# Calculate power for multiple rounds of public goods experiment

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

$$G=\sum_{i=1}^{n}(g_i)$$

$$p_i$$ 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.