I would like to calculate/simulate the a-priori necessary sample size for a repeated public goods experiment.

$N$ Participants play $R$ rounds of a public goods game (linear, voluntary contribution mechanism, anonymous, no punishment, no communication, simultaneous decisions) in groups of $n$ (with $n \leq N$).

Let private payout of a participant $i$ be $\pi_i$ calculated as $\pi_i = p_i + \alpha \times G$, with


$p_i$ the contribution to the private account,

$g_i$ the contribution to the public account,

$ 0 < \alpha <1< \frac{\alpha}{n}$, which is the marginal per capita return (MPCR).

Each participant decides how much of their $E$ tokens she contributes to the public account, $0 \leq g_i \leq E$, whereas $p_i = E - g_i$.

Each round $r$ ($0 \leq r \leq R$) each individual $i$ starts with a new endowment $E$.

In the experiment, participants are randomly allocated to conditions. The conditions vary by two factors. Factor 1 has 2 levels, factor 2 has 2 levels, making this a 2x2 full factorial design. The levels are categorical. Random allocation is between-subjects, i.e. each subject $i$ is allocated to the same combination of factor levels each round. In other words: Treatment allocation does not vary with round $r$.

I want to test for significance of the interaction between F1 and F2 on contributions to the public good $g_{ij}$. I am not quite clear on whether to use a random or fixed effects regression model for this, since the dependent variable varies with $r$ but the independent variables stay constant across rounds $r$.

Either way I would like to calculate, resp. simulate the power of the interaction effect, given n. Since these types of experiments are frequently condcuted I wanted to ask whether someone could provide me with R or Stata Code for calculation or simulation, or any other type of resource.



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