Informational nudges and public goods in networks

ABSTRACT

We present a model of voluntary contributions for a local public good, with individuals in a fixed network. We consider the introduction of an informational nudge, and model individuals' reaction to the nudge using a moral cost function. Regardless of the regulator's level of information, an informational nudge may induce higher levels of aggregate contributions in circle and complete networks, and reduces strategic uncertainty, as long as individuals' sensitivity to the nudge is high enough (contrary to the star and line networks). If in star and line networks agents' sensitivity to the nudge also matters, the regulator's degree of knowledge regarding each individual position in the network becomes crucial, as the efficiency of our nudge is lowered under incomplete information (it is not possible to send personalized information to each agent). Our main conclusion is therefore that a nudge policy should target specific individuals (those being the most sensitive to the nudge or having the highest interest for the public good) in specific networks (those in which each agent should contribute the same). We finally discuss some ethical concerns related to nudge implementation because of their potential for manipulation.

KEYWORDS:

• Information disclosure
• local public goods
• moral cost
• network
• nudge

JEL CODES:

• C72
• D83
• H41

Acknowledgments

We would particularly like to thank Gisèle Umbhauer, Yann Bramoullé, Jocelyn Donze and Rabah Amir for their helpful comments. We are also grateful to the participants of the BIOECON conference (Cambridge, 2016), of the French-German Workshop on Experimental Economics (Konstanz, 2016), of the EAERE conference (Athens, 2017), of the APET conference (Paris, 2017) and of the FAERE conference (Nancy, 2017).

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 If the energy consumption of the household was below (above) the mean, a smiley (sad emoticon) was used.

2 In our model, we also explain that the moral cost function may depend on individuals' environmental sensitivity, their confidence in the institution implementing the nudge, in their interest in the public good under consideration, etc. In a sum, we can give several interpretations to this psychological component.

3 The complete network is a special case in which each individual is linked to everyone else.

4 They are not interested in what individuals should contribute, but in what individuals actually contribute.

5 Different Nash equilibria are possible ranging from distributed (each individual contributes) to specialized (some contribute at the level of the Nash equilibrium; others do not contribute at all), and hybrid (between the two previous kinds of equilibria).

6 In the context of a neighbourhood, $g_{ij}=1$ if individual j is the direct neighbour of individual i. In the context of social networks (Facebook, Twitter, Linkedin, etc.), $g_{ij}=1$ if individual j is a ‘friend’ of individual i.

7 López-Pintado (2013) proposed a model of voluntary contributions to a public good in networks with directed links.

8 Since each player's payoff is jointly continuous in the actions and strictly concave in own action, the reaction curves are continuous functions, and thus the existence of a pure-strategy Nash equilibrium follows in a standard way from Brouwer's Fixed Point Theorem (see e.g. Friedman 1977). We will actually produce an explicit Nash equilbrium below.

9 Note that a condition to ensure a positive total amount of contributions is that $f^{\mathrm{\prime }}\left(0\right)>c$. In that case, the first-order condition is such that $f^{\mathrm{\prime }}\left(0\right)-c>0$: the individual has an interest in increasing her level of contribution.

10 A graph is said to be regular if each individual has the same number of neighbours $k_i$.

11 Bramoullé and Kranton (2007) explain that it may be more efficient in a non-regular graph for some individuals to not contribute in an efficient profile (p. 485). In particular, if the neighbourhood of some agent is a subset of the neighbourhood of another agent, then it is more efficient if the agent with the largest neighbourhood contributes because more agents benefit from her contributions. In that case, the agent with the smallest neighbourhood should not contribute.

12 In this setting, the formulation of the moral cost is similar to that of Figuières, Masclet, and Willinger (2013), who consider a moral cost function that depends on the distance to a moral ideal that individuals have. It is also similar to the model proposed by Brekke, Kverndokk, and Nyborg (2003), in which the authors assume that individuals will incur a moral cost if they depart from their personal self-image.

13 This condition can also be interpreted in terms of individuals' trust in the regulator.

14 ‘As if’ individuals had the same position in the network.

15 Everyone is told what the individual in the centre should contribute, as well as what individuals in the periphery should contribute.

16 This point may appear obvious. Notwithstanding, efficiency in this type of network requires some individuals to not contribute. This motivated the study of these two strategies.

17 This level of contribution has been computed using the same utility function as in the rest of the paper.

18 This last issue could be considered as an extension of this paper.

19 We have for a targeted individual$-h^{\mathrm{\prime }}\left(a_i^N-9.75\right)=-m\left(a_i^N-9.75\right)=-0.03(0.76-9.75)=0.27$ and$f^{\mathrm{\prime }}\left(A^P\right)-f^{\mathrm{\prime }}\left(a_i^N+\sum _{j\in n_i}{a}_j\right)=\frac{4}{1+3}-\frac{4}{1+2.24+0.76+1.48}=1-0.73=0.27$ and the sum of contributions for individuals who are not targeted is always equal to 3 (i.e. $A^P$).

20 According to Kahneman (2003), individuals act according to two systems of thinking. The first one, System 1, is quick and automatic. The second one, System 2, is slow and rational (this is the system that is used when individuals need to think before acting).

21 Note that we have:$f^{\mathrm{\prime }}\left(0\right)=4>1=c$

22 Hybrid and distributed equilibria add complexity since it is more difficult for individuals to coordinate.

Additional information

Funding

Benjamin Ouvrard acknowledges funding from ANR under grant ANR-17-EURE-0010 (Investissements d'Avenir program).