Final answer:
The game in 'The Man Who Would Not Shake Hands' isn't specified, but the reference to Golden Balls illustrates the prisoner's dilemma, where individuals might not cooperate despite mutual benefit.
Step-by-step explanation:
The game being referenced in 'The Man Who Would Not Shake Hands' is not explicitly described within the context of the details provided. However, the mention of the British game show Golden Balls reveals a different game that showcases the prisoner's dilemma, a concept in game theory that occurs when two individuals might not cooperate, even if it appears that it is in their best interest to do so. This concept is clearly illustrated when two players on the show face a decision that affects both their outcomes, emphasizing a tension between cooperation and self-interest.