Ballot box with multiple parties. All can read it, or none can read it
See malleability and commitment schemes.

You are apparently looking for a collusion-preserving implementation of simultaneous broadcast.

By letting each processor control at least one player and directing each processor to choose a random bit for each of its players and outputting the xor of all players' random bits, the resulting coin-flipping protocol is as fair as the system. $\:$ Thus, one smacks straight into this paper's impossibility result.

The ways I know of to get around that impossibility result are:

$\;$ time-lock puzzles, with which the amount of work needed for cooperating players

$\;$ to read the messages is "not too much more" than the amount of work needed for

$\;$ adversarial players to read the messages, and in both cases; the relevant work only

$\;$ needs a small amount of memory and is not (known to be feasibly) parallelizable

$\;$ partial fairness, so that when more than 1/3 of the players are cooperating

$\;$ (in particular, when there are only 2 players) and the number of possible messages is small,

$\;$ cooperating players get "not much less" information than adversarial players get

$\;$ having lots of moderators that only need to be contacted if a player stops participating

$\;$ before or during a reveal phase, each of whom is assigned a small positive integer weight

$\;$ (presumably less than the threshold I'll mention later in this text-block, otherwise there's no point

$\;$ in using more than one moderator), so that if [the sum of the weights assigned to adversarial

$\;$ moderators] is less than [the threshold chosen before the reveal phase begins] is less than or

$\;$ equal to [the sum of the weights assigned to the moderators who appear to be cooperating]]

$\;$ then the "All can read it, or none can read it" property holds

.
(A moderator that merely cannot be contacted or has lost its private key

is neither adversarial nor one who appears to be cooperating.)

To emphasize, even if all moderators are adversarial, the only thing they can do is let players

who stop participating violate the desired "All can read it, or none can read it" property.

In particular, each message must still be chosen independently of the other messages.

It may be that there are other ways around that impossibility result; in particular,

I don't see a reason why the 1/3 threshold should be critical for partial fairness.

Even if there aren't, it appears to me that one could combine the "partial fairness" option with the

"lots of moderators" option in a way that is at least as good as the latter but also provides partial fairness when the latter's inequalities are not too far off and the number of possible messages is small.

Note that I have no idea which of the three options I

described are compatible with being collusion-preserving.