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it is clear that cooperation comes first and is even necessary to bring about the conditions for competition. To use a simple metaphor : People see the competing athletes but are blind to the cooperation required for the setting of the competiton, i.e. the buildings, teams, schedules, infrastructure, etc. This myopic view is what makes it ideological.
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It seems you're confusing self-interested cooperation with cooperation in all things, a position which is itself myopic and ideological. Yes, the herdsmen must have cooperated at some point to even establish a commons. They must cooperate at a level that precludes or minimizes theft of stock or murder of competitors. They must cooperate with the greater society that facilitates their trading their stock for other goods. There are probably other things I'm not thinking of. All these things are indeed examples of the 'hidden cooperation' you refer to, but in each case, the herdsman gains more than he loses. In unilaterally limiting the size of his heard, his loss (the utility of n animals) usually exceeds his gain (not having to care for n animals) unless some incarnation of one of the OP solutions facilitates some significant gain (sustainable pasture due to other herdsmen also limiting their herds).
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Until the economists start using a solid framework, and with mathematical tools that fit the complexity of the subject ... The meta(n) function will simply perfectly describe yesterday's data but will have no predictive power for tomorrow's data.
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Not 'no' predictive power, just Limited predictive power. Truly comprehensive mathematical models are effectively impossible due to the variables involved, just as the weather man cannot predict with 100% certainty.
Gasoline sales tomorrow can be reasonably predicted based on day of the week, season, price, weather, and possibly a few other factors like holidays, sporting events, etc. Gasoline sales ten years from now may be similarly predicable, or maybe the economy will collapse, or somebody will invent usable cold fusion, or there will be considerable advances in fuel efficiency or public transportation, or maybe we really will annex Iraq, or I'm sure I could think of dozens of other factors and I'm sure there are dozens of possibilities that would never occur to me. So because we have only a vague guess with 55% reliability (or less) for the 10-year forecast, we should instead base decisions on a monkey sitting at a typewriter? Or worse, ignore the 90+% certain prediction for tomorrow when trying to determine sales stocks, distribution plans, tax strategies, and whatever else?