You only pay an action’s coin cost when taking that action. For “play a dragon” abilities found on cards and the dragon guilds, the only payment is the cost printed on the dragon card. For “play a cave” abilities found on cards and the dragon guilds, the only payment is the egg cost in the 3rd and 4th columns on the player mat. Even though the cost to play the card is discounted or free with these types of abilities, further optional costs found on some dragons, caves, and the 4th row of the player mat are not discounted/free.