Set collection

King's Progress

From the producer's website:

After the success of City and Guilds, Steve's new game Kings Progress was inevitable. This game is based upon the typical life of a late medieval English court. Many Kings came under the influence of a select inner group of courtiers who used their influence to gain gifts of land, titles, money etc.

This game recreates the desperate race to get the best and the most gifts for yourself. The game is played over three rounds; each round the King visits a royal castle or house (The Kings Progress). Your aim is to gain the most prestige for your family by collecting courtier cards, melding them to build your influence and thus gain control of the courtiers, advancing those courtiers to the royal castle and then using the courtiers to select various gifts for yourself. Gifts and courtier control gain victory points at the end of each round. As the game progresses gifts become more valuable. Each courtier also has a character ability which can be used by the player in control to gain extra actions or other advantages.

Medici

Another Reiner Knizia standby, this game plays very well with varying numbers of people. The object is to accrue the most points during three rounds, which you do by spending your points to bid on sets of cards. Each turn the current player turns up one to three cards for all the players to bid on, with the highest bid taking all cards. The cards denote a commodity type and quantity/value. The round ends when each player's ships are full, or the commodity card deck is exhausted. After each round, points are awarded to each player having the most of a given commodity, and to the one with the most valuable total "cargo load".

Part of the Knizia auction trilogy.
One of the Knizia Florentine auction games.

Related Games:

Medici vs Strozzi (two-player version)
Strozzi

Rise of Augustus

In Augustus, you vie with your fellow players to complete "objective" cards for special powers and ultimately for victory points. Each card has 2-6 symbols which you must populate with legionnaire meeples in order to complete the card. These symbols are drawn one at a time from a bag, with all players gaining the benefit equally, but interestingly, the bag contains more of some symbols than others.

So the pivotal skill you'll deploy is in making your choice of which three objectives you'll start the game with (you're dealt six) — balancing potential difficulty of completion against value of the reward — and then which of five available objectives you'll add to your plate each time you complete one of your three. The game ends when someone completes seven objectives.

Forbidden Desert

Game description from the publisher:

Gear up for a thrilling adventure to recover a legendary flying machine buried deep in the ruins of an ancient desert city. You'll need to coordinate with your teammates and use every available resource if you hope to survive the scorching heat and relentless sandstorm. Find the flying machine and escape before you all become permanent artifacts of the forbidden desert!

In Forbidden Desert, a thematic sequel to Forbidden Island, players take on the roles of brave adventurers who must throw caution to the wind and survive both blistering heat and blustering sand in order to recover a legendary flying machine buried under an ancient desert city. While featuring cooperative gameplay similar to Forbidden Island, Forbidden Desert is a fresh new game based around an innovative set of mechanisms, such as an ever-shifting board, individual resource management, and a unique method for locating the flying machine parts.

New Amsterdam

Nieuw Amsterdam was founded by the Dutch West Indies Company in order to encourage the lucrative beaver pelt trade with the local Native American hunters along the Hudson River. To establish a trading post there, they needed a town and a fort, which was built on the tip of Manhattan Island. To encourage European patrons – that is, settlers of means or noble birth – to populate the colony, they granted them both land and indentured servants. The patrons became the lords of a new feudal system not unlike that seen in Europe.

In Nieuw Amsterdam, players are those patrons, and they bid on action lots in order to build businesses, work land for both food and building materials, compete in elections, ship furs to the Old World, and trade with the Lenape Indians – a process that gets more complicated as players claim more land and push the Lenape camps farther up the Hudson River.