Final answer:
The equilibrium of this game is 1 lion.
Step-by-step explanation:
The total number of lions in the hierarchical group is 138. In this game, each lion has the preference of eating rather than being hungry, but prefers to be hungry rather than being eaten. To find the equilibrium of this game, we need to determine the number of lions that make the game stable at every level of the hierarchy. Starting with Lion 1, if it doesn't eat the prey, the game ends. So, there are 138 possible outcomes for Lion 1. If Lion 1 eats the prey, it becomes fat and slow, and Lion 2 can eat it. However, Lion 2 prefers to eat than be hungry, so it will always eat Lion 1. This means that there are 137 possible outcomes for Lion 2. Following this pattern, we can determine the number of possible outcomes for each lion. In the end, the equilibrium is reached when there is only 1 lion left, as it prefers to be hungry rather than being eaten. Therefore, the equilibrium of this game is 1 lion.