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Understanding the notations in Bayesian game definition

I am having trouble understanding the definition of a Bayesian game based on the following definition from class. I would appreciate it if you could explain the notations and overall meaning for point ...
coderDcoder's user avatar
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The concept of 'truthfulness' and 'indirect' in mechanism design

I'm a beginner in mechanism design. I learned that 'a (direct) mechanism is truthful if an agent truthfully reveals his/her type.' Then, how can we define a truthful indirect mechanism? I'm not sure ...
John Wong's user avatar