Experimental Design Details
•The CRSD game involves multiple rounds during which players contribute to a public good; if the threshold is not met, all players incur negative consequences. CRSD has several features which make it a good fit for modelling climate change: There are repeated decisions before the outcome is evident, the remaining private good is at risk if the threshold is not met, and the value of the public good is unknown
Following Bachler et al. (2024), the CRSD game was adapted for a consumption context in this experiment. In each round, players are given four tokens. They must choose in each round how many tokens to invest in a good. When a token is contributed to the good at the start of a round, four times as many tokens are returned to the player at the end of the round. Tokens not contributed to the good are kept.
All tokens held at the end of the round are equivalent to one unit of byproduct produced in the round. If across all rounds a threshold of 140 units of byproduct is passed, a catastrophic event, in which all players lose all their tokens, occurs with 70% probability.
The game is played in Groups of 2, which remain consistent throughout the experiment. These groups are randomly assigned and anonymous. There is no communication between players. There are 10 rounds per section of the game, regardless of whether the threshold is passed at any point. If the threshold is crossed, whether the catastrophic event occurs will be randomly generated.
This experiment uses three variations of the CRSD game. A baseline game, A game with a carbon tax added, equivalent to 50% of the token returns from investing in the good. A game with a carbon tax as before, which also creates inequality between the two players by redistributing some of the earnings from investing in the good. All pairs play the untaxed game and either the equal- or unequal-taxed game.
Success in the game occurs when the pair completes all 10 rounds without passing the threshold; a pair is not treated as successful if they pass the threshold, but the catastrophe is not realised.
The experiment will consist of 5 stages. Section 1: all players play an initial CRSD game with or without a welfare-improving tax. Section 2: players then play the CRSD game they did not play in Section 1, so they have experienced both types of game.
In stage 3, players will be asked to vote on the game they have played so far that they would like to play again. Before the vote results are revealed, players will be asked how they expect their opponent to behave in each game. The winning game will be the one with the majority of votes, with ties broken at random by a computer.
This voting stage is important for evaluating the presence of failure in equilibrium reasoning because it allows us to see whether players still demand the game with lower payoffs, even after experiencing both games. It also shows whether they can correctly assess their opponent's strategy.
In a selection of randomly selected groups, an intervention will be implemented during the voting phase to address failures in equilibrium reasoning. A feature of FCTs is that when the problem is presented to players in a way which helps them focus on all contingencies, they can optimise the problem. The intervention aims to assess whether this feature is present.
Finally, in Section 4, they play the winning game they voted for,, and Section 5 then presents a post-experimental questionnaire to elicit risk aversion, inequality aversion, environmental attitudes, and opinions on taxes.
It will use the Revised New Environmental Paradigm (NEP) scale (Dunlap et al., 2000) to elicit views on Environmentalism. To elicit risk aversion, we will use the method described in Eckel and Grossman (2008). For inequality aversion, we will use a variation of the dictator game. where players can choose how much to split with their opponent. Finally, we will use the Resistance to Change Beliefs Scale (White et al., 2020) to establish conservatism.
The 10-round game, belief elicitation task, and risk and inequality aversion tasks are incentivised, with tokens earned in these games converted into a bonus payment.
Players will be excluded if they fail any one of an attention check question, a question using a visual allusion designed to catch the use of AI, or if they cannot answer a set of understanding questions after the instructions after 4 attempts.
In the game without tax, there are two equilibria. In the cooperative one, players coordinate so their combined contributions stay just below the threshold, and each contributes at least 4 tokens. For example, Player 1 puts in 10 tokens, and Player 2 puts in 8, totalling 18 and yielding payoffs of (70, 64), maximising joint welfare while staying below the threshold.
In the non-cooperative equilibrium, both players put all 40 tokens into the good, crossing the threshold and leaving each with an expected 48 tokens, accounting for the probability of the catastrophic event. A key problem is that one player can cross the threshold alone; for example, Player 1 putting in all 40 tokens is enough to do so without any contribution from Player 2. This means that cooperation is fragile
In the game under equal tax, due to the tax-effective threshold for the number of tokens that can be put into the good without exceeding it, the threshold rises to 58 combined tokens, meaning no single player can cross it with just their own contribution. Even if Player 1 puts in all 40 tokens, gaining a payoff of 80, Player 2 can respond with 18, with a payoff of 58, to stay just below 58 total tokens put into the good. This removes the non-cooperative equilibrium entirely, meaning coordination is the only equilibrium.
This is welfare-improving if the groups were not coordinating under no tax, as both now earn more than 48 tokens, and equal if the groups cooperate under the game with tax.
In the unequal tax, total joint welfare is unchanged relative to the equal-tax game, but it is redistributed. Both players still fare better than in the no-tax non-cooperative outcome of 48 tokens each, but the more heavily taxed player may end up worse than under no-tax cooperation, potentially giving them reason to prefer the untaxed game.