When an international prospect receives his first offer, his negotiation timetable is outlined. This means that he will make a decision on which offer to accept no later than date X. As he receives offers during that timeframe, his chance of accepting an offer increases the closer he gets to date X.
This means that the chance of him and his agent informing other franchises of better offers is higher earlier in the process. This varies from player to player, agent to agent. Some are more patient and will drag the negotiating cycle to the end. Others will be more impatient and accept an offer more quickly.
Each negotiation is different, although most follow the same pattern of back and forth negotiating until a decision is made. Furthermore, when a player receives an offer that is significantly higher than his other offers on the table, this also increases his likelihood of making a quick signing.