The word "collusion" comes from the Latin word colludere, meaning "to play together".   It is formed from the prefix co-l-com ("together" "with") and ludere ("to play"). While its roots are playful, the word has always had an underlying sense of deceit, and has evolved to mean a secret agreement for fraudulent or illegal purposes.  The three main types of collusion are overt, tacit, and vertical.  Overt collusion involves open, explicit agreements, while tacit collusion is a form of implicit coordination without direct communication, often using price leadership.  Vertical collusion occurs between companies at different levels of the supply chain, such as a manufacturer and a retailer.  

According to the Oxford English Dictionary (OED),  the first known use of "collusion" in English was around 1397, in the writings of Geoffrey Chaucer. 

Examples of "collusion" used in a sentence:  
"Mason points out that accusations of collusion between the two companies were nothing new." 
"The investigation revealed that there had been collusion between certain officials to rig the election."  
"Athletes from different teams faced penalties for collusion to fix the outcome of the game." 
"OPEC has been accused of collusion when various member countries have agreed to limit the production of oil, in order to keep the price of oil artificially high." 

Categories of "collusion":
Academic: 
Working with another student on an assignment and submitting the joint work as if it were individual. 
Allowing another student to copy your work or sharing your answers to a test. 
Having another person write or edit your work without authorization. 
Coordinating a plan for an individual assessment and then copying that plan for the final submission.