Ten lions confront a single Christian The most ferocious lio

Ten lions confront a single Christian. The most ferocious lion can eat the Christian if he wants to. If the most ferocious lion does not eat the Christian, everyone goes home. If the most ferocious lion eats the Christian, the most ferocious lion turns into a Christian, the second most ferocious lion becomes the most ferocious lion, and the game is repeated. And so forth. A lion’s first priority is to avoid being eaten and second priority is to eat. Does the most ferocious lion eat the Christian? Please explain with the knowledge of game theory (nash equilibrium).

Solution

This game has some traits of prisoners dilemma game in which in the repeated game nash equilibrium is everyone choosing not to default and everybody in the game gets the highest payoff.

Similarly, using that analogy here in the repeated game one can come to a nash equilibrium by avoiding to be eaten by other.

Hence, not being eaten by lion is the nash equilibrium.