Strictly Dominent Strategy

Question

I know this is probably the easiest question ever, but for some reason I can do advanced calculus yet I can't get my head around Game Theory.

I understand the concept of Strictly Dominant Strategy.

I see that for player 1, c is the strictly dominant strategy. It says there's only 1, but doesn't player 2 have a strictly dominant strategy? being y?

Perhaps I'm overlooking something very simple here.

Thanks

Answer 1

When player 1 chooses $a$, player 2 gets 2 from playing either $x$ or $y$. This violates the strictness required for a strictly dominant strategy, since $2\not>2$, as @palmpo says.

Answer 2

I am interpreting the question as that you want to find the outcome of the Iterated Elimination of Strictly Dominated Strategies (IESDS), whose outcome is in the form $(k,l)$, where $k\in \{a,b,c,d\}$ and $l\in \{x,y,z\}$.

Take note of @palmpo's and @HerrK.'s comments, which will answer your question. For the benefit of others, to add on, to find the strictly dominant strategy, we proceed in the following manner:

Firstly, note that $a,b,d$ are strictly dominated strategies for Player 1. So after removing the strictly dominated strategies or Player 1, you end up with only the row for when strategy $c$ is played by Player 1, together with the 3 strategies $x,y,z$ for Player 2, and their respective outcomes are $(5,2),(4,4),(7,0)$.

Now, for Player 2, note that $x$ and $z$ are strictly dominated by $y$, since $2<4$ and $0<4$. So removing the strictly dominated strategies, you arrive at the unique outcome of the IESDS: $(4,4)$, whose corresponding strategy is $(c,y)$.

Answer 3

Let's get two things out of the way: 1) strictly dominant strategy is one which is better than (or offers strictly higher payoff) than ANY other strategy of the person. 2) if each player in a game has a strictly dominant strategy, they will only play that strategy (Because whatever they do, that is the strategy that will give them the highest payoff from all their other strategies)

Now, for player one, c is the strictly dominant strategy : compare the payoffs from c to those of a,b and d. Now, as you can see that player 2 doesn't have a strictly dominant strategy. However, since player 1 will only play c regardless of whatever player 2 chooses, we can delete the a,b and d rows from the matrix. Which leaves with (c,x), (c,y) and (c,z). Of these, y yields highest payoff for player 2 and the outcome will be (c,y)

Answer 4

This is an interesting example in that the strictly dominate strategy yields the best result for both players, i.e., there is no other strategy where both players can get more than 4 each. Many examples (perhaps most examples in textbooks) have a better solution for both players which is not the strictly dominate strategy. For example in the Prisoners' dilemma (see https://en.wikipedia.org/wiki/Prisoner's_dilemma), both criminals decide to cooperate with the police and do not collectively remain silent which would be a better strategy for both.