To those dissatisfied with both Jesus and John the Baptist, Jesus used a simple illustration that must have happened many times in each city of ancient Israel.
“But to what shall I compare this generation? It is like children sitting in the marketplaces and calling to their playmates, “‘We played the flute for you, and you did not dance; we sang a dirge, and you did not mourn.’ For John came neither eating nor drinking, and they say, ‘He has a demon.’ The Son of Man came eating and drinking, and they say, ‘Look at him! A glutton and a drunkard, a friend of tax collectors and sinners!’ Yet wisdom is justified by her deeds.” (Matthew 11:16-19 ESV; see also Luke 7:31-34) Some English versions use market places).
Keener, in The IVP Bible Background Commentary: New Testament, explains:
Spoiled children who pretend to have weddings and funerals (one later game was called “bury the grasshopper”) stand for Jesus’ and John’s dissatisfied opponents; dissatisfied with other children who will not play either game, they are sad no matter what. The term for “mourn” here is “beat the breast,” a standard mourning custom in Jewish Palestine. Custom mandated that bystanders join in any bridal or funeral processions.
This photograph made at Nazareth Village helps to illustrate the Biblical text.
Children at Nazareth Village. Photo by Ferrell Jenkins.
Ferrell's Travel Blog 
Thanks for the great explanation of these verses. I now have a much better understanding of them. I wondered if it had something to do with a game.