Stag Hare inefficient Nash Equilibrium and level-K thinking 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:

The player believes that hare is attractive enough for the other (this is discussed in a textbook); or, more generally if the player is a level-k thinker (k&gt;0)
If the player is a max-min decision maker.
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 (&quot;non-sabotagable&quot; NE) is reasonable or covered by literature.
Level-k reasoning in the stag hunt game is analyzed in
Gracia-Lázaro, Carlos, Luis Mario Floría, and Yamir Moreno. &quot;Cognitive hierarchy theory and two-person games.&quot; Games 8.1 (2017): 1.
The idea that playing $s$ guarantees its payoff is discussed in
Aumann, Robert &quot;Nash equilibria are not self-enforcing, in ‘‘Economic Decision-Making: Games, Econometrics and Optimization’’(JJ Gabszewicz, J.-F. Richard, and LA Wolsey, Eds.).&quot; (1990).
The stag hunt game is due to Aumann.
Related to that is the idea of risk dominance of Harsanyi and Selten in their 1988 book &quot;A general theory of equilibrium selection in games.&quot; The stag hunt is pretty much the leading example. It formulates the idea that this Pareto inefficient equilibrium is less risky to play.
It should be noted that the game has a third equilibrium in mixed strategies.