danielluopi.bsky.social
bayesian persuasion, taylor swift, and yuzuru hanyu stan | happy free confused and lonely at the same time | phd and @nsf grf @mitecon | past @northwesternu
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one of them found a typo!
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are you calling me smelly :(
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i go to mit :(
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That is, funnily enough, a different set of corrections.
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MANY ARE SAYING!!!
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edit: link update here drive.google.com/file/d/1KmPJ...
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That's everything for now! The paper does a lot more and can be found below -- any feedback is welcome :) (15/15)
drive.google.com/drive/u/0/fo...
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Thus, we show that in a majority of cases, the commitment assumption is relatively innocuous, but there are also some situations where it does have real bite and can't necessarily be microfounded reputationally, as first suggested by Rayo and Segal (2010). (14/15)
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We identify a graph-theoretic condition that ensures sender can secure their Bayesian persuasion payoff, which accomodates all deterministic signals, monotone partitions (with randomization at the boundaries), upper censorship, etc. but does *not* include all bi-pooling policies. (13/15)
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Finally, we use this characterization to think about state-independent persuasion when (1) receiver never sees past state realizations and (2) sender has a "grain of truth," e.g. pays a vanishingly small cost for sending messages. (12/15)
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The CM condition tightly characterizes equilibrium payoffs in one-dimensional games where the LR players payoff between their signal and action is strictly supermodular: they get (at most) at least their payoff from a monotone strategy when SR players break ties (for) against them. (11/15)
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This also gives an upper bound: in *any* equilibrium, if the LR player is likely to be rational, their highest possible payoff is a strategy inducing a (weakly) cyclically monotone graph. The proof is a new application of the martingale convergence theorem, if anyone's interested :)
(10/15)
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Our condition is stated in optimal transport terms: a strategy is confound-defeating if and only if its graph has (strictly) cyclically monotone support. This is a new, strict version of well-known sufficiency conditions in the optimal transport literature, dating back to Rochet, 1987. (9/15)
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The key idea is that the LR player's commitment strategy must outperform in the stage game all other strategies that generate the same marginals. If this is the case, then SR players can draw the "right" inference about what the LR player is doing from just marginal data. (8/15)
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However, all is not lost. In fact, we identify a new condition, "confound-defeatingness," which is sufficient to guarantee the LR player a high payoff even in the game above. (7/15)
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This phenomena is much more general; for example, in repeated communication games, we can never rule out the equilibrium where the LR player babbles and produces a marginal distribution identical to the one produced by their commitment strategy. (6/15)
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Thus, both challenging and not challenging are 0-confirmed best replies to the commitment in this game. Formally, the standard reputation literature can only guarantee our long-run player their minimax payoff, which is far from optimal! (5/15)
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Standard reputation results (e.g. Fudenberg-Levine 1992) can't tell us much in this case: the conditional strategy (fight iff challenge detected) generates the same marginal distribution over actions as one that fights with independent probability after each signal. (4/15)
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Consider a deterrence game. An incumbent privately detects if a challenger has entered, and can choose to fight or not fight. Their optimal action is to fight if and only if a challenge is detected, but all future potential challengers see is if they fought, not why they did.
(3/15)
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We study repeated games where a long-run player privately observes some signal, then takes a publicly monitored action. Short-run players see only the LR player's past actions, and thus the LR player can only develop a reputation for marginal play over actions, not their entire strategy. (2/15)
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for example, weakening universal domain to preferences which are only single peaked allows us to characterize voting procedures that uniquely selection the median outcome. weakening IIA allows us to characterize the borda count as axiomatically (see attached). these should be discussed more!
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i don't think this is true? arxiv.org/abs/2311.04374
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omg the queen has joined
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yea i just moved over so
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\varepsilon