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 Fat Boy ????

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MKeeney
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PostSubject: Re: Fat Boy ????   Thu Jun 12, 2014 3:27 am

pukerimu wrote:
Big As is a type - there are things we really like about him ie moderation, easy fleshing, beautifully shaped and even feet, kind and quiet nature.  He was retained as we had used his sire and his grand sire before selling both (Grand sire as a stud) and he has a nice maternal line.  We would definitely not see him as terminal as really it is his females that we are interested in seeing (first crop of calves due in August).  Likewise there are things that we do not think are so crash hot about him - he might be a little too moderate to get the bulls up to the weights that some of our buyers like (only time will tell that), he may be just a little more lighter in the bone than we really like and his scrotal could be bigger - we like the good about him enough to settle on the not so - like all the bulls we use - our own and other's if he does not work over our cows (which are always hand picked to go with certain sires) then he is considered surplus to requirements - so far we have avoided falling into the trap of "we picked him so he must be good enough" - a very critical eye is used on all animals born and if they are not up to scratch as they grow then we start looking at the dam and sire very closely.

The name plays on his very fat rump, .......... his Grand sire is named Big A (logo for branded Angus meat in NZ is a big red A), his sire was named Big Al (carrying on the theme).  Also grammatically challenged youth are known to add an "as" to the end of their statements to emphasise the message ie "that was cool as" ......................... we like to have our little jokes.  Small things being amusing and all that  Wink 

Megan,
would increasing the number of bulls you sell; either percentage retained as bulls; or increasing herd numbers, be in your future direction to actually lower the price of your bulls...or seemingly to me, price is not really a concern to your customer?
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pukerimu



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PostSubject: Re: Fat Boy ????   Thu Jun 12, 2014 3:33 am

Crossbreeding will be the saviour of some commercial herds where they have been following the mantra of EBV's in NZ. Hybrid vigour is totally underrated by Breed Assn's. A major meat company has introduced a non breed specific "Premium Beef" product - so long as the meat meets their parameters it is eligible - they do not care what colour, shape or size the animal is so long as the premium cuts (which lets face it account for very little of the total carcass weight) meets their specifications. Going to give the two branded Angus products a run for their money - as patriotic Angus breeders we are supposed to be threatened and angry about this intrusion into our turf - we say ............... whatever makes our commercial customers the most money makes us happy. We are confident that they will continue to want our bulls to breed their base cows and if the cull progeny then make them a premium then we are even happier and our breeding goals are proven - based on our sale results we are confident that we are ticking their boxes.
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pukerimu



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PostSubject: Re: Fat Boy ????   Thu Jun 12, 2014 3:42 am

As much as we would like to make as many bulls as we can we are limited by our ability to work harder. We can manage the number of cows we have, we catalogue as many bulls as we can that meet our parameters - and we do not wish to adjust those - the confidence that our buyers have in us to only present them with the soundest, meatiest etc is why our buyers are prepared to pay what they need to.

There was much competition for the best of the best and we were lucky to secure a new buyer who had bought a new property and wanted 5 new bulls - he was happy to bid on the bulls later in the catalogue and we were very happy to have him there - he won't want 5 bulls next year but hopefully the bulls he bought will make him smile and when he gets into a bull rotation we will be the place of choice to buy from. We are in the lucky (if luck actually has anything to do with it - more like 7 days a week) position of having loyal buyers who do not want just any angus bull they want one of ours and are prepared to pay for them.
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pukerimu



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PostSubject: Re: Fat Boy ????   Thu Jun 12, 2014 3:48 am

I have had a wine with dinner - if I come across all pious and sanctimonious it is not my intention - ask Leroy - hopefully he'll tell you that we are actually quite nice  Very Happy 
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PostSubject: Re: Fat Boy ????   Thu Jun 12, 2014 8:26 am

pukerimu wrote:
I have had a wine with dinner - if I come across all pious and sanctimonious it is not my intention - ask Leroy - hopefully he'll tell you that we are actually quite nice  Very Happy 

poor ole wine; fruit of the vine...blamed for most all the human whines  Evil or Very Mad Evil or Very Mad  Laughing   

just kidding....don`t you worry about being pious and sanctimonious; the Corner disposes of those traits in due time; it takes a little longer to rid the sociopaths; it takes a tough skin to go your own way breeding cattle; here`s a good place to toughen up; those that can`t; leave in their own due time of their own accord...
but the greatest vice to a forum is boredom; thx Megan, for keeping discussion lively...
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PostSubject: Re: Fat Boy ????   Thu Jun 12, 2014 3:42 pm

I so wish "best of the best" was a mainstream clique...but fact it; we all prefer one half to another; a best of the upper half...where does the upper half {of any herd} come from? the middle 50% that hovers around the preferred type and performance...with the outliers above and below creating the bottom 50%? if not, then the herd direction must be to move the average? no wonder we have epds; to attempt to describe where we are; and where we wish to be in those characteristics that can be quantified with numbers...
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PostSubject: Re: Fat Boy ????   Thu Jun 12, 2014 3:49 pm

"...we catalogue as many bulls as we can that meet our parameters - and we do not wish to adjust those..."

I probably should know, but what do you cull and do you cull on both ends? Example: too big and too small, slow growth and too much growth to knowingly fit back in the herd, ...

Glad that your sale went well and it is always a sign that things are right as you have mentioned several times about repeat buyers.

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PostSubject: Re: Fat Boy ????   Thu Jun 12, 2014 9:08 pm

I suppose the industries reliance on using the superior phenotype of the individual works well enough since no one but LL has ever ventured to change the selection criteria; I`m sure $15,000 works for Megan Smile  {it would work a long time for me  Smile }; will it work $7500 better for the commercial buyer/breeder/producer...I have my doubts; the industry has used the supposed superior individual since breeding began...so here we are 200 years later; is everything superior?
I`m always reminded of LL asking Hilly, Ben and I about the 10 "superior cows" I had selected from a 100 cows at Red Lodge...LL asked how many female progeny I would need before I got another 10 phenotypes like I had just chosen...we sat pretty quietly, until LL suggested I would need about 100...since it took a 100{the milk} to make the superior 10{the cream}; only logical to believe it will take 100 progeny to reproduce the cows I bought...provided of course, they are bred to the same type bulls...after 4 years now, I can now attest that theory is working  Crying or Very sad 
so this course a few of us are on of worrying more about what the worst of the worse looks like is not too popular...the worse, and especially the worst, are merely culled away and everything rolls on looking beautiful...unfortunately, beauty breeds beauty randomly  Smile  thankfully, for my kids, so does ugly  Laughing cheers 
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pukerimu



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PostSubject: Re: Fat Boy ????   Fri Jun 13, 2014 12:52 am

EddieM wrote:
"...we catalogue as many bulls as we can that meet our parameters - and we do not wish to adjust those..."

I probably should know, but what do you cull and do you cull on both ends?  Example: too big and too small, slow growth and too much growth to knowingly fit back in the herd, ...

Glad that your sale went well and it is always a sign that things are right as you have mentioned several times about repeat buyers.


It will be easier to explain with actual data - we had a bull calf drop of 90 in 2012 - which is the mob of bulls which we have just auctioned.  10 were automatic culls at the yearling stage and of those 5 were sold as yearling breeding bulls.  These were the animals with low BW deemed to be pretty good but unlikely to make it to the 2 year old sale mob - we have a couple of repeat buyers who took their pick. The other 5 were hand reared - orphans or rejected twins, or had some other issue which negated them from being suitable to carry through to 2 year olds.  They were kept at the front of the farm for easy sale - both breeding and fattened.  The remaining 80 were put at the back of the farm and wintered on kale. In early October the A (25 bulls) mob came to the front of the farm (after the cows had finished calving and been put out on the hills) and the B (46 bulls) were rotated on new grass pastures at the back of the farm.  9 more culls (for various reasons) were then surgically docked in the spring and then sold as steers in the sales yards (not long after Leroy visited in January/February - summer).  From the remaining 61 bulls, 54 were catalogued in March and the spares sent to the works.  The mobs were split up depending on weight ranges.

Heifer replacements are selected on family lines, dams performance, structure, their own personal weight gain performance, phenotype and temperament - in no apparent order of importance - just have to tick all the boxes.  We keep from 48 - 50 heifers every year the rest being fattened and killed.  There is little appetite for commercial farmers to buy heifers for more than works value and so we find it easier to kill them when it suits us than to pay agent commission and cartage to sell them when it suits others.  Most people who have breeding cows or want breeding heifers breed their own replacements  Some studs have a few heifers at a time to sell but it is not a common practise in NZ.  Usually registered female breeding stock is only available by private treaty when a stud breeder is approached specifically to sell some heifers, at our National show and sale or at stud dispersals.  We do not have the studs come and go as there are no tax write-offs or other financial incentives, just huge costs to establish - it is a tough business to break into and several studs are over 100 yrs old - there are many in their 40's and 50's - studs that is .......... not stud masters -the average age of an angus breeder in NZ would be higher than the average age of farmers which is getting into the 60's
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PostSubject: Re: Fat Boy ????   Fri Jun 13, 2014 9:00 am

a pertinent re-read from the days when love was everywhere...but never forever  Shocked Laughing 

http://www.keeneyscorner.com/t699-a-bankers-view-wanted
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PostSubject: Re: Fat Boy ????   Fri Jun 13, 2014 5:02 pm

Funnily enough I was a banker - have now decided though that no mere mortal shall tell any other how much is to much for a bull  lol! Of course yearling bulls in NZ sell for about half what the equivalent two year old bull would and under normal NZ conditions they would only be relied on to get yearling heifers and a third to half the number of females in calf, that a 2 year old bull would be expected to, when run with mature cows. Back to Fatboy - he only ran with 16 cows (we did not yet appreciate his value) in 2011 and of that 6 of his bulls made up the catalogue. We will have many more by him to select from next year.
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PostSubject: Re: Fat Boy ????   Sat Jun 14, 2014 7:09 am

Producing that two year old bull is expensive; for sure...what I ask for a bull beyond the obvious "what will the marketplace pay" is "what would I pay for a bull"...and I sure wouldn`t pay $5000...if you won`t pay it; you can`t ask it...maybe the critic says "he knows what his bulls are worth"...as I told  farao when he was telling how to promote/sell bulls...I don`t want $5000 for my bulls; because I know they aren`t worth it...and I know yours {Pharo} aren`t worth it either...
The nice thing about an auction; the buyer determines the top; the seller determines the bottom...
if a breeder is creating uniformity and prepotency around a preferred type, how much difference is there in the genetic value of a set of bulls? not much imo...
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PostSubject: Re: Fat Boy ????   Sat Jun 14, 2014 7:30 am

MKeeney wrote:
Producing that two year old bull is expensive; for sure...what I ask for a bull beyond the obvious "what will the marketplace pay" is "what  would I pay for a bull"...and I sure wouldn`t pay $5000...if you won`t pay it; you can`t ask it...maybe the critic says "he knows what his bulls are worth"...as I told  farao when he was telling how to promote/sell bulls...I don`t want $5000 for my bulls; because I know they aren`t worth it...and I know yours {Pharo} aren`t worth it either...
The nice thing about an auction; the buyer determines the top; the seller determines the bottom...
if a breeder is creating uniformity and prepotency around a preferred type, how much difference is there in the genetic value of a set of bulls? not much imo...

Not personal questions:

Are all of your cows equal?
Do all bulls have the same purpose(s)?
Is the eye of the breeder(buyer) to be discounted?
Do all buyers have the same supply of money or the same amount of time to buy bulls?
Is data bad if it helps a person make a decision or feel more comfortable in their decision?
Do you cull bottom end bulls to increase the floor price?
Do you decrease supply to match or stimulate demand?
Do buyers ever see differences in calves sired by any of your bulls?
Is any discussion of a bull, sire groups or bulls bad (i.e. promotion?)
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PostSubject: Re: Fat Boy ????   Sat Jun 14, 2014 9:59 am

Grassfarmer wrote:
So 51% black hided = good, but purebred Red Angus = bad in a program that is supposed to be about "Angus beef"  scratch Logic anyone?

How can you "certify" something as Angus when you don't require any proof of Angus genetics???
American marketing...got to love it.
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PostSubject: Re: Fat Boy ????   Sat Jun 14, 2014 10:04 am

EddieM wrote:


Not personal questions:

Are all of your cows equal?
Do all bulls have the same purpose(s)?
Is the eye of the breeder(buyer) to be discounted?
Do all buyers have the same supply of money or the same amount of time to buy bulls?
Is data bad if it helps a person make a decision or feel more comfortable in their decision?
Do you cull bottom end bulls to increase the floor price?
Do you decrease supply to match or stimulate demand?
Do buyers ever see differences in calves sired by any of your bulls?
Is any discussion of a bull, sire groups or bulls bad (i.e. promotion?)

I got a headache just reading those questions.

Mike, on your "superior cows" and middle 50%...I believe herd improvement is when you make that middle 50% into that middle 60%...and then that middle 75%...
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PostSubject: Re: Fat Boy ????   Sat Jun 14, 2014 12:50 pm

RobertMac wrote:
EddieM wrote:


Not personal questions:

Are all of your cows equal?
Do all bulls have the same purpose(s)?
Is the eye of the breeder(buyer) to be discounted?
Do all buyers have the same supply of money or the same amount of time to buy bulls?
Is data bad if it helps a person make a decision or feel more comfortable in their decision?
Do you cull bottom end bulls to increase the floor price?
Do you decrease supply to match or stimulate demand?
Do buyers ever see differences in calves sired by any of your bulls?
Is any discussion of a bull, sire groups or bulls bad (i.e. promotion?)

I got a headache just reading those questions.

Mike, on your "superior cows" and middle 50%...I believe herd improvement is when you make that middle 50% into that middle 60%...and then that middle 75%...

Oh, come on! Take an aspirin and make a run at it. Later I know I can count on Mike to discuss a few of them as soon as he gets through driving through, teeing off and such. As hard as he tries at golf I do not know if he will ever make a 100 on the test or not. Even the guys on TV do so poorly that they are "Cee and Dee golfers" and seldom make over 70 or so on their tests.  jocolor 
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MKeeney
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PostSubject: Re: Fat Boy ????   Sat Jun 14, 2014 1:00 pm

RobertMac wrote:
EddieM wrote:


Not personal questions:

Are all of your cows equal?
Do all bulls have the same purpose(s)?
Is the eye of the breeder(buyer) to be discounted?
Do all buyers have the same supply of money or the same amount of time to buy bulls?
Is data bad if it helps a person make a decision or feel more comfortable in their decision?
Do you cull bottom end bulls to increase the floor price?
Do you decrease supply to match or stimulate demand?
Do buyers ever see differences in calves sired by any of your bulls?
Is any discussion of a bull, sire groups or bulls bad (i.e. promotion?)

I got a headache just reading those questions.

Mike, on your "superior cows" and middle 50%...I believe herd improvement is when you make that middle 50% into that middle 60%...and then that middle 75%...

before my aspirin and tackling Eddie`s questions, our ideas of herd improvement mirror Robert... cheers 
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PostSubject: Re: Fat Boy ????   Mon Jun 16, 2014 7:45 am

http://en.wikipedia.org/wiki/Nash_equilibrium

introduction
In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.[1] If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.

Stated simply, Amy and Will are in Nash equilibrium if Amy is making the best decision she can, taking into account Will's decision, and Will is making the best decision he can, taking into account Amy's decision. Likewise, a group of players are in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others in the game.
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PostSubject: Re: Fat Boy ????   Mon Jun 16, 2014 7:59 am

MKeeney wrote:
http://en.wikipedia.org/wiki/Nash_equilibrium

introduction
In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.[1] If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.

Stated simply, Amy and Will are in Nash equilibrium if Amy is making the best decision she can, taking into account Will's decision, and Will is making the best decision he can, taking into account Amy's decision. Likewise, a group of players are in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others in the game.
Are we saying "win win"?
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PostSubject: Re: Fat Boy ????   Mon Jun 16, 2014 8:28 am

EddieM wrote:
MKeeney wrote:
http://en.wikipedia.org/wiki/Nash_equilibrium

introduction
In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.[1] If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.

Stated simply, Amy and Will are in Nash equilibrium if Amy is making the best decision she can, taking into account Will's decision, and Will is making the best decision he can, taking into account Amy's decision. Likewise, a group of players are in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others in the game.
Are we saying "win win"?

no player can benefit by changing strategies while the other players keep theirs unchanged

I think the application is "the breeder doing the best he can monetarily given the decisions of the customer" ...if the customer changed, then the breeder must change?...or does the breeder change the customer through promotion etc ?
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PostSubject: Re: Fat Boy ????   Mon Jun 16, 2014 8:58 pm

According to Nash, both would have to change. And Nash never says anything about winning or losing. Seems to imply a stalemate if both parties are equal. Does promotion change a customer the most or is the combination of education and experiences the real Ace in the pocket? I do not see how a steady customer base can be had with a win/lose or a lose/win. If the seller loses enough he does not make the AAA 7 year mark. If the buyer loses, he goes elsewhere.

We all change. We all read, ponder, discuss and consider what others say. I remember a story about a guy known as a big liar that worked in the same plant as my father. One day around lunchtime, the man of fiction was sitting by a guy from another division who had not been there before. One after the other, the stories rolled out with a finger tap on the new listener's leg occasionally to emphasize a major point. The listener was there nodding and un-huhhing and eating his lunch for the whole of it. When the fibber left, a concerned friend told him that the stories he hear were not true. The patient listener said, "Yea, I know, but my nodding and saying uh-huh doesn't mean I believe what I am hearing either". We all cull the junk if we want to. I think that some of the people who get caught up in the fads and pricing games want to enjoy a thrill, are fighting boredom with their actions or want to buy a feeling of superiority from what they do and who they outdo.
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PostSubject: Re: Fat Boy ????   Mon Jun 16, 2014 9:21 pm

Obviously, Megan is winning by my standards, and her repeat customer is happy to pay the price...so win/win?

need further proof?
Alternate proof using the Brouwer fixed-point theorem[edit]

We have a game G=(N,A,u) where N is the number of players and A = A_1 \times \dotsb \times A_N is the action set for the players. All of the action sets A_i are finite. Let \Delta = \Delta_1 \times \dotsb \times \Delta_N denote the set of mixed strategies for the players. The finiteness of the A_is ensures the compactness of \Delta.

We can now define the gain functions. For a mixed strategy \sigma \in \Delta, we let the gain for player i on action a \in A_i be
\text{Gain}_i(\sigma,a) = \max \{0, u_i(a, \sigma_{-i}) - u_i(\sigma_{i}, \sigma_{-i})\}.\
The gain function represents the benefit a player gets by unilaterally changing his strategy. We now define g = (g_1,\dotsc,g_N) where
g_i(\sigma)(a) = \sigma_i(a) + \text{Gain}_i(\sigma,a)\
for \sigma \in \Delta, a \in A_i. We see that
\sum_{a \in A_i} g_i(\sigma)(a) = \sum_{a \in A_i} \sigma_i(a) + \text{Gain}_i(\sigma,a) = 1 + \sum_{a \in A_i} \text{Gain}_i(\sigma,a) > 0.\
We now use g to define f\colon \Delta \rightarrow \Delta as follows. Let
f_i(\sigma)(a) = \frac{g_i(\sigma)(a)}{\sum_{b \in A_i} g_i(\sigma)(b)}
for a \in A_i. It is easy to see that each f_i is a valid mixed strategy in \Delta_i. It is also easy to check that each f_i is a continuous function of \sigma, and hence f is a continuous function. Now \Delta is the cross product of a finite number of compact convex sets, and so we get that \Delta is also compact and convex. Therefore we may apply the Brouwer fixed point theorem to f. So f has a fixed point in \Delta, call it \sigma^*.

I claim that \sigma^* is a Nash Equilibrium in G. For this purpose, it suffices to show that
\forall 1 \leq i \leq N, ~ \forall a \in A_i, ~ \text{Gain}_i(\sigma^*,a) = 0 \text{.}
This simply states that each player gains no benefit by unilaterally changing his strategy, which is exactly the necessary condition for a Nash equilibrium.

Now assume that the gains are not all zero. Therefore, \exists i, 1 \leq i \leq N, and a \in A_i such that \text{Gain}_i(\sigma^*, a) > 0. Note then that
\sum_{a \in A_i} g_i(\sigma^*, a) = 1 + \sum_{a \in A_i} \text{Gain}_i(\sigma^*,a) > 1.
So let C = \sum_{a \in A_i} g_i(\sigma^*, a). Also we shall denote \text{Gain}(i,\cdot) as the gain vector indexed by actions in A_i. Since f(\sigma^*) = \sigma^* we clearly have that f_i(\sigma^*) = \sigma^*_i. Therefore we see that
\sigma^*_i = \frac{g_i(\sigma^*)}{\sum_{a \in A_i} g_i(\sigma^*)(a)} \Rightarrow \sigma^*_i = \frac{\sigma^*_i + \text{Gain}_i(\sigma^*,\cdot)}{C} \Rightarrow C\sigma^*_i = \sigma^*_i + \text{Gain}_i(\sigma^*,\cdot) \left(C-1\right)\sigma^*_i = \text{Gain}_i(\sigma^*,\cdot) \Rightarrow \sigma^*_i = \left(\frac{1}{C-1}\right)\text{Gain}_i(\sigma^*,\cdot).
Since C > 1 we have that \sigma^*_i is some positive scaling of the vector \text{Gain}_i(\sigma^*,\cdot). Now I claim that
\sigma^*_i(a)(u_i(a_i, \sigma^*_{-i}) - u_i(\sigma^*_i, \sigma^*_{-i})) = \sigma^*_i(a)\text{Gain}_i(\sigma^*, a)
\forall a \in A_i. To see this, we first note that if \text{Gain}_i(\sigma^*, a) > 0 then this is true by definition of the gain function. Now assume that \text{Gain}_i(\sigma^*, a) = 0. By our previous statements we have that
\sigma^*_i(a) = \left(\frac{1}{C-1}\right)\text{Gain}_i(\sigma^*, a) = 0
and so the left term is zero, giving us that the entire expression is 0 as needed.

So we finally have that
0 = u_i(\sigma^*_i, \sigma^*_{-i}) - u_i(\sigma^*_i, \sigma^*_{-i}) = \left(\sum_{a \in A_i} \sigma^*_i(a)u_i(a_i, \sigma^*_{-i})\right) - u_i(\sigma^*_i, \sigma^*_{-i}) = \sum_{a \in A_i} \sigma^*_i(a) (u_i(a_i, \sigma^*_{-i}) - u_i(\sigma^*_i, \sigma^*_{-i})) = \sum_{a \in A_i} \sigma^*_i(a) \text{Gain}_i(\sigma^*, a) \quad \text{ by the previous statements } = \sum_{a \in A_i} \left( C -1 \right) \sigma^*_i(a)^2 > 0
where the last inequality follows since \sigma^*_i is a non-zero vector. But this is a clear contradiction, so all the gains must indeed be zero. Therefore \sigma^* is a Nash Equilibrium for G as needed.

there it is; proof that epds work ...mk Smile  Smile  Smile
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jonken



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PostSubject: Re: Fat Boy ????   Mon Jun 16, 2014 10:07 pm

MKeeney wrote:
Obviously, Megan is winning by my standards, and her repeat customer is happy to pay the price...so win/win?

need further proof?
Alternate proof using the Brouwer fixed-point theorem[edit]

We have a game G=(N,A,u) where N is the number of players and A = A_1 \times \dotsb \times A_N is the action set for the players. All of the action sets A_i are finite. Let \Delta = \Delta_1 \times \dotsb \times \Delta_N denote the set of mixed strategies for the players. The finiteness of the A_is ensures the compactness of \Delta.

We can now define the gain functions. For a mixed strategy \sigma \in \Delta, we let the gain for player i on action a \in A_i be
\text{Gain}_i(\sigma,a) = \max \{0, u_i(a, \sigma_{-i}) - u_i(\sigma_{i}, \sigma_{-i})\}.\
The gain function represents the benefit a player gets by unilaterally changing his strategy. We now define g = (g_1,\dotsc,g_N) where
g_i(\sigma)(a) = \sigma_i(a) + \text{Gain}_i(\sigma,a)\
for \sigma \in \Delta, a \in A_i. We see that
\sum_{a \in A_i} g_i(\sigma)(a) = \sum_{a \in A_i} \sigma_i(a) + \text{Gain}_i(\sigma,a) = 1 + \sum_{a \in A_i} \text{Gain}_i(\sigma,a) > 0.\
We now use g to define f\colon \Delta \rightarrow \Delta as follows. Let
f_i(\sigma)(a) = \frac{g_i(\sigma)(a)}{\sum_{b \in A_i} g_i(\sigma)(b)}
for a \in A_i. It is easy to see that each f_i is a valid mixed strategy in \Delta_i. It is also easy to check that each f_i is a continuous function of \sigma, and hence f is a continuous function. Now \Delta is the cross product of a finite number of compact convex sets, and so we get that \Delta is also compact and convex. Therefore we may apply the Brouwer fixed point theorem to f. So f has a fixed point in \Delta, call it \sigma^*.

I claim that \sigma^* is a Nash Equilibrium in G. For this purpose, it suffices to show that
\forall 1 \leq i \leq N, ~ \forall a \in A_i, ~ \text{Gain}_i(\sigma^*,a) = 0 \text{.}
This simply states that each player gains no benefit by unilaterally changing his strategy, which is exactly the necessary condition for a Nash equilibrium.

Now assume that the gains are not all zero. Therefore, \exists i, 1 \leq i \leq N, and a \in A_i such that \text{Gain}_i(\sigma^*, a) > 0. Note then that
\sum_{a \in A_i} g_i(\sigma^*, a) = 1 + \sum_{a \in A_i} \text{Gain}_i(\sigma^*,a) > 1.
So let C = \sum_{a \in A_i} g_i(\sigma^*, a). Also we shall denote \text{Gain}(i,\cdot) as the gain vector indexed by actions in A_i. Since f(\sigma^*) = \sigma^* we clearly have that f_i(\sigma^*) = \sigma^*_i. Therefore we see that
\sigma^*_i = \frac{g_i(\sigma^*)}{\sum_{a \in A_i} g_i(\sigma^*)(a)} \Rightarrow \sigma^*_i = \frac{\sigma^*_i + \text{Gain}_i(\sigma^*,\cdot)}{C} \Rightarrow C\sigma^*_i = \sigma^*_i + \text{Gain}_i(\sigma^*,\cdot) \left(C-1\right)\sigma^*_i = \text{Gain}_i(\sigma^*,\cdot) \Rightarrow \sigma^*_i = \left(\frac{1}{C-1}\right)\text{Gain}_i(\sigma^*,\cdot).
Since C > 1 we have that \sigma^*_i is some positive scaling of the vector \text{Gain}_i(\sigma^*,\cdot). Now I claim that
\sigma^*_i(a)(u_i(a_i, \sigma^*_{-i}) - u_i(\sigma^*_i, \sigma^*_{-i})) = \sigma^*_i(a)\text{Gain}_i(\sigma^*, a)
\forall a \in A_i. To see this, we first note that if \text{Gain}_i(\sigma^*, a) > 0 then this is true by definition of the gain function. Now assume that \text{Gain}_i(\sigma^*, a) = 0. By our previous statements we have that
\sigma^*_i(a) = \left(\frac{1}{C-1}\right)\text{Gain}_i(\sigma^*, a) = 0
and so the left term is zero, giving us that the entire expression is 0 as needed.

So we finally have that
0 = u_i(\sigma^*_i, \sigma^*_{-i}) - u_i(\sigma^*_i, \sigma^*_{-i}) = \left(\sum_{a \in A_i} \sigma^*_i(a)u_i(a_i, \sigma^*_{-i})\right) - u_i(\sigma^*_i, \sigma^*_{-i}) = \sum_{a \in A_i} \sigma^*_i(a) (u_i(a_i, \sigma^*_{-i}) - u_i(\sigma^*_i, \sigma^*_{-i})) = \sum_{a \in A_i} \sigma^*_i(a) \text{Gain}_i(\sigma^*, a) \quad \text{ by the previous statements } = \sum_{a \in A_i} \left( C -1 \right) \sigma^*_i(a)^2 > 0
where the last inequality follows since \sigma^*_i is a non-zero vector. But this is a clear contradiction, so all the gains must indeed be zero. Therefore \sigma^* is a Nash Equilibrium for G as needed.

there it is; proof that epds work ...mk Smile  Smile  Smile




   Too  much greek for me . Zero equals zero forward slash comma greater than lesser than .     Jon
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MKeeney
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PostSubject: Re: Fat Boy ????   Mon Jun 16, 2014 10:08 pm

Are all of your cows equal?

no, and the inequality is different each year...but on a herd basis, about the same yearly...

Do all bulls have the same purpose(s)?

ultimately yes; maternal...but...differing tweak possibilities...

Is the eye of the breeder(buyer) to be discounted?

let the buyer pick; because everyone doesn`t agree on "best"...question for Meagan, was the top selling bull also "best" by her evaluation
Do all buyers have the same supply of money or the same amount of time to buy bulls?

all my customers have plenty of money to buy my bulls...maybe not enough to buy someone elses..maybe that`s why they are my customer  Very Happy other customers have plenty to buy any ones bull; and intend to keep it...


Is data bad if it helps a person make a decision or feel more comfortable in their decision?

all data/knowledge is good...that data makes fools of people is people`s fault; not data`s fault...

Do you cull bottom end bulls to increase the floor price?

no; limit numbers by how much demand I think I have at my price...

Do you decrease supply to match or stimulate demand?

yes; to match demand...

Do buyers ever see differences in calves sired by any of your bulls?

I do at home; and the astute customers do as well...


Is any discussion of a bull, sire groups or bulls bad (i.e. promotion?)

no...but making choices based on internet discussion/questions is bad  Twisted Evil ask enough; you`ll find the answer you wanted  Smile 
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pukerimu



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PostSubject: Re: Fat Boy ????   Tue Jun 17, 2014 3:48 am

EddieM wrote:

Not personal questions:

Are all of your cows equal?

No - some are equal than others - they are becoming more equal though in that our replacement heifer selection is heavily weighted to dam, grand-dam, sister and aunt performance - the cows are all getting more and more closely related

Do all bulls have the same purpose(s)?

Yes - the majority of our buyers are looking for bulls to breed replacement heifers and steers and cull heifers that finish early or they can sell as well grown 18 month olds to specialist finishers.

Is the eye of the breeder(buyer) to be discounted?

The eye of the buyer was the reason we ignored the trends and fashions and dare I say figures 16 years ago - we asked our buyers what was important to them - happily it was the same things that were important to us but at that time and probably still now completely contrary to what many Stud breeders were "educating" their buyers as to what is really important - we now have a blueprint of cattle selection, assessment and breeding and sticking to it - so far so good.  Mike - the highest priced bull was placed at Lot 1 - there were several others which I liked as well but he was the most impressive and obviously more than one bidder was after him.  The best bull of the 2012 crop was a similarly bred bull who was fabulous if I say so myself - we kept him - got incredibly smug about our breeding ability (well at least I did - Kevin does not have a smug bone in his body) and Murphy put a stop to all that nonsense by having another older bull break his back leg - they had been as good as gold together - sadly no hope of repair - he is now dog tucker but happily we can repeat the mating - breeding cattle sure know how to knock you down a peg or two  Twisted Evil 

Do all buyers have the same supply of money or the same amount of time to buy bulls?

Definitely not - we have large stations which are multi generational with little debt and we have first farm buyers with high levels of debt - despite our average being $7112 over 47 bulls, we had 15 bulls sell for $5,000 or less and some very happy smaller budget buyers

Is data bad if it helps a person make a decision or feel more comfortable in their decision?

We provide as much data as we would like to see in a catalogue - the growth, maternal (milk and b/w) and carcase EBV's along side all the actuals for the relevant ages ie all weights from birth through to 600 days and all raw scanning data and scrotal circumference.  Unlike many others we put 3 generations of pedigree and sire reference pedigrees and EBV's - we do discuss in the foreword the fish hooks of EBV's - ie easily manipulated, useless unless at least 85%+ accurate and totally skewed by both many links (usually overseas) or none (as is the most case with our cattle)

Do you cull bottom end bulls to increase the floor price?

No - we are trying to increase our numbers to ensure that all have a chance to buy a bull - we will not compromise on our quality and structure bottom lines though - we guarantee the bulls for three years - if they do not perform not only have we annoyed someone who put their faith in our breeding nous and integrity - it costs us money

Do you decrease supply to match or stimulate demand?

As above

Do buyers ever see differences in calves sired by any of your bulls?

Fat Boy is an example of buyers specifically wanting his bulls - our buyers are becoming more and more interested in the cow lines and keep catalogues from year to year to help them with their selection process - the main comment we get is a general improvement in finishing ability and temperament - regardless of what sire group

Is any discussion of a bull, sire groups or bulls bad (i.e. promotion?)

So long as it is balanced, factual and useful discussion, I believe all information is useful in decision making - hype and promotion can go over board though and NZ'ers generally tend to be band wagon jumpers of the first order - Chisum is a popular choice over here at the moment - I would be happy to hear any insights from those that have seen him or his progeny in the States?  No, we are not considering him or his progeny - we like to see them on the ground before introducing anything into our herd.

Been away down in the South Island - sorry for late response.  Because of the auction system the buyers end up with the absolute final say in our breeding decision and choices - if they don't like 'em they don't buy 'em - simple really
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