Government
a loose alliance of groups in which each member is working for its own benefit is called a

amalamation
corporation
coalition
special-interest groups

In a government, a 'loose alliance' of groups in which each member is working for its 'own benefit' is called a coalition.

Explanation:

In politics, a coalition of parties is formed when a single political group or party fails to fetch the majority and take the mandate to itself. The seats secured by allied parties are shared to form a coalition in order to establish a stable government. All the parties in the coalition are benefited by the powers that they get to exercise for being a part of the government.

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