<p>A payoff pair <span class="math-container">$(x,y)$</span> is Pareto efficient if it is not Pareto dominated. This means that there does not exist another payoff pair <span class="math-container">$(x', y')$</span> such that <span class="math-container">$x &lt; x'$</span> and <span class="math-container">$y &lt; y'$</span>. (Depending on the exact definition, sometimes of of the two inequalities can be weak).</p>
<p>All payoffs in the payoff matrix except for <span class="math-container">$(C,\beta), (B, \beta)$</span> and <span class="math-container">$(C, \delta)$</span> are dominated by <span class="math-container">$(C, \beta) = (13, 13)$</span>, so they are not Pareto efficient.</p>

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2021-04-10T09:01:17.807Z
2021-04-10T09:01:17.807Z
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<p>Here I want to find Pareto efficient payoff set.</p>
<p>The answer is (C,β), (B, β), (C, δ)</p>
<p>But I don’t understand why? Please explain clearly this answer. Thanks a lot</p>

<microeconomics><game-theory><self-study>
Find the set of Pareto efficient payoffs in game theory
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# Find the set of Pareto efficient payoffs in game theory

(Asked by: username_0 on 2021-04-09)

[![enter image description here](https://i.sstatic.net/xL3sP.jpg)](https://i.sstatic.net/xL3sP.jpg)

Here I want to find Pareto efficient payoff set.

The answer is (C,β), (B, β), (C, δ)

But I don’t understand why? Please explain clearly this answer. Thanks a lot

**Tags:** microeconomics, game-theory, self-study

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## 1 answers

### Answer by username_1 on 2021-04-10. Score: 3 | Accepted answer

A payoff pair $(x,y)$ is Pareto efficient if it is not Pareto dominated. This means that there does not exist another payoff pair $(x', y')$ such that $x < x'$ and $y < y'$. (Depending on the exact definition, sometimes of of the two inequalities can be weak).

All payoffs in the payoff matrix except for $(C,\beta), (B, \beta)$ and $(C, \delta)$ are dominated by $(C, \beta) = (13, 13)$, so they are not Pareto efficient.


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