Are there strictly dominated strategies? Two players simultaneously announce a prime number less than 20.Denoting $p_{i}$ the number announced by the player $i$, the payoffs are:

-If $p_{1}+p_{2}&lt;14$ each player receives as payment the value of $p_{i}+1$.

-If $p_{1}+p_{2} \geq{14}$ and $p_{i}&lt;p_{j}$, player $i$ receives $p_{j}$ and the player $j$ receive $20-p_{i}$.

-If $p_{1}+p_{2} \geq{14}$ and $p_{i}=p_{j}$, each player receives a payoff $p_{i}$.

Q1:My game in normal form is correct?

\begin{array}{|c|c|c|c|}
\hline
 &amp; 2 &amp; 3&amp;5&amp;7&amp;11&amp;13&amp;17&amp;19 \\ \hline
2&amp;3,3&amp; 3,4&amp;3,6 &amp; 3,8&amp;3,12&amp;13,18&amp;17,18&amp;19,18\\ \hline
3 &amp; 4,3 &amp; 4,4&amp; 4,5&amp;4,8&amp;11,17&amp;13,17&amp;17,17&amp;19,17\\ \hline
 5&amp; 6,3 &amp; 6,4&amp; 6,6&amp;6,8&amp;11,15&amp;13,15&amp;17,15&amp;19,15\\ \hline 
7&amp; 8,3 &amp; 8,4&amp; 8,6&amp;7,7&amp;11,13&amp;13,13&amp;17,13&amp;19,13\\ \hline 
11&amp; 12,3 &amp; 17,11&amp; 15,11&amp;13,11&amp;11,11&amp;13,9&amp;17,9&amp;19,9\\ \hline 
13&amp; 18,13 &amp; 17,13&amp; 15,13&amp;13,13&amp;9,13&amp;13,13&amp;17,7&amp;19,7\\ \hline 
17&amp; 18,17 &amp; 17,17&amp; 15,17&amp;13,17&amp;9,17&amp;7,17&amp;17,17&amp;19,3\\ \hline 
19&amp; 18,19 &amp; 17,19&amp; 15,19&amp;13,19&amp;9,19&amp;7,19&amp;3,19&amp;19,19\\ \hline 
\end{array}

Q2:There are strictly dominated strategies?
For the table, I think not. Is correct?

Thanks!
I agree with Herr, the payoff matrix looks right. Also, there are no strictly dominated strategies because a strictly dominated strategy cannot be a best response for any possible belief. However, If any player believes that the other player is choosing 19, then every strategy (both pure and mixed) is a best response.