There are other kinds of markets, though. This is most easily demonstrated if we stick to the most abstract definition of a market where it is described as a system by which people engage in exchange. The trade of goods and services directly as in barter or indirectly through the use of money is just one style that works for alienable stuff. There are also two styles of gifting that fit the definition with the first being something like charity with no expectation of return and the second being prestation where a return of equal or greater value is very much expected. Everything from commodities to experiences can be exchanged in these ways and we occasionally mix them with varying results. All these methods, though, tend to support the kind of market we might call Commerce. Exactly which rules apply depends on the stuff being traded. For example, I might buy and sell what I produce from a farm in a cash-based marketplace, but if there is a famine, I might be expected to gift what I produce as charity or with a delayed expectation of reciprocity. In another example, I might never be permitted to trade for kidneys using cash, but in some places I might get away with brokering such deals through barter. Getting the trade rules right can be tricky when crossing cultural borders and those who get them wrong can easily wind up being chased by a lynch mob.
There are other kinds of exchange, though, and these also point to partial solutions to a 'resource' optimization problem. Consider our concept of Justice. If someone does wrong to my kin I can respond in kind. This is a classic form of justice practiced by humanity over countless generations, but it motivates a negative sum game when done in the presence of markets for goods and services. If one market participant steals from my brother and I steal from them in return, all participants will consider the marketplace to be risky and spend resources guarding their resources. If this continues too far, the marketplace collapses when participants find it cheaper to stay away or trade elsewhere. The solution to this, therefore, is to trade with the rules of justice themselves. If one participant can dominate a marketplace and dictate the rules, the 'trade' is simplified to a simple decision of whether to participate or not. If no one dominates, then the 'trade' is in the rules and expectations regarding responses. Is it an eye for an eye and a tooth for a tooth, or is it a hand for stealing a loaf of bread and a life for poaching on the King's land? Are infractions decided vigilante style or are judges, juries and executioners required? Rules of justice that enable the other markets have the potential to make participants rich, well defended, and well off, so this is important stuff to decide. Whatever the rules are, this market is called Justice.
Next, consider our inclination to seek consensus when making decisions at a group level that imply impacts to all individuals in the group. Whether these groups are families, communities, or nations is just a matter of scale that can impact the practicality of how we determine a consensus. Whether these groups decide through votes, debates, gift giving, or shouting matches is just a matter of process and can impact the perceived validity of the resulting consensus. Since these decisions could impact the rules of Justice and what is brought to market for Commerce, there is a strong motivation to trade support for decisions. In the western sense we might call this market Democracy, but it need not look much like the Greek ideal. In the most abstract form, some people get to have a say in determining the consensus and they trade their willingness to support one decision for another. In this market, one Senator might support the spending of money on a bridge to nowhere if another Senator supports funding for a sports arena. They might also trade a change to immigration law for tougher penalties for certain crimes. Whether these trades are moral or not is judged by society, but the trades happen, thus a market exists and determining the rules governing these trades is just another form of trading.
So far, we have three basic markets and they are enough to cover most of human history. There are no clear lines separating them, so it is best not to think of them as boxes into which a particular exchange must fit. There are far too many counter examples for this to be even possibly true. Just think of a general case of a legislator accepting bribe money (Commerce) in exchange for a vote (Democracy) to make a particular kind of trade illegal (Justice). It doesn't take much to search recent history in any country to find examples.
If we define modernity from the birth of this fourth marketplace, we can point to a time on the calendar that occurred in the mid to late 17th century in northern Europe and later decades elsewhere. The impact of this fourth market is hard to understate when one notices that the Industrial Revolution kicked off a few decades later after people had some time to adopt and adapt to the new market. Look at the history of the early adopting nations and you'll see changes to their wealth and status in Europe even before the industrial age.
Is it a lack of humility to argue that humans have invented a fourth market after countless generations of relying on our traditional triplet? I think not. The fact that our population has exploded from roughly half a billion to over seven and still climbing proves something dramatic happened. A future archeologist from an alien race might have difficulty finding anything in the rock strata to explain this explosion beyond the obvious fact that it happened, yet those of us here living it know the cause. We figured out how to predict many things we couldn't predict in the past. We figured out how to put men on the Moon and we figured out how to eradicate Small Pox from the face of the Earth. We figured this out because we invented a new system and it has proven to be wildly successful by being incredibly useful. This system is just another market, but humanity doesn't invent those very often. That last time we did... we became human. What will we become now?