One does not serve the interests of a man who wants a new coat by giving him a pair of shoes or those of a man who wants to hear a Beethoven symphony by giving him admission to a boxing match. - Ludwig von Mises, Theory and History: An Interpretation of Social and Economic Evolution

Ran across that passage a few days ago and I almost didn't collect it. But now here I am sharing it.

You're trying to teach rationality and I'm trying to teach economics. Why are you trying to teach rationality and why am I trying to teach economics? I'm trying to teach economics so people can understand how their interests are served.

Using your graphic... we can imagine that if the girl had $20 then she would have given it to the guy who correctly guessed that she wanted a baseball bat rather than a vampire bat. Markets work because consumers reward whichever producers correctly guess their preferences. To use your terminology... producers that "succeed at other minds" will gain more influence over how society's limited resources are used.

The producer whose product turns out to have the combination of features that are closest to what the consumers really want may be no wiser than his competitors. Yet he can grow rich while his competitors who guessed wrong go bankrupt. But the larger result is that society as a whole gets more benefit from its limited resources by having them directed toward where those resources produce the kind of output that millions of people want, instead of producing things that they don't want. - Thomas Sowell, Basic Economics

If consumers really want baseball bats... then it would be a huge waste to supply them all with vampire bats. Markets, because they operate on the basis of consumer sovereignty, help prevent this from happening. Consumers don't give their money to producers who fail at other minds.

With the public sector, on the other hand, people like to believe that producers of public goods succeed at other minds...

For example, the discussion assumes that the community of consumers has a well-functioning, formal state structure. Like a benevolent dictator, this state somehow guesses the preferences that people have for public goods. - Meghnad Desai, Providing Global Public Goods

But in the absence of consumer sovereignty in the public sector.... how can we be sure that the government supplies the public goods equivalent of baseball bats rather than vampire bats?

Anyways, this is the economic relevance of succeeding vs failing at other minds.