Each other player returns a Victory card from his hand to the Supply, and may gain a Victory card costing less than it (or reveals a hand containing no victory cards.)
Each other player must return a Victory card in their hand to the Supply. If they have more than one Victory card in hand, they may choose one among them. They are not required to gain a Victory card, but if they do, it must cost less than the card they returned to the Supply.
For example, if the only Kingdom Victory card in a set was Vineyard, a player with a Duchy in hand would only be able to gain an Estate, or nothing, when hit by the Soldiers, because the Potion cost of the Vineyard is not less than 5 Coins.