Experimental Design
The core of the data collection instrument is a multi-round public-goods game played on individual tablets.
The framing of the games is around carbon storage: contributions to the global public good are framed as being contributions towards carbon storage in the community's rangelands.
Participants play all public-goods games both in groups of about five players (a standard public-goods design) and individually (a group of one).
Group membership is reshuffled across games and drawn from the entire session of participants, so that over the course of a session a participant interacts with essentially all session-mates.
The games were designed as follows.
In each round, participants receive an endowment of 100 tokens and decide whether to fund rotational grazing, a binary choice ($g = 20$ tokens or $g = 0$), and unobserved contributions, $e$, representing a continuous choice of an additional conservation margin that others cannot observe, from zero up to the total remaining budget.
At the end of each round, the number of participants who contributed to rotational grazing are observable to all participants within the group, while individual decisions and unobserved contributions $e$ are not observable other than through their effect on the final aggregated payment outcome, which is contract-dependent and explained below.
We designed five different payment rules for the public-goods game and refer to them as contracts. Each contract is played twice: first solo (a single-person group), which serves as the individual principal-agent benchmark, and then in a group. The combination (contract by individual-or-group mode) is referred to as a game. One game is randomly selected for payment, and the number of paid rounds per game is determined by a block-random-termination rule.
The five contracts vary three design features: (a) whether the contract pays for observable (grazing) inputs or for measured output, (b) whether the output is exposed to a production shock, and (c) whether, in addition to the observed contributions, the output is affected by an additional unobservable margin, in which the individual chooses her contribution without revealing any signal to the group.
The full carbon (public good) production function is set to $F(G,E) = (2G + 1.5E)\varepsilon$, where $G$ and $E$ are the sums grazing and unobserved (extra) contributions in the community that is playing together, respectively. The production shock $\varepsilon$ is drawn from a two-point (Bernoulli) distribution with equally likely outcomes 0.5 and 1.5. The shock is therefore mean-preserving, and it is applied to the public good production after all contributions have been summed but before payments are distributed. Therefore, the contracts that inherit risk pay participants on the final outcome after the risk shock. All five contracts pay participants for their grazing contribution. Furthermore, the expected private marginal return of this contribution is set equal across all contracts within the same game-mode (solo or collective), ensuring equivalence in grazing incentives. On the other hand, only some contracts pay for unobserved contributions. Contracts C3 and C5 offer a positive return for extra contributions, while the other contracts do not.
The order in which the contracts appear is randomized across sessions. In every session, participants always begin with playing C1 then C2. From then on, the order of C3, C4, and C5 varies by community. For each contract, participants play the solo mode first, followed by the collective mode.
All in all, experimental assignment happens in two ways. First is within individuals since we have every individual engage with different types of contracts in the lab. From this engagement, we extract within-individual changes in behavior caused by the contract features they are facing. The second experimental assignment is in the order that these contracts appear. This assignment is at the session level. The variation is in which contract features comes first, second, third, fourth and fifth. That is, the order in which different contract features appear to all participants in a specific session.