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\begin{document}


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\flushleft
\begin{frontmatter}

\journal{}

\title{Does risk communication really decrease cooperation in climate change mitigation?-- Supplementary Material}

\author[lnu,disa]{Mike Farjam\corref{cor}}
\ead{mike.farjam@lnu.se}

\author[jena]{Olexandr Nikolaychuk}
\ead{olexandr.nikolaychuk@uni-jena.de}

\author[lnu,disa]{Giangiacomo Bravo}
\ead{giangiacomo.bravo@lnu.se}

\cortext[cor]{Corresponding author: Department of Social Studies, Linnaeus University, 35195 V\"axj\"o, Sweden}
\address[lnu]{Department of Social Studies, Linnaeus University, V\"axj\"o, Sweden}
\address[disa]{Linnaeus University Centre for Data Intensive Sciences \& Applications (DISA@LNU), V\"axj\"o, Sweden}
\address[jena]{Faculty of Economics and Business Administration, Friedrich Schiller University, Jena, Germany}

\end{frontmatter}


\begin{appendix}

\section{Lottery selection}\label{sec:lottery}

The decision whether or not to invest into a climate change mitigation initiative can be seen as a choice between two lotteries: $L_1$, where climate change occurs with some known \textit{a priori} probability $p$ and leads to the loss of the whole endowment $E$; and $L_2$, where this probability is reduced to a \emph{residual} level $\pi$ at the cost $C$ ($\pi < p$). As such, the expected utility of $L_1$ is equal to $(1 - p) \cdot E$ whereas the expected utility of $L_2$ is equal to $(1 - \pi) \cdot (E - C)$. The rational agent will choose $L_2$ over $L_1$ as long as $(1 - \pi) \cdot (E - C) > (1 - p) \cdot E$, which is equivalent to the following condition:
\begin{equation}
C < \frac{p-\pi}{1-\pi} \cdot E \label{eq:lottery}
\end{equation}


\section{Experimental instructions (translated from German)}
\label{sec:instructions-eng}

\begin{center}
\textbf{Instructions\\ Welcome to the Experiment!}
\end{center}

\subsection*{1. General Information}

You can earn money in this experiment. All transfers made during the course of the experiment will be denominated in ECU. \textbf{3 ECU correspond to 1 Euro}. For the experiment to be successful, you must not talk to the other participants or make yourself stand out in any way. Please read the following rules of the experiment carefully. If you have questions, press the red button on the computer keyboard. Press the Start button on the computer screen when you are done reading the instructions. You will then have to answer some control questions. Your answers will be checked by the computer.

\subsection*{2. Climate Change}

Below, we will present a game that simulates the climate change. The worldwide climate change is a real environmental problem faced by mankind. The majority of climate scientists expect that by the year 2100, the \textbf{average temperature} in the world is going to increase by \textbf{1.1--6.4 degrees Celsius}. It is also estimated that mankind significantly contributes to the climate change by emitting greenhouse gases, carbon dioxide ($CO_{2}$) being the major one. Among other things, $CO_{2}$ is produced as the result of burning fossil fuels such as coal, oil and natural gas as part of industrial processes or energy production as well as when using internal combustion engines in automobiles. $CO_{2}$ is a global pollutant. i.e., it has the same effect on the climate regardless of the emission site.

\subsection*{3. Game Rules}

Altogether, \textbf{6 players} participate in the game, i.e., 5 other players besides you. The decision problem is the same for each player. At the beginning of the experiment, an initial endowment (= \textbf{40 ECU}) will be credited to your personal account. In the course of the experiment, you can choose whether or not to invest the money from your account. In the end, what remains in your account will be paid out to you in cash. The decisions you make are anonymous. To ensure that, you will be given a pseudonym for the whole duration of the game. These pseudonyms correspond to the names of the moons in our Solar system (Ananke, Telesto, Despina, Japetus, Kallisto or Metis). Your name can be found on the bottom left of the screen.

In the course of this experiment you will play exactly \textbf{ten climate rounds}. In these rounds, you can invest in an attempt to protect the climate and lower the probability of the climate change. Among other things, dangerous climate change leads to serious economic losses, which is being simulated in this experiment. In each climate round of the game, all six players will be asked \textbf{simultaneously}:

\begin{center}
\emph{"How much would you like to invest into climate protection?"}
\end{center}

The permissible answers are 0, 2 or 4 ECU. As soon as every player has made their decision, all six decisions are displayed simultaneously. After that, all the contributions made are credited to the climate protection account ("climate account") by the computer.

At the end of the game (that is, after exactly 10 rounds), the computer compares the climate account to the predefined amount (= \textbf{120 ECU}). This amount must be collected in order to reduce the probability of a dangerous climate change. It will be reached if \textbf{each} player pays an \textbf{average} of \textbf{2~ECU} for climate protection \textbf{every} round. In that case, there would be 12 ECU payed to the climate account every round. In case the 120 ECU needed for the climate account is collected, each player receives what remains in their private account, i.e., the initial endowment of 40 ECU minus the amount payed by the player to the climate account, with a probability of \{\textbf{100\%} \textcolor{gray}{(Baseline)} / \textbf{80\%} \textcolor{gray}{(RR1 and RR2)}\}. If the 120 ECU is collected, the players lose the amounts in their private accounts with a probability of \{\textbf{0\%} \textcolor{gray}{(Baseline)} / \textbf{20\%} \textcolor{gray}{(RR1 and RR2)}\}. In case the 120 ECU needed for the climate account is \textbf{not} collected, the dangerous climate change, followed by serious economic losses, happens with a probability of \{\textbf{70\%} \textcolor{gray}{(Baseline and RR1)} / \textbf{90\%} \textcolor{gray}{(RR2)}\} (that is, in \{7 \textcolor{gray}{(Baseline)} / 9 \textcolor{gray}{(RR1 and RR2)}\} out 10 cases). With this probability, you lose the money remaining in your private account, and nobody gets paid out anything. With the probability of \{\textbf{30\%} \textcolor{gray}{(Baseline and RR1)} / \textbf{10\%} \textcolor{gray}{(RR2)}\}, you keep your money and get paid out what remains in your private account after the game. The chance will be resolved in your presence. In any case, the payments will be made anonymous. Your identity will be kept secret from the other players.

\subsection*{4. Example}

Here, you can see an example of the decisions made by the 6 players in a given round (round 6). The right panel ("Investitionen Runde 6") shows the investments made in the current round. Players Ananke, Telesto and Despina paid nothing to the climate account whereas players Japetus, Kallisto and Metis each paid 4 ECU. In total, there was 12 ECU paid this round, which was then credited to the climate account.

\begin{center}
\includegraphics[width=.75\textwidth]{_alias_screenshot.png}
\end{center}

The left panel ("Investitionen Runden 1-6 insgesamt") shows the investments made by each player throughout the first six rounds. So, players Ananke, Telesto and Kallisto each paid 12 ECU to the climate account throughout the first six rounds. Despina paid 14 ECU, Japetus paid 10 ECU and Metis paid 8 ECU throughout the first six rounds. As such, there was 68 ECU paid to the climate account throughout the first six rounds altogether. This exact information will be given to you after each climate round.

\subsection*{5. Use of Climate Account Money}

In case the 120 ECU needed to reduce the probability of a dangerous climate change is collected, we will spend \textbf{all} the money from the climate account on the United Nations (UN) projects to support offsetting $CO_{2}$ emissions. In case the 120 ECU needed for the climate account is \textbf{not} collected, we will spend only \textbf{half} the money from the climate account to support such projects. The amount transferred by us to the United Nations will be used as a contribution to \textbf{combat climate change}. In what follows, we will briefly explain how that works.

Within the framework of the United Nations, one can choose developmental projects at offset.climateneutralnow.org. Financing a project like that allows for, e.g., buying energy efficient appliances. For each Euro donated, the website shows how many tonnes of $CO_{2}$ can be spared by realizing a given project. Currently, the most efficient project is estimated at 0.5 Euro per tonne of $CO_{2}$. On March 1, 2017, we will invest the money from the climate account into the project with the best trade off between Euro and $CO_{2}$.

In summary, if the players pay, e.g., 120 ECU (40 Euro) to the climate account then approximately 120 tonnes of $CO_{2}$ will be neutralized (as of this writing). This corresponds to approximately 23 return flights from Berlin to New York worth of emissions per passenger.

If you wish, you can leave your e-mail address with us at the end of the experiment and we will send you an overview of projects supported through the climate account.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Control questions}
\label{sec:cquestions}

Control questions as presented to the participants after reading the instructions (English version in italics, possible answers in parentheses).

\begin{enumerate}
\item Welchen Betrag muss jeder Spieler im Durchschnitt in den zehn Runden
insgesamt in den Klimaschutz investieren, um die Wahrscheinlichkeit
des Klimawandels zu reduzieren? (12 ECU; 20 ECU; 40 ECU; 120 ECU)

\emph{How much does each player have to invest in the climate account during the 10 rounds in total in order to reduce the probability of climate change? (12 ECU; 20 ECU; 40 ECU; 120 ECU)}


\item Angenommen, der notwendige Betrag von 120 ECU zur Reduzierung der
Wahrscheinlichkeit des Klimawandels wurde erspielt und Sie haben dabei
in den zehn Runden insgesamt 16 ECU in den Klimaschutz investiert.
Wie hoch ist Ihre Auszahlung in ECU? (sicher 24 ECU; mit 80\% Wahrscheinlichkeit
24 ECU, mit 20\% 0 ECU; mit 80\% Wahrscheinlichkeit 24, mit 20\% 16 ECU;
sicher 16 ECU)

\emph{Assume that the amount of 120 ECU necessary to reduce the probability of climate change has been collected and that you have invested 16 ECU during the 10 rounds in total. How large is your final payment in ECU?
(24 ECU for sure; 24 ECU with 80\% chance and 0 ECU with 20\%; 24 ECU with 80\% chance and 16 ECU with 20\%; 16 ECU for sure)}


\item In wie vielen Runden können die Spieler frei über ihre Investitionen
in den Klimaschutz entscheiden? (in 3 Runden; in 5 Runden; in 7 Runden;
in 10 Runden)

\emph{In how many rounds can the players freely decide upon their investments in climate protection? (3 rounds; 5 rounds; 7 rounds; 10 rounds)}


\item Betrachten Sie das Zahlenbeispiel, das unter Punkt 4 angegeben wurde.
Wie hoch ist der Betrag auf Despinas privaten Konto nach Runde 6?
(freie Antwort)

\emph{Take a look at the numerical example provided in paragraph 4. How large is the amount in Despina's private account after round 6? (open question)}


\item Betrachten Sie das Zahlenbeispiel, das unter Punkt 4 angegeben wurde.
Wie hoch ist der Betrag auf Metis privaten Konto nach Runde 6? (freie
Antwort)

\emph{Take a look at the numerical example provided in paragraph 4. How large is the amount in Metis' private account after round 6? (open question)}


\item Betrachten Sie erneut das Zahlenbeispiel, das unter Punkt 4 angegeben
wurde. Wie viel müsste die Gruppe in den folgenden vier Runden insgesamt
auf das Klimakonto einzahlen, um die Wahrscheinlichkeit des Klimawandel
zu reduzieren? (12 ECU; 52 ECU; 68 ECU; 120 ECU)

\emph{Take another look at the numerical example provided in paragraph 4. How much would the group as a whole have to pay to the climate account in the next 4 rounds in order to reduce the probability of climate change? (12 ECU; 52 ECU; 68 ECU; 120 ECU)}


\item Angenommen, der notwendige Betrag von 120 ECU zur Reduzierung der
Wahrscheinlichkeit des Klimawandels wurde nicht erspielt. Mit welcher
Wahrscheinlichkeit verlieren Sie das verbliebene Geld auf Ihrem privaten
Konto? (10\%; 30\%; 50\%; 70\%; 90\%; 100\%)

\emph{Assume that the amount of 120 ECU necessary to reduce the probability of climate change has not been collected. With which
probability are you going to lose the money remaining in your private account?
(10\%; 30\%; 50\%; 70\%; 90\%; 100\%)}\end{enumerate}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Auxiliary materials}
\label{sec:addAna}

\begin{table}[ht!]
  \begin{center}
\begin{tabular}{rllll}
  \hline
 & $\beta$ & $\sigma$ & $t$ & $P>|t|$ \\ 
  \hline
Intercept & 2.0150 & 0.051 & 39.20 & 0.00 \\ 
  RR1 & -0.0774 & 0.071 & -1.10 & 0.27 \\ 
  RR2 & -0.0511 & 0.070 & -0.73 & 0.46 \\ 
  LastRound & -0.0494 & 0.144 & -0.34 & 0.73 \\ 
  RiskAv & -0.0058 & 0.028 & -0.21 & 0.84 \\ 
  NEP & -0.0325 & 0.027 & -1.19 & 0.23 \\ 
  LastRound $\times$ RR1 & 0.5790 & 0.196 & 2.95 & 0.00 \\ 
  LastRound $\times$ RR2 & 0.6285 & 0.192 & 3.27 & 0.00 \\ 
   \hline
\end{tabular}

  \end{center}
\caption{Model~\eqref{eq:meModel} estimation results without the outlier group (in the baseline), p-values obtained via bootstrap (10K samples).}
\label{tab:meEstNoOutlier}
\end{table}

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	\begin{scope}
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	\path[draw=drawColor,line width= 0.4pt,line join=round,line cap=round] ( 49.63,239.34) rectangle (231.54,319.99);
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}



\end{knitrout}
\caption{Difference between a climate account where every participant is contributing the reference contribution of 2 ECUs per period to the climate account and the actual ECUs in that account. Each line represents one group. Treatments with $\{p=0.5, \pi=0.0\}$ and $\{p=0.9, \pi=0.0\}$ are from Milinski et al.}
\label{fig:contrLastRounds}
\end{figure}

\begin{align}
contr_{gr, sub, period}
  &=\beta_{0}+\beta_{RR1} \cdot RR1+\beta_{RR2} \cdot RR2+\beta_{LastRound} \cdot LastRound+\nonumber\\
  &\beta_{LastRound \times RR1} \cdot LastRound \cdot RR1+\beta_{LastRound \times RR2} \cdot LastRound \cdot RR2+\nonumber\\
  &\beta_{RiskAv} \cdot RiskAv_{sub}+\beta_{NEP} \cdot NEP_{sub}+\epsilon_{gr}+\epsilon_{sub}+\epsilon
\label{eq:meModel}
\end{align}

\begin{align}
contr_{gr, sub, period}
  &=\beta_{0}+\beta_{p=0.9} \cdot p=0.9+\beta_{\pi=0.2} \cdot \pi=0.2+\beta_{LastRound} \cdot LastRound+\nonumber\\
  &\beta_{LastRound\times p=0.9} \cdot LastRound \cdot p=0.9+\beta_{LastRound\times \pi=0.2} \cdot LastRound \cdot \pi=0.2+\nonumber\\
  &\beta_{Milinski} \cdot Milinski+\epsilon_{gr}+\epsilon_{sub}+\epsilon
\label{eq:meFulFac}
\end{align}


\end{appendix}

\end{document}
