What were some reasons the united states entered into the imperial game?

International influence, also they had just defeated Spain when they begun having imperial ambitions, therefore they may want to fill that gap

a social contract.

"a social contract is an agreement between citizens and their leader where the citizens give up certain freedoms in exchange for protection. the constitution of the united states is an example of a social contract."

a system of cooperative federalism emerged, as the powers of the federal government expanded.