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Math Help - Game Theory Question with strange wording

  1. #1
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    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
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  2. #2
    Senior Member tukeywilliams's Avatar
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    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).
    Last edited by tukeywilliams; October 16th 2007 at 05:24 PM.
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  3. #3
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    Quote Originally Posted by tukeywilliams View Post
    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?
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  4. #4
    Senior Member tukeywilliams's Avatar
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    No because each hunter could prefer a hare to  \frac{1}{10} of a stag.
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  5. #5
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    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?
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