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) - ThreadSky

danielluopi.bsky.social • 172 days ago

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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danielluopi.bsky.social•172 days ago

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)

danielluopi.bsky.social•172 days ago

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)

danielluopi.bsky.social•172 days ago

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)

danielluopi.bsky.social•172 days ago

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)

danielluopi.bsky.social•172 days ago

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)

danielluopi.bsky.social•172 days ago

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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