# Math Help - Game Theory Question with strange wording

1. ## Game Theory Question with strange wording

You don't really need to know any economics for this question but i just can't understand the wording of the question. So I figured some logical math brains could possibly help me out.

Each hunter has two options: hunting a stag or hunting a hare. There are a total of "n" hunters and, of these, the total number of stag hunters is denoted by "m". If 2 or more hunters go for the stag they catch it and divide it equally and get the highest payoff. If only 1 person goes for the stag they can't catch it and get the lowest payoff. If the hunter decides to catch a hare they get a middle payoff.

Each hunter prefers the fraction 1/k of the stag to a hare, but prefers a hare to any smaller fraction of the stag, where k is an integer with m <= k <= n.

I don't understand what that last sentence means. If someone could illustrate it to me by using an example such as 5 hunters of which are 3 stag hunters that would be great.

Thanks

2. So $n = 5$ and $m = 3$. So there are 2 hare hunters.

$3 \leq k \leq 5$.

Each hunter say prefers $\frac{1}{3}, \frac{1}{4}$ or $\frac{1}{5}$ (highest payoff) of the stag to a hare, but prefers a hare (medium payoff) to $\frac{1}{5}$ of the stag (lowest payoff).

3. Originally Posted by tukeywilliams
So $n = 5$ and $m = 3$. So there are 2 hare hunters.

$3 \leq k \leq 5$.

Each hunter say prefers $\frac{1}{3}, \frac{1}{4}$ or $\frac{1}{5}$ (highest payoff) of the stag to a hare, but prefers a hare (medium payoff) to $\frac{1}{5}$ of the stag (lowest payoff).
Does that mean that each hunter value both 1/5 of a stag and a hare the same?

4. No because each hunter could prefer a hare to $\frac{1}{10}$ of a stag.

5. I still don't think I get it completely but i'll try asking some other questions:

Example with n=5
If m=5 then would I prefer to get 1/k of the stag or a hare?
If m=2 and I am a stag hunter, would I prefer to get 1/k of the stag or a hare?
If m=2 and I am a hare hunter, would I prefer to get a hare or a stag?