<blockquote>
  <p>what does  exactly represent? Is a threshold?</p>
</blockquote>

<p>Yes, <span class="math-container">$n$</span> is the threshold above which the benefit <span class="math-container">$B$</span> realizes. Think of this as a situation where a public good with benefit <span class="math-container">$B$</span> is provided only if more than half of the population votes for it. <span class="math-container">$C$</span> is the cost of voting, and <span class="math-container">$n=\lceil\frac12N\rceil$</span> is the smallest integer greater than half of the population size (<span class="math-container">$N$</span>).</p>

<blockquote>
  <p>Why would rational players prefer everybody to cooperate?</p>
</blockquote>

<p>While a rational player would choose <span class="math-container">$\mathbf{D}$</span> regardless of what others would choose, he/she would still prefer the outcome with benefit <span class="math-container">$B$</span> to the outcome with <span class="math-container">$0$</span> benefit. Hence, he/she would prefer everyone else chooses <span class="math-container">$\mathbf{C}$</span>, i.e. bearing the cost of providing benefit <span class="math-container">$B$</span>, while he/she enjoys <span class="math-container">$B$</span> without incurring any cost by choosing <span class="math-container">$\mathbf{D}$</span>. </p>

<p>Additionally, suppose there are <span class="math-container">$N$</span> players, and that <span class="math-container">$n&lt;N-1$</span>. Then with all the other <span class="math-container">$N-1$</span> players playing <span class="math-container">$\mathbf{C}$</span>, it doesn't really matter if the remaining player chooses <span class="math-container">$\mathbf{C}$</span> or <span class="math-container">$\mathbf{D}$</span>. So arguably it's less morally objectionable for the last player to choose <span class="math-container">$\mathbf{D}$</span>. </p>

CC BY-SA 4.0
2019-02-09T02:02:01.627Z
2019-02-09T02:09:59.270Z
2019-02-09T02:09:59.270Z
Herr K.
<p>In the formulation of the Tragedy of the Commons below, what does <span class="math-container">$n$</span> exactly represent? Is a threshold? The text is from plato.stanford.edu website on Kuhn's Prisoner's dilemma.</p>

<p>Also, it says that <span class="math-container">$\bf D$</span> strongly dominates <span class="math-container">$\bf C$</span> for all players, and so rational players would choose <span class="math-container">$\bf D$</span> and achieve <span class="math-container">$0$</span>, while preferring that everyone would choose <span class="math-container">$\bf C$</span> and obtain <span class="math-container">$C+B$</span>.</p>

<p>I don't understand the last part. The reason <span class="math-container">$\bf D$</span> dominates <span class="math-container">$\bf C$</span> is because either the player gets <span class="math-container">$B$</span> or <span class="math-container">$0$</span> which are better from <span class="math-container">$C+B$</span> or <span class="math-container">$C$</span>. Why would rational players prefer everybody to cooperate?</p>

<p><a href="https://i.sstatic.net/kQ0lw.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/kQ0lw.png" alt="enter image description here"></a></p>

<game-theory>
Understanding a multi-player Tragedy of the Commons game
johnny09
# Understanding a multi-player Tragedy of the Commons game

(Asked by: username_0 on 2019-02-08)

In the formulation of the Tragedy of the Commons below, what does $n$ exactly represent? Is a threshold? The text is from plato.stanford.edu website on Kuhn's Prisoner's dilemma.

Also, it says that $\bf D$ strongly dominates $\bf C$ for all players, and so rational players would choose $\bf D$ and achieve $0$, while preferring that everyone would choose $\bf C$ and obtain $C+B$.

I don't understand the last part. The reason $\bf D$ dominates $\bf C$ is because either the player gets $B$ or $0$ which are better from $C+B$ or $C$. Why would rational players prefer everybody to cooperate?

[![enter image description here](https://i.sstatic.net/kQ0lw.png)](https://i.sstatic.net/kQ0lw.png)

**Tags:** game-theory

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## 1 answers

### Answer by username_1 on 2019-02-09. Score: 3 | Accepted answer

> what does exactly represent? Is a threshold?

Yes, $n$ is the threshold above which the benefit $B$ realizes. Think of this as a situation where a public good with benefit $B$ is provided only if more than half of the population votes for it. $C$ is the cost of voting, and $n=\lceil\frac12N\rceil$ is the smallest integer greater than half of the population size ($N$).

> Why would rational players prefer everybody to cooperate?

While a rational player would choose $\mathbf{D}$ regardless of what others would choose, he/she would still prefer the outcome with benefit $B$ to the outcome with $0$ benefit. Hence, he/she would prefer everyone else chooses $\mathbf{C}$, i.e. bearing the cost of providing benefit $B$, while he/she enjoys $B$ without incurring any cost by choosing $\mathbf{D}$.

Additionally, suppose there are $N$ players, and that $n. Then with all the other $N-1$ players playing $\mathbf{C}$, it doesn't really matter if the remaining player chooses $\mathbf{C}$ or $\mathbf{D}$. So arguably it's less morally objectionable for the last player to choose $\mathbf{D}$.


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