Experimental Investigation of Different Public Good Mechanisms
Liwen Chen1 Yue Liu2
Alexander Matros3
We conducted a series of experiments where players could freely choose between two public good
mechanisms: voluntary contribution and lottery mechanism. We showed that overwhelming majority of
the players preferred the voluntary contribution mechanism (VCM) over the lottery mechanism, even
when the latter was expected to bring higher payoffs. In a follow-up experiment, we reduced the risks in
the lottery game by splitting one lottery prize into two, which led to half of the players shifting to the
lottery mechanism. Prior research comparing public good mechanisms has focused on settings where
players have no freedom to choose the mechanism that they prefer.
Key words: experiment, public good provision, VCM, lottery
I.
Questions & Hypotheses
Recently scholars of charitable economics have propagated to use lotteries to raise public funds
(Morgan, 2000; Morgan & Sefton, 2000; Lange, List & Price, 2007). In experimental settings, players
who played the public good game based on lottery mechanism contributed more than those playing the
game based on voluntary contribution mechanism (VCM). According to a typical setup, the player either
participated in the lottery mechanism only, or in the VCM only. In the real world, however, public goods
donors are rarely obligated to participate in one certain charity; rather, they have the freedom to choose
from co-existing charities of different kinds. Thus we may wonder: when the donors have the freedom to
choose, which mechanism will they prefer, lottery mechanism or VCM? How do the freedom of choice
affect their contributions to the public good? Which mechanism will generate greater public good?
To investigate the questions, we designed a series of public good experiments where 10 players have
to choose either to join the VCM island (where the public good game based on VCM is played) or the
lottery island (where the public good game based on lottery mechanism is played). The number of players
that ends up in either island could be between 1, if the player is the only person who chooses this island,
and 10, if all players choose the same island. We give money to the islands in different ways. In the VCM
island, we put extra bonus to the common pool: each player in this island will get the bonus on top of
what they earn from playing the public good game. In the lottery island, we put a lottery prize to the pool:
one (and only one) player among those choosing the lottery island will win. Specifically the more the
player contributes, relative to the total contributions made to the lottery island, the more likely that she
will win. Based on the Two-Island Public Good Game we recently developed (Chen, Liu & Matros,
2016), we specified 3 scenarios with various amounts of bonuses and lottery prizes, and we predicated
that different islands will be chosen by players facing different scenarios (Table 1):
Experiment #
1
2
3
1
Table 1. Summary of settings and hypotheses
VCM island:
Lottery island:
Hypotheses: between the two
Bonus token
Lottery prize
islands, players will choose:
5.8
5.5
VCM island
3.2
5.5
lottery island
0
5.5
lottery island
Darla Moore School of Business, University of South Carolina
Department of Sociology, University of South Carolina
3 Darla Moore School of Business, University of South Carolina
2
II.
Experiment procedure
Each experiment consisted of 2 groups of 10 players. Instructions and decision-makings were
computerized using the z-Tree software (Fischbacher, 2007). Players were not allowed to communicate
with one another. Each session consisted of 10 rounds; and each round followed the similar two stages:
Each player was given an endowment of 20 tokens. In Stage 1, each was solicited for 20
contributions that she would make, for all numbers of players and for both islands. Specifically, they first
played as if they were in VCM island, and they decided how much out of 20 tokens they would contribute
when the number of players choosing the island is from 1 to 10. Then they made the similar 10 decisions
as if they were in the lottery island. By asking for the 20 possible decisions before asking for the preferred
island, we are able to gather much more information as to how players behave in all possible situations.
In Stage 2 each player was asked to choose one island between the VCM and the lottery island.
Afterwards the computer calculated payoffs immediately, based on the realized number of players in each
island, as well as the entered contributions for the realized numbers of players retrieved from Stage 1.
III.
Observations
1. Players preferred the VCM over the lottery island when the latter had higher expected payoffs.
We first look at the choice of island. Experiment 1 confirmed our prediction, showing that players
quickly converged on choosing the VCM island. It is surprising that, however, in Experiment 2 where
lottery brought higher expected payoffs, players unambiguously converged on the VCM island too.
Experiment 3 served as a baseline where we completely removed the bonus given to the VCM island, and
players turned to the lottery island instead. Figure 1 depicted where and when the convergence happened.
Prior studies on mechanism comparison focused on settings where the players cannot choose the
mechanism, confirming the overwhelming advantage of lotteries over VCM. However we should not
assume the two mechanisms are equally popular in real life --- as suggested by Experiment 2, the lottery
mechanism may not be chosen by players who “vote with their feet”, even when it expects higher profits.
Figure 1. Players’ choice of island and realized average contributions, displayed for each experimental group
Experiment 1:
VCM bonus =
5.8;
Lottery prize =
5.5
Experiment 2:
VCM bonus =
3.2;
Lottery prize =
5.5
Experiment 3:
VCM bonus =
0;
Lottery prize =
5.5
Players’ choice of island is measured as the percentage of total players of each group. The realized average
contributions are measured as the percentage of endowment contributed based on the realized number of players.
2. The public good provision was more efficient when we placed less bonus to the VCM island.
Regarding contributions to the public goods, consistent with previous findings we saw players
contributed higher than equilibrium predictions (purple lines in Figure 3 & 4 in Appendix) for both
islands. More interestingly, in our two-island setting, their contributions were negatively associated with
the bonus we initially placed in the VCM pool. With the least initial money, Experiment 3 solicited the
most contributions, Experiment 2 solicited less, and Experiment 1 solicited the least with highest
investment. Competition of coexisting institutions may benefit fund raising by boosting contributions.
3. Players contributed more in either island as the number of players in the island increases.
In prior research, players interacted with a fixed number of people in either the VCM game or the
lottery game. By employing the two-island setup, we are able to observe different contributions when
they are playing with different numbers of people. We found that players slightly increased contributions
as more players chose the VCM island, though the dominant strategy of VCM is to contribute zero
regardless. Players increased their contributions in similar ways in the lottery island, which is consistent
with our model prediction (Figure 4).
IV.
Follow-up experiment: does risk affect choice of island?
Why did the players fail to choose the lottery island with higher expected payoffs? One explanation
is uncertainty of the lottery: players would rather gain less from VCM with certainty, than gain more from
the lottery game via gambling. We ran a follow-up study with 20 players to test the explanation. We held
everything the same as Experiment 2 except that we reduced the risks of losing the lottery by splitting the
single prize of 5.5 tokens into two prizes of 2.75 tokens. Successfully we observed a shift in choice of
island: half of the players chose the lottery island, half the VCM island (Figure 2 in Appendix).
V. Results
We experimentally investigated different public good mechanisms by allowing players to freely
choose between the VCM and the lottery mechanism. The results allow us to question the well-accepted
propagation of using lotteries to raise public funds---lottery mechanism may not be chosen by players
with free choice, even when lotteries are expected to be more profitable. Yet with risk-averse donors, the
disadvantage of lotteries may be countered when funds raisers employ multiple-prize lotteries rather than
single-prize ones.
References
Chen, L., Liu, Y., & Matros, A. (2016). What do you choose for public good provision: VCM or
lottery? Working paper.
Fischbacher, U. (2007). z-Tree: Zurich toolbox for ready-made economic experiments. Experimental
economics, 10(2), 171-178.
Lange, A., List, J. A., & Price, M. K. (2007). Using lotteries to finance public goods: Theory and
experimental evidence. International Economic Review, 48(3), 901-927.
Morgan, J. (2000). Financing public goods by means of lotteries. The Review of Economic Studies,
67(4), 761-784.
Morgan, J., & Sefton, M. (2000). Funding public goods with lotteries: experimental evidence. The
Review of Economic Studies, 67(4), 785-810.
Appendix: Supporting Figures
Figure 2. Players’ choice of island and realized average contributions in follow-up experiment
VCM bonus =
3.5;
Lottery prize =
2.75*2
Players’ choice of island is measured as the percentage of total players of each group. The realized average
contributions are measured as the percentage of endowment contributed based on the realized number of players.
Figure 3. Voluntary contribution to VCM island from Round 1 to 10.
Voluntary contributions were collected by asking the players how much they would contribute when the number of
players is from 1 – 10 in the VCM island. We missed the last round data of Experiment 1 due to technical problem.
Figure 4. Contribution to the lottery island from Round 1 to 10
Voluntary contributions were collected by asking the players how much they would contribute when the number of
players is from 1 – 10 in the lottery island. We missed the last round data of Experiment 1 due to technical problem.