A simple proof of Renner's exponential de Finetti theorem

We give a simple proof of the exponential de Finetti theorem due to Renner. Like Renner's proof, ours combines the post-selection de Finetti theorem, the Gentle Measurement lemma, and the Chernoff bound, but avoids virtually all calculations, including any use of the theory of types

A simple proof of Renner's exponential de Finetti theorem

We give a simple proof of the exponential de Finetti theorem due to Renner. Like Renner's proof, ours combines the post-selection de Finetti theorem, the Gentle Measurement lemma, and the Chernoff bound, but avoids virtually all calculations, including any use of the theory of types

Estimating Subjective Probabilities

Subjective probabilities play a central role in many economic decisions, and act as an immediate confound of inferences about behavior, unless controlled for. Several procedures to recover subjective probabilities have been proposed, but in order to recover the correct latent probability one must either construct elicitation mechanisms that control for risk aversion, or construct elicitation mechanisms which undertake “calibrating adjustments” to elicited reports. We illustrate how the joint estimation of risk attitudes and subjective probabilities can provide the calibration adjustments that theory calls for. We illustrate this approach using data from a controlled experiment with real monetary consequences to the subjects. This allows the observer to make inferences about the latent subjective probability, under virtually any well-specified model of choice under subjective risk, while still employing relatively simple elicitation mechanisms

Parallel repetition via fortification: analytic view and the quantum case

In a recent work, Moshkovitz [FOCS'14] presented a transformation n two-player games called "fortification", and gave an elementary proof of an (exponential decay) parallel repetition theorem for fortified two-player projection games. In this paper, we give an analytic reformulation of Moshkovitz's fortification framework, which was originally cast in combinatorial terms. This reformulation allows us to expand the scope of the fortification method to new settings. First, we show any game (not just projection games) can be fortified, and give a simple proof of parallel repetition for general fortified games. Then, we prove parallel repetition and fortification theorems for games with players sharing quantum entanglement, as well as games with more than two players. This gives a new gap amplification method for general games in the quantum and multiplayer settings, which has recently received much interest. An important component of our work is a variant of the fortification transformation, called "ordered fortification", that preserves the entangled value of a game. The original fortification of Moshkovitz does not in general preserve the entangled value of a game, and this was a barrier to extending the fortification framework to the quantum setting