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Maximum payoff,minimaz,savage and hurwicz criterion

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  • 14-04-2012 4:47pm
    #1
    eoins23456
    Registered Users Posts: 603 ✭✭✭


    Hi Just wondering do these answers to this question seem correct as I dont have solutions.Thanks in advance

    A farmer has to decide between using a field for grazing and using it to plant potatoes.The state of nature in the coming season can be described by the random variable X which has a uniform distribution on the interval [0,1]. If the farmer decides to use the land for grazing, he obtains a payoff of 1 with certainty. If the farmer decides to plant potatoes and the state of nature is x,then his payoff is 7x(1-x)

    a)Find the minimum and maximum possible payoffs from planting potatoes.

    Well differentiating and putting equal to zero yields .5 and putting into the payoff formula you get 1.75 so I think thats the maximum then the minimum would just be 0.

    b)What decision should the farmer take according to the minimax criterion?

    Ok so from grazing you have a minimum payoff of 1. Then from planting potatoes you have a minimum payoff of zero. So to maximise the minimum
    payoff you choose grazing

    c) What decision should the farmer take according to the regret(Savage) criterion?

    Well the the maximum regret would be 0-1=-1 so minimizing this regret you would pick option grazing as 1> .-1

    d)What decision should the farmer take according to the Hurwicz criterion with index of optimism a=0.4?

    Well grazing equals .4(max gain)+(1-.4)(min gain) =.4(1)+.6(1)=1
    Planting yields .4(1.75)+.6(0) =0.7
    So go with grazing

    e)What decision should the farmer take,in order to maximise his expected payoff?
    Well the expected payoff from grazing is 1.
    I think the expected payoff from the planting would be integral of x*f(x) between 1 and 0 which works out at 7/12 so you should choose option grazing.


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