tokensent is 0.74 and the standard deviation 0.44. |

22 | In one case, we failed to record whether the token was sent or not. |

23 | Period 1 only (30 observations): the mean of contPG is 4.5 and the standard deviation 3.11. The mean of payoff is 16.3 and the standard deviation 3.38. The mean of tokensent is 0.83 and the standard deviation 0.38. |

24 | |

25 | Simple linear regressions of the contributions on the round number find a significant negative trend in each control and treatment. Contributions appear to fall faster in the control and bracelet studies (coefficient estimates= −0.28 and −0.29 respectively, 95% confidence intervals [−0.4, −0.17] and [−0.36, −0.22]), followed by the cardboard (coefficient estimate: −0.2, 95% confidence interval [−0.3, −0.12]), home object (coefficient estimate: −0.19, 95% confidence interval [−0.27, −0.1]) and control with delay (−0.10, 95% confidence interval [−0.18, −0.02]) studies. The confidence intervals in the cardboard and home object studies overlap to a large extent to include the two studies’ point estimates of the time trend. The time trend in the bracelet study appears instead steeper than the time trends in the cardboard and home object studies. |

26 | This way of defining the dummy variables does not differentiate between the cases in which a token was available to be sent and was not sent, and the case in which a token was not available, and therefore it could not have been sent. The receiver of the token could not differentiate between these two cases, but only observed whether the token was received or not. |

27 | In two cases, we failed to record whether the token was sent or not. |

28 | An English translation of the instructions of the bracelet study can be found in Appendix. The instructions of the other treatments are minor variant of these instructions, available upon request from the corresponding author. |

**Figure 5.**Contributions to the public good and proportion of tokens sent/received in each round (cardboard studies only).

a. Control Study17 | |||||

Variable | Obs | Mean | Std. Dev. | Min | Max |

contPG | 288 | 3.22 | 3.56 | 0 | 10 |

payoff | 288 | 14.51 | 3.86 | 4.8 | 24.4 |

b. Control with Delay Study18 | |||||

Variable | Obs | Mean | Std. Dev. | Min | Max |

contPG | 432 | 2.83 | 2.80 | 0 | 10 |

payoff | 432 | 13.97 | 3.08 | 5.4 | 23.6 |

c. Bracelet Study19 | |||||

Variable | Obs | Mean | Std. Dev. | Min | Max |

contPG | 648 | 3.39 | 3.3 | 0 | 10 |

payoff | 648 | 14.73 | 3.74 | 4 | 25.2 |

tokensent | 64520 | 0.39 | 0.49 | 0 | 1 |

d. Cardboard Study21 | |||||

Variable | Obs | Mean | Std. Dev. | Min | Max |

contPG | 648 | 4.26 | 3.91 | 0 | 10 |

payoff | 648 | 15.97 | 4.7 | 4 | 29.6 |

tokensent | 64722 | 0.31 | 0.46 | 0 | 1 |

e. Home Object Study23 | |||||

Variable | Obs | Mean | Std. Dev. | Min | Max |

contPG | 360 | 2.98 | 2.75 | 0 | 10 |

payoff | 360 | 14.17 | 3.08 | 5.6 | 24 |

tokensent | 360 | 0.52 | 0.5 | 0 | 1 |

Coefficient | RE | FE |
---|---|---|

${\widehat{\beta}}_{1}$ | 0.3404 * | 0.3730 * |

${\widehat{\beta}}_{2}$ | 0.2635 | 0.2980 * |

${\widehat{\beta}}_{3}$ | 0.0175 | −0.0127 |

${\widehat{\beta}}_{4}$ | 0.1078 *** | 0.0961 *** |

constant | 1.312 *** | 1.518 *** |

Coefficient | RE |
---|---|

${\widehat{\gamma}}_{1}$ | 1.5813 * |

${\widehat{\gamma}}_{2}$ | 1.3827 * |

${\widehat{\gamma}}_{3}$ | 0.3833 |

${\widehat{\gamma}}_{4}$ | −0.6250 |

constant | 3.2222 *** |

Variable | Obs. | Mean | Std. Dev. | Min. | Max. |
---|---|---|---|---|---|

contPG | 432 | 4.05 | 3.52 | 0 | 10 |

payoff | 432 | 15.67 | 3.93 | 4 | 25.2 |

tokensent | 43027 | 0.57 | 0.49 | 0 | 1 |

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**MDPI and ACS Style**

Danese, G.; Mittone, L.
The Circulation of Worthless Tokens Aids Cooperation: An Experiment Inspired by the Kula. *Games* **2018**, *9*, 63.
https://doi.org/10.3390/g9030063

**AMA Style**

Danese G, Mittone L.
The Circulation of Worthless Tokens Aids Cooperation: An Experiment Inspired by the Kula. *Games*. 2018; 9(3):63.
https://doi.org/10.3390/g9030063

**Chicago/Turabian Style**

Danese, Giuseppe, and Luigi Mittone.
2018. "The Circulation of Worthless Tokens Aids Cooperation: An Experiment Inspired by the Kula" *Games* 9, no. 3: 63.
https://doi.org/10.3390/g9030063