There are $N$ number of people and $X$ amount of objects with different values. Each person will choose an object and will obtain that objects value. If multiple people choose the same object then the value of the object is shared among the people. For example, If there are 2 objects and 3 people, one of the objects will be chosen by at least 2 people, thus the value of the object is divided over 2.
Each round the people make their decisions with new objects and new values, how can a person maximize their expected values accumulated from their choices in Q number of rounds, in order to win(i.e accumulated most value)? ($Q$ belongs to [1, +infinite).
Note that keeping track of other player's decisions and their accumulated values can help in future decision making.
Note: An approximation would be great as well, so far my strategy is to choose a random object at each round, I am looking for ways to maximize this strategy.