Two players $i,j$; both have two strategies $\{h,s\}$.

The payoffs vector of $i,j$:

$u(h,h)=(5,5)$ (if both players choose $\{h\}$ then $i$ receives 5 and $j$ receives 5)

$u(h,s)=(10,0)$

$u(s,h)=(0,10)$

$u(s,s)=(15,15)$

The Nash equilibria include $(s,s)$ and $(h,h)$. Experimental evidence suggests that with communication, most people will realize $(s,s)$.

However, when information is incomplete, it could be rational for one player to play $h$ if one of the following conditions hold:

1. The player believes that [hare is attractive enough for the other](https://books.google.ca/books?hl=en&lr=&id=g79A7TzV4zIC&oi=fnd&pg=PA237&dq=Stag%20hunt%20%20without%20communication&ots=fF12kQRmFX&sig=nVyHsei7wKlVR-hkZaGXM-yutEI&redir_esc=y#v=onepage&q=Stag%20hunt%20%20without%20communication&f=false) (this is discussed in a textbook); or, more generally if the player is a level-k thinker (k>0)
2. If the player is a max-min decision maker.
3. If the player is picking a Nash Equilibrium such that that his profit cannot be sabotaged by the other.

I wonder if the level-k results and/or the third interpretation ("non-sabotagable" NE) is reasonable or covered by literature.