apply these strategies to your won blog. ]]>

keep up writing. ]]>

Hence, for two-player games the relative notion of approximation does not run into the trouble of exponentially long answers and finding it is a valid algorithmic question.

The two notions of approximation, additive and relative, inherit different invariance properties of the exact Nash equilibrium (with respect to changing the payoffs of the game): the additive approximations are shift invariant and the relative scale invariant. Which of the two invariance properties of an approximate notion of equilibrium is more natural depends on the underlying application…

]]>Indeed unrelated to the post, but the problem is a definitional one: for each specific instance of valuations you can obviously extract the full 1st price, but this cannot be done by a single auction for all valuations, so you need some quantification over players’ valuation. The distributional one is natural and has a developed theory. It is not easy to think of another meaningful quantification in this general setting. In various special cases interesting competitive results are known. Chapter 13 of the “agt book” deals with these issues.

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