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

Cheap talk game Two agents: Sender (S) and Receiver (R) Timing and actions: Sender observes state , sends message Receiver observes message , choses action Preferences: R: S: Uniform prior distribution of types Equilibrium in C-S?

K=2 replica of CS problem identical issues (2 dimensional type space) Preferences No agenda on such set (incentive compatibility automatically holds) Partition of a state space with R-choices on such indifference curve?

Today: Comparative cheap talk Partitions generated by messages in the form Comparative cheap talk equilibria exist under general assumptions on preferences require symmetry of different issues partly (but not fully) informative welfare predictions ambiguous

Relative cheap talk (rankings) Assume Consider two messages Optimal response of R? S choice

More generally Assume By denote distributions of the first and second order statistic Let Response of R: Utility of S: Symmetry and additivity!

Welfare (Example) Assume Bubbling vs comparative cheap talk

Ex ante s welfare (Example) Assume Bubbling vs comparative cheap talk

More generally Assume P: Sender is better off (is worse off) in partly informative equilibrium if his preferences are strictly quasiconvex (quasiconcave) For quasiconcave, why relative cheap talk is an equilibrium?

Extensions Type dependent (supermodular) preferences K issues Partial rankings Asymmetric issues

Type dependent preferences Supermodularity

Supermodular preferences Order statistics Conditional distributions (=order statistic distributions) Optimal R actions (Topkis, Theorem 3.10.1) Best response of R

Incentive compatibility R Equilibrium strategy Which types prefer

Supermodular preferences Strict supermodularity = strict incentives to reveal Welfare benefit for S in more informative equilibrium Simple ``quasiconvex’’ preference rule need not hold