Multidimensional Cheap Talk (Quasiconvex preferences) Comparative cheap talk (JET 2007) Persuasion by Cheap Talk (AER 2010) Chakraborty an Harbaugh

Multidimensional Cheap Talk Two agents: Sender (S) and Receiver (R) Timing and actions: Sender observes state , convex, compact, message Receiver observes message , choses action R preferences S preferences Can we find a partition even if preferences are asymmetric?

Spinning argument Persuasion by Cheap Talk (AER 2010)

General argument compact and convex, absolutely continuous, full support R preferences S preferences, type independent, continuous For any and define P: For any. there exists such that Borsuk-Ulam theorem

Substantive insight Partly revealing (influential) equilibrium Exists! R prefers revealing equilibrium (Blackwell) to bubbling S prefers revealing equilibrium if preferences strictly quasiconvex Finer partitions linear preferences (straighforward) strictly quasiconvex preferences (harder)

S utility linear in For N=1,2,.. one can construct 2^N element partition, Probability mass of each element Sender essentially reveals all the information in K-1 dimensions Argument extends for strictly quasivonvex preferences

Strictly quasiconvex utility: problem Argument extends for strictly quasivonvex preferences

Strictly quasiconvex utility: solution Argument extends for strictly quasivonvex preferences

Quasiconvex preferences: Desirability of quasiconvex preferences: Partly revealing equilibria improve S (ex ante) welfare For such preferences infinite partitions exist Former property important given easy commitment to ``not to talk’’ Argument extends for strictly quasivonvex preferences

Benefits from randomness of ? Which economic settings give rise to quasiconvex preferences Let , When variation in is good? Four settings: 1. Separable convex utility per each issue (advertising) 2. Settings in which determines the outcome - unit demand (recommendation game) - unanimous voting - second price auction

Application 1: Advertising S: Two-good monopoly, (olive oil, wine) zero cost Unobserved quality of commodity k Independent ``linear’’ markets, expected utility Q: advertise quality in of products or one market? Argument extends for strictly quasivonvex preferences

Advertising: Solution Profit S preferences: continuous, strictly quasiconvex Bubling v.s ranking equilibrium

Application 2: Recommendation game 2 objects, quality observed by a seller R: buyer, unit demand, outside option S: salesperson maximizes probability of selling Interpretation: Professor with Ph.D. students on the market Dealer charging commission fee Lobbyist advising a senator on several bill proposals

Recommendation game (solution) S preferences: continuous, strictly quasiconvex

Logit model K products Discrete choice Buyers utility Remark: logit model (McFadden) with extreme value distribution

Application 3: Jury trial Two aspects, evidence observed by defense R: Jury two types, each cares bout one aspect privately observed threshold probability of voting for conviction S: defense attorney, utility =probability of acquittal Unanimous voting: Defense needs to persuade one of the two

Jury trial: Solution S preferences: continuous, strictly quasiconvex

Application 4: Disclosure in SP auction Second price auction One objects with two characteristics R: N buyers Unobservable independent types Value of an object S: utility = sexpected econd highest bid

Application 4: Disclosure in SP auction For