A funny old game

A significant proportion of this summer's transfers have thus far indicated that players have been signed from an undisclosed fee e.g. Emmanuel Adebayor, from Arsenal to Manchester City.
What does an undisclosed fee mean though, what does it signify, and why are so many football clubs refusing to disclose the fees they have paid for players? What is it about this summer's transfers that means clubs and/or players do now want anyone to know the fee exchanged between two clubs in return for the services of a player? Is there information that one of the parties involved in a transfer would like to be kept secret? Is the avoidance of specifying a value an attempt to ward-off unwanted intrusion by fans, the media and other interested parties? Or is there an element to the transfer of players that is best explained by referring to Game Theory? If a club goes public, might it weaken (or possibly strengthen) its position in the transfer market? And how might the notion of 'Prisoner's Dilemma' contribute to understanding the use of 'undisclosed fees' and the football player transfer market?

N.B. Game theory can be explained thus: Game theory attempts to mathematically capture behavior in strategic situations, in which an individual's success in making choices depends on the choices of others. While initially developed to analyze competitions in which one individual does better at another's expense (zero sum games), it has been expanded to treat a wide class of interactions, which are classified according to several criteria.
Prisoner's dilemma can be explained thus: "Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies (defects from the other) for the prosecution against the other and the other remains silent (cooperates with the other), the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation. How should the prisoners act? In casual usage, the label 'prisoner's dilemma' may be applied to situations not strictly matching the formal criteria of the classic or iterative games, for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it merely difficult or expensive, not necessarily impossible, to coordinate their activities to achieve cooperation."