TL;DR. Civic crowdfunding, the process of raising voluntary contributions from interested agents for public projects, such as public parks, libraries, etc., has grown in popularity in recent decades. As these projects are non-excludable, strategic agents often free-ride, i.e., choose not to contribute. To address this, researchers have used incentive engineering to construct mechanisms that incentivize strategic agents to contribute. This incentive is in the form of a “refund,” which is paid out to contributing agents in case the project was not funded. In this work, we characterize this refund — theoretically as well as practically. First, we present sufficient conditions that a refund bonus scheme should satisfy to crowdfund a project at equilibrium successfully. Then, we provide certain desirable conditions that are useful for crowdfunding in practice. We then present three novel refund schemes (and their respective mechanisms) that satisfy these conditions. We show that the mechanisms presented are better than the current state-of-the-art: (i) In terms of cost-efficiency when deployed as a smart contract over Ethereum; and (ii) In terms of performance in a Bagnoli and Lipmanreal-world setting through simulations using Reinforcement Learning (RL).

Crowdfunding has been gaining momentum, thanks mainly to the success of online platforms such as Kickstarter and GoFundMe. When used to fund non-excludable public goods, the process is referred to as civic crowdfunding. This success, however, necessitates the need for transparency and anonymity of payments. As a result, crowdfunding is now being deployed as smart contracts over EthereumWeiFund and Starbase are some examples of Ethereum based crowdfunding platforms. Bagnoli and Lipman present the baseline approach for civic crowdfunding with their mechanism, Provision Point Mechanism (PPM). In PPM, the social planner announces a target, known as provision point, and a deadline. If the agents’ contribution meets the target (by the deadline), the project is said to be provisioned. Otherwise, each agent is returned its contribution. While PPM has been used successfully, it leads to free-riding. This is because, as public projects are non-excludable, strategic agents may prefer not to contribute. Thus, the major challenge in civic crowdfunding is to incentivize strategic agents to contribute.

Zubrickas addresses the free-riding problem through his mechanism, the Provision Point mechanism with Refunds (PPR). PPR introduces a “refund bonus” to be paid to contributing agents, along with their contributions. The refund bonus scheme in PPR offers a bonus to agents, which is proportional to their contribution, in the case underprovisioning, i.e., the project not being provisioned. This incentivizes greater contributions from the agents. With this incentive structure, the author shows that PPR results in a simultaneous-move game in which the project is provisioned at equilibrium.

As observed by Chandra et al., PPR applied in online platforms results in agents delaying their contributions until the deadline. This is because the refund bonus scheme in PPR is independent of the time of an agent’s contribution. Thus, in an online setting, wherein agents can observe the history of the contributions, it becomes beneficial for agents to delay their contribution until the deadline. We define this delaying of contributions as a race condition. The race condition is undesirable as it can lead to the project not being provisioned due to server failures, transactions not being processed in time, etc. Towards this, the authors present Provision Point mechanism with Securities (PPS). PPS uses complex prediction markets (Abernethy et al.) to refund agents — such that an agent contributing early gets a higher refund than an agent contributing later, for the same contribution. This induces a sequential game in PPS, unlike PPR.

Observe that a refund bonus scheme plays a crucial role in designing provision point mechanisms for civic crowdfunding. Motivated by this, in this paper, we look at all the conditions a refund scheme should satisfy to be used for civic crowdfunding in online settings, to avoid free riding as well as the race condition. Towards this, we define (i) Contribution Monotonicity: the refund increases with contributions; and (ii) Time Monotonicity: the refund is non-increasing with time. We then prove that a refund bonus scheme satisfying these two conditions induces a game in which the project is provisioned, and all agents contribute as soon as they arrive. This is the first general result of a refund bonus scheme in civic crowdfunding literature. Also, we require that a refund bonus scheme must be clear to a layperson as well as cost-efficient when deployed as a smart contract.

Figure 1. Various Refund schemes satisfying Contribution and Time Monotonicity for an Agent.

Figure 1 presents three novel refund bonus schemes along with the mechanisms which deploy them — PPRG, PPRE, PPRP. Observe that each of these schemes decay with time, geometrically, exponentially, and polynomially, respectively. Moreover, it is trivial to see that these schemes are easier to explain than PPS with its sophisticated logarithmic scoring rule. Figure 2 shows that these schemes are significantly more cost-efficient than PPS when deployed as a smart contract over Ethereum.

Figure 2. Gas Consumption comparison between PPS, PPRG, PPRE, and PPRP.

To show that these mechanisms do not trade-off performance for cost-efficiency, we employ Reinforcement Learning based simulations to compare them with PPS. In our simulator, agents go through repetitive iterations and learn their best strategy through rewards as given by the respective mechanisms. We measure the performance through provision accuracy, i.e., the fraction of the public projects provisioned by the mechanism. Figure 3 presents one such result. Observe that, for a reasonable budget, PPRG performs similar to PPS. Additional results, as well as equilibrium analysis of the mechanisms, are available in the complete version of the paper.

Figure 3. Comparison of provision accuracy of PPRG, PPRE, and PPRP with PPS.

In summary, in this paper, we identify Contribution Monotonicity and Time Monotonicity as sufficient conditions for a refund bonus scheme to satisfy for the project to be funded at equilibrium. Further, we present PPRG, PPRE, and PPRP based on three simple refund bonus schemes that satisfy these conditions. We then show that PPRG is the most cost-efficient when deployed as a smart contract. Lastly, using reinforcement learning-based simulations, we show that PPRG performs at par with PPS, thereby not trading off cost-efficiency for performance.

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