Are markets 0 sum?

There are some many voices around that put forward the idea that markets are not a 0 sum game, such as the stock market. But other markets, such as the options/derivatives markets are.

Here a few arguments are presented to support the idea that: any market is a 0 sum game.

Argument 1 - against

If a market is not a 0 sum game, then consider these steps

1. All participants start with a total capital of C $,
2. A number of assets are released to a random set of participants for free (considered so for simplicity, it can also be for a value of K$, thereby creating the total amount of capital between participants of C-K, which excludes the 'market maker' who received K for releasing those assets), 
3. Trading starts, a finite number of trades are carried on, in steps, between any random subset of the participants
4. Assume the market capitalization grew, the wealth is now C2 > C, which is simply the sum of all prices (assuming different assets, one for each class) 
5. All participants now decide to cash in their investments, feeling happy about their growth, in doing so, in random steps, some end with more money and some with less (depending on which sells first, at high price or last, at the lowest)
6. The total capital in cash is now C2 > C, therefore money must have been created in the process, this must be impossible (consider money as another kind of asset, creating money simply means introducing X $ to any of the participants

Argument 2 

To make the claim even more obvious, consider this simple trading example: 3 participants A, B and C each starts with 10$, A already has 5 shares of asset X, valuing his position at 1$/share 

1. Market is bullish, other 2 want to own some shares, A sells 1 for 2$ to each participant, a higher price than is initial valuation.
2. A went from 5$ asset wealth to 6$ = 2$*3 net wealth, other have each 2$ asset wealth
3. We can see that from the initial 5$ in asset values, the sum of all asset values is 10$ now

Is that even correct?! Let's summarize

Participant	A	B	C
Cash	14	8	8
Asset	6	2	2

A started with a valued worth of 10+5 = 15$. Therefore, wealth has been increased. Right?!

Let the participants cash in their new wealth now. B and C sell for 3$ to A, thinking they are worth that much, then A buys in (for an obvious?) loss, now we have

Participant	A	B	C
Cash $	8	11	11
Asset in $	5*3=15	0	0

Still, wealth has been created, but sum of cash is constant through all 3 steps, suppose now nobody wants to by shares for A, due to bad news or so, hence A has 5 illiquid assets, but, if an external participant (we can suppose that could be the Central Bank), thinks his assets are worth 15$. He is payed with 15$ and now has 23$. Notice how only by cash injection can wealth be increased

Through any number of trades, sum of cash for all participants is constant.

This argument is valid in any kind of market.

Demonstration 

For a more comprehensive look at how a market can work, one could look at a very simple simulation. This example represents a minimal definition for a market which is, nevertheless, conceptually close to real markets

Here is the demonstration hosted, more information about different aspects worthwhile to notice are described in the document.

Economic Perspective

If, indeed, the stock market does not produce wealth. Then why has it been growing for so much and created value for the average holder?

In an economy the only source of cash is the National Bank which regulates the money supply.

The S&P 500 shows a steady growth: 

Figure 1, S&P 500 1980-2013

At about a an exponential level sometimes

Figure 2, Money Supply 1960 - 2013

Indeed, if one thinks about the resemblance of the 2 charts, then wealth generation is obvious. Moreover, the similarity shows how, with several years lag, the stock market begun growing at a similar rate as the money supply.
Around 1995, S&P 500 starts a real growth, after 30 years since the money supply started its exponential growth, why? Simply because there are several major investment markets (debt - bonds, commodities - gold, etc...), and, probably, the stock market received more audience by the 90s.

Where is the value, then? - In the ability to drive out incapable participants while promoting capable others.

Why?

Then, if all markets are 0-sum. What is the purpose of them. It can be seen as participants who by trading lose money are ultimately driven out, while those who do are motivated to continue the process - markets reward the capable and punishes the incapable. Consequently, the only value it provides is competition. 

Criticism

An article describes this problem. But we can se