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Can anyone please tell me what is the term used for games with incomplete information and there are no prior beliefs about other players' private information.

For example, let $ v_i(a_i,\theta_i) $ be the utility function of the player $ i $ and $ a_i $ be decided for each player some how. $ \theta_i $ be the private information for player $ i $. Player $ i $ has no belief (no knowledge of probability distribution) about others' private information except that it is a real number. Few authors call such games to be pre-Bayesian games. But there seems to be no standard. It would be great if any one can let me know this. Thanks!

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Uncertainty in the absence of a prior distribution is sometimes called Knightian Uncertainty in economics. There are a couple of recent papers studying how to deal with knightian uncertainty in mechanism design. See for example:

The Knightian Truthfulness of Classical Mechanisms

Knightian Auctions

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  • $\begingroup$ Thanks for your reply. Knightian Auctions seems to consider scenarios where the player $ i $ has uncertainty over her private information. I was looking for scenarios where the player $ i $ knows her private information precisely but has no prior beliefs about others' private information. $\endgroup$
    – Vinay
    Jun 17, 2013 at 10:59

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