No Pay? No Play.
What's the best way to handle an employee who asks "what's in it for me?" when invited to participate in fun, work-related tasks, like a contest to see who can come up with the best tagline for our company? The only reward is to have the winner's name appear alongside the tagline, which will be on the company's home page. In fact, any task that ventures outside his job description is met with "what's in it for me if I do this?" Is he right or are we being stingy?
In my opinion, the employee is neither right or wrong and you are not being stingy. Employees bring different motivations to the workplace and act accordingly.
In my experience, these types of contests or activities are voluntary. If that's the case here, I would simply be pragmatic about the response. You've already identified the reward: the ability for the winner's name to appear alongside the tagline. If that reward is not motivation enough for the employee to participate, that's the choice they can make.