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in a current market design problem set I am very confused by the given questions. We are often asked to find "an equilibirum of the [auction type, e.g. second-price auction]".
The amount of bidders is three and the utility values are drawn randomly from the interval [4,10].
Therefore my question what exactly am I asked to do when I have to find an equilibrium in auction theory given the information of the task.

Thank you in advance for your help!

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The equilibrium referred to in your question is theNash-equilibrium; to be more precise, it is the Bayes-Nash equilibrium.

what exactly am I asked to do

Have you studied Game Theory before? If yes, then find the Bayes-Nash equilibrium. If not, your options are learning about it very quickly (optionally alerting your lecturer about your deficiency and asking for sources), dropping the course, or hoping that you can somehow absolve this graduate level course without the prerequisites.

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