Lions and Lambs
https://theconversation.com/lions-and-lambs-can-you-solve-this-classic-game-theory-puzzle-81288
This article covers a classic game theory puzzle, called lions and lambs. In this puzzle there are lions on an island who are players who compete over the resources(food) on the island. In the problem, all of the lions on the island are aware that all of the lions are equal in all ways including their physical strength, and their rational minds. As a consequence of this, the lions will not attempt to eat each other, but rather have 2 strategies to play for consuming food. The lions can either eat an endless supply of grass, or eat a lamb that also exists on the island. Every lion prefers eating lambs to grass, and so the lambs have a higher payoff than the grass for each lion. Also, each lion wants to live, and will not eat a lamb if it results in them being eaten by another lion due to their reduced physical prowess from a full stomach.
The problem is solved with backward induction which involves answering the problem by “going back, step-by-step” until the problem is reduced to a base case. In this problem the base case is when there is only one lion on the island. In this case the lion would pick the strategy of eating the lamb over the grass, as the lamb has the higher payoff. It can be reasoned that for two lions on the island neither will eat the lamb and will instead choose the strategy of eating grass, as if one lion chooses the strategy of eating the lamb, they will be eaten by the other lion due to their full stomach. If the number of lions is 3 then any lion that chooses the strategy of eating the lamb will reduce the situation to an island of 2 lions with 1 lamb, and in that case neither lion will eat the lion with a full stomach. Problems that have Islands with more lions can be reduced down to the base case and solved. It turns out that for an island with an even number of lions the lamb will survive, and will not survive with an odd number of lions.
This can be related to class on the lectures from game theory. In class we talked about how each player in the game is trying to maximize their payoff. And we can see that here by how each lion’s goal is getting “meaty” food without dying. If it is possible( the case where there is an odd number of lions) a lion will pick the strategy of eating the lamb because it knows that it will get meaty food and will not die. Eating meaty food and not dying is a higher payoff than eating grass and not dying. Otherwise the lions maximize their payoff by picking the strategy of just eating grass as getting eaten as a result of eating the lamb would result in a lower payoff than just eating grass without dying.