<p>I'm trying to determine which strategy is stochastically stable.</p>
<p><a href="https://i.sstatic.net/U1GYL.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/U1GYL.png" alt="enter image description here" /></a></p>
<p>In my lecture notes, we assign probabilities <span class="math-container">$a$</span>, <span class="math-container">$b$</span> <span class="math-container">$1-a-b$</span> to player 2 strategies <span class="math-container">$T,M,B$</span> resp.</p>
<p>Hence we have the payoffs</p>
<p><span class="math-container">$$u(t)=2a+1-a-b$$</span> <span class="math-container">$$u(m)=b+2-2a$$</span> <span class="math-container">$$u(b)=4-2b-3a$$</span></p>
<p>And it is inferred from this that <span class="math-container">$b,b$</span> is stochastically stable. I tried using the utilities to derive a system of three equations, and showing that <span class="math-container">$B$</span> yields the highest payoff for the largest range of <span class="math-container">$a$</span> and <span class="math-container">$b$</span>, but this did not seem to succeed.</p>

<microeconomics><mathematical-economics><game-theory>
Finding a stable equilibrium
user526463
# Finding a stable equilibrium

(Asked by: username_0 on 2018-03-31)

I'm trying to determine which strategy is stochastically stable.

[![enter image description here](https://i.sstatic.net/U1GYL.png)](https://i.sstatic.net/U1GYL.png)

In my lecture notes, we assign probabilities $a$, $b$ $1-a-b$ to player 2 strategies $T,M,B$ resp.

Hence we have the payoffs

$$u(t)=2a+1-a-b$$ $$u(m)=b+2-2a$$ $$u(b)=4-2b-3a$$

And it is inferred from this that $b,b$ is stochastically stable. I tried using the utilities to derive a system of three equations, and showing that $B$ yields the highest payoff for the largest range of $a$ and $b$, but this did not seem to succeed.

**Tags:** microeconomics, mathematical-economics, game-theory

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## 0 answers

