Bounded rationality with Quantal Response Equilibrium model for an Extensive Form game I am working on my Master thesis based on bounded rationality in behavioral game theory models, I wanted to know if QRE(Quantal Response Equilibrium) can be applied to games where players have different strategy sets as opposed to what I have seen in resource allocation games, if yes, how?
I'm not sure what capacity allocation games you're applying QRE to. But here's a very stylized example where QRE is applied to an asymmetric game where the strategy spaces of the two players are (nominally) different: 
\begin{array}{c|cc}
&amp;L&amp;R\\\hline
T&amp;1,0&amp;0,9\\
D&amp;0,1&amp;1,0
\end{array}
This game can be easily represented in the extensive form as well.

In the standard formulation of QRE, each player $i$ plays a mixed strategy $\sigma_i$, where the probability of pure strategy $s_i$ being played is determined by the following formula: 
\begin{align}
\sigma_i(s_i)&amp;=\frac{\exp(\lambda u_i(s_i,\sigma_{-i}))}{\sum_{s_i'\in S_i}\exp(\lambda u_i(s_i',\sigma_{-i}))},
\end{align}
where $\lambda\in[0,\infty)$ measures the precision of the response; the larger the $\lambda$ the more precise the response. 

Applying to the game above, let $p$ be the probability that player 1 chooses $T$, and $q$ the probability that player 2 chooses $L$. Note that $p$ and $q$ parameterize the two players' respective mixed strategy. Then, player 1's quantal response to any given mixed strategy by player 2 (parameterized by $q$) is to play $T$ with probability $p$ and $D$ with $1-p$, where
\begin{equation}
p=\frac{\exp(\lambda\cdot (1q+0(1-q)))}{\exp(\lambda\cdot(1q+0(1-q)))+\exp(\lambda\cdot(0q+1(1-q)))}.\tag{1}
\end{equation}
Similarly, player 2's quantal response to any given mixed strategy by player 1 (parameterized by $p$) is to play $L$ with probability $q$ and $R$ with $1-q$, where 
\begin{equation}
q=\frac{\exp(\lambda\cdot(0p+1(1-p)))}{\exp(\lambda\cdot(0p+1(1-p)))+\exp(\lambda\cdot(9p+0(1-p)))}.\tag{2}
\end{equation}

In a quantal response equilibrium, $(\sigma_1,\sigma_2)$, the two player's strategies must be quantal responses to each other; that is,
\begin{align}
\sigma_1(T)&amp;=\frac{\exp(\lambda \cdot \sigma_2(L))}{\exp(\lambda\cdot\sigma_2(L))+\exp(\lambda(1-\sigma_2(L)))}&amp;\sigma_1(D)&amp;=1-\sigma_1(T)\\[12pt]
\sigma_2(L)&amp;=\frac{\exp(\lambda\cdot(1-\sigma_1(T)))}{\exp(\lambda\cdot(1-\sigma_1(T)))+\exp(9\cdot\lambda\cdot\sigma_1(T))}&amp;\sigma_2(R)&amp;=1-\sigma_2(L)
\end{align}

In the following graphs, the dashed lines plot the best responses of each player; the solid curves represent the quantal responses under different levels of precision. That is, the solid curves plots equations $(1)$ and $(2)$ above. The intersection of the two solid curves is the quantal response equilibrium point, described by the last set of equations above.