Question

Hungry Lions: The members of a hierarchical group of hungry lions face a piece of prey. If Lion 1 does not eat the prey, the prey escapes and the game ends. If it eats the prey, it becomes fat and slow, and Lion 2 can eat it. If Lion 2 does not eat Lion 1, the game ends. If Lion 2 eats Lion 1 , then it may be eaten by Lion 3 , and so on. Each lion prefers to eat than to be hungry, but prefers to be hungry than to be eaten. There are a total of 138 lions. Find the equilibrium of this game.

Answer 1

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.

Answer 2

In this hierarchical game, the equilibrium occurs when Lion 137 eats Lion 136, Lion 136 eats Lion 135, and so on until Lion 2 eats Lion 1, leaving Lion 138 with the prey.

How to explain

Each lion prefers eating to being hungry but prefers being hungry to being eaten. With 138 lions, Lion 138 gets the prey as Lion 137 chooses not to eat Lion 136, maintaining the hierarchy.

This outcome aligns with the lions' preferences, ensuring no lion faces being eaten while satisfying their preference for food, thus establishing the equilibrium of the game in this hierarchical order.