Alice and Bob are sitting on an online casino table which exposes the following game: the table randomly generates a number R and piblishes this number. The player which "bids" the highest number between 0 and R wins. If two players bid the same number, they are both excluded from the game (only unique bids can win). Players must be assured that the table didn't cheat by allowing a colluding player to bid while other players are revealing their bids.
The game is so structured: 1. All players, individually, choose a number and publish a non-malleable commitment to that number, which any player can see. 2. After some time, the table stops accepting bids. 3. Each player reveals their bid along with the commitment proof. 4. The table declares the winner.
The "closing bid" signal doesn't necessarily reach all players at the same time, but there can be a delay of some seconds.
How can the players be sure that table didn't cheat by accepting bids in the middle of the revelation process? Or to figure out that a bid has been made after all others? Is there a way to "timestamp" the bids without trusting any third party?