I'm not an expert on game theory, but here's my response, based on what I know about it. If someone could correct me, I'd greatly appreciate it
The first key is to understand the assumption involved in game theory. I'll use the "prisoner's dilemma" as an example. In the prisoner's dilemma, Larry and Barry are being questioned in separate rooms as to their involvement in a crime. They are both guilty of the crime, though the police do not know this. The decision Larry and Barry must make is whether or not to rat out the other. If Larry rats out Barry, then Barry goes to jail for 10 years and Larry goes for 5 (in exchange for his cooperation), and vice versa if Barry rats out Larry. If neither rats, they both go free; if both rat, they both go to jail for 10 years. Clearly, the best outcome for the two is that neither rats, and they both go free. But, they are in separate rooms, so they do not know what the other player will do. If only there were someone who could make the decision for both Larry and Barry, the "optimal" outcome could occur every time.
So it is with the economy, according to this game-theory critique of the free market. There is limited knowledge available to the many parties in an economic system, and if it were possible to increase knowledge -- or, better yet, invest in one group the authority to plan the economy altogether -- then better, more rational, more efficient, more productive results would follow.
Take producing a pharmaceutical. The interests of the consumer and the producer are, say game theorists, at odds: the consumer wants a safe, effective, inexpensive drug, and the producer wants to make profit. One way to increase per-item profit is to forgo safety procedures in the manufacturing process, to leave impurities in the drug, or to use a less potent version of the active ingredient. The game-theory regulation can take the form of FDA regulations to let the consumer know that the drugs they take are safe and standardized.
The major unstated premise is that the government can perform this task better than the free market. If you attack that point, I think the argument from effect put forward by game theory falls apart.