Doggy one, you are proposing a fundamental misunderstanding of the relationship between the role of governnment and the role of the market.
First, for the purposes of this discussion, I will stipulate that the right-wing model of a free-market, capitalist society with minimal government is the only "true" or "correct" one. (In reality, of course, that is a deeply questionable assumption, but let's assume that we agree on that. We can ponder alternative conceptions of the proper role of government at some other time. For now, let's just agree to take the extreme right-wing view that it is the duty of government to get out of people's lives as far as possible.)
In the view of the extreme right, and also in the view of many more moderate groups) the best, indeed the only efficient regulator of economic activity is the market. Only a free, competitive market (this view argues) can divide up the spoils of production fairly, and (more importantly in this context) maximise productive efficiency by ensuring that we have the best possible allocation of resources to different tasks. The laws of supply and demand (Adam Smith's "invisible hand"), acting invisibly, and without any conscious intent on the part of government, automatically reallocate resources to the tasks tha most need them. This is because the most demanded products increase in price until such time as producers reallocate productive resources away from non-demanded products and, before too long, equilibrium is restored.
Now the only thing the government must do to achieve this happy and efficient state is preserve the market. Everything else "just happens" as if by magic. (Sounds crazy, I know, but it really is true. The entire science of economics is based on this fact, on the "invisible hand", and while much of economics remains fuzzy and contested, this one great truth shines through and is unchallenged by evidence to the contrary.)
Obviously, a government has the duty to guard against acts of war from outside the country and civil insurrection. It is only marginally less obvious, but equally true, that it must prevent more subtle damage to the market, which we can define quite simply as anything which prevents the market functioning as a market.
One example of this is where non-market forces are used to influence market events. If I hold a gun to the head of passers-by and require then to buy my wares at any price I care to set, this is not a market transaction, and it is the duty of the government to put a stop to it.
A more difficult (but equally fundamental) example is the circumstance where a market participant uses non-market means to gain or maintain control over common (i.e., shared) resources. If, for example, I were to fence an area of sea off the coast of California and, without payment, permission, or negotiation, simply assert my sole right to a monopoly over the entire fish stocks in that area, simply because that is what I wanted to do, then it would be the duty of the government to put a stop to it. Similarly, if I were to do the same thing by means of bribery or subversion (as Standard Oil did with United States oil reserves), the government must take action.
A third and rather similar circumstance is the situation where, by whatever means, I manage to establish an externality - a situation where I do not pay a fair market price for the thing I consume. The classic example of this is the situation where a mining company (perfectly legitimately) extracts (say) copper from a hillside. So far, so good. For the purposes of the example we will assume that the mining company is paying a fair and reasonable (i.e., a market) rate for the right to extract that copper. But in the course of smelting the ore, the company discharges massive amounts of toxic waste into the river, destroying the livelihood of the fishing village downstream. This is "externality" - the company has managed to externalise the cost of their toxic waste: i.e., make someone else pay for it. Again, it is the duty of the government to prevent this.
These three duties of government to preserve the market against particular threats, however, pale into insignificance compared the most important threat of all: not the threat of non-market interference with the market or of externalities to it, but the threat to the market itself.
This one is really, really easy to understand. Even bankers (and apes) can get their minds around this one: a market consists of many buyers and many sellers.
If you do not have many buyers and many sellers, you do not have a market, and from here on in the only thing you can do is turn away from the science of economics (for without a market, normal economics does not exist) and invoke the ghost of Joe Stalin.
All profit-maximizing firms play the market power game against each other (and obviously, those with more market power take advantage of those with less market power). I don't know how you can cite the role of government as a clear-cut argument for government intervention when there are a hundred shades of grey here. In fact, market power plays are so prevalent in business that Havard Business professor Michael Porter spelled out such market dynamics years ago; any business student should be able to recite "Porter's Five Forces" to you.