TITLE: Determinacy from $\omega_1\rightarrow(\omega_1)^{\omega_1}$
QUESTION [8 upvotes]: Assuming the Axiom of Determinacy (abbreviated AD), Martin showed how to derive a rather strong partition on $\omega_1$, namely that $\omega_1\rightarrow(\omega_1)^{\omega_1}$. In "Infinitary Combinatorics and the Axiom of Determinateness", Kleinberg goes through Martin's proof that $\omega_1\rightarrow(\omega_1)^{\omega_1}$ under AD, and from there he goes on to prove much about the large cardinal structure of ZF+AD below $\aleph_\omega$. In fact, he does this directly from the partition relation. In particular, Kleinberg shows that $\aleph_1$ and $\aleph_2$ are measurable, for each $n>2, \aleph_n$ has cofinality $\aleph_2$ and is Jonsson, and that $\aleph_\omega$ is Rowbottom.
We see that the existence of such a partition relation is inconsistent with choice. In fact, the following is a theorem of Erdos and Rado:

For all infinite $\tau$, there is no $\kappa$ such that $\kappa\rightarrow(\tau)^\tau$

However, I am curious about the following:

How much is known about the amount of determinacy one can derive from ZF + DC + $\omega_1\rightarrow(\omega_1)^{\omega_1}$?

In particular, any references would be greatly appreciated.
Edit:
I elaborated on the nature of the question in a comment to an answer. For sake of visibility, I'm pasting the relevant portion here:
To elaborate on the question, it's interesting that one can derive so much about the large cardinal structure of ZF + AD directly from the strong partition relation on $\omega_1$. As far as I know, "$\omega_1$ is measurable" and "$\omega_2$ is measurable" alone allow us a fragment of determinacy. I was curious as to what is known beyond what can be derived from these measures, as $\omega_1\rightarrow(\omega_1)^{\omega_1}$ gives us these measures.

REPLY [6 votes]: There is some sort of equivalence between partition properties and determinacy. The question is treated in Kechris, Kleinberg, Moschovakis, Woodin, Determinacy, partition properties, nonsingular measures in the Cabal reprints, Volume I. More specifically the weak partition property on $\omega_1$ implies analytic determinacy (which is provable in ZF). Concerning the strong partition property I am not really sure, I think it implies $\Pi^1_1$-determinacy (remember this is equivalent to $0^{\sharp}$ and originally the strong partition on $\omega_1$ was proven using properties of indiscernibles). The KKMW article has the details