3.2 The Game Without Commitment........................ 6

This paper studies persuasion as a game. A speaker must decide which arguments to present and a listener which arguments to accept. Glazer and Rubinstein (2006) showed that a listener’s optimal persuasion rule is credible in the sense that commitment has no value for the listener. This paper provides an algorithm for finding an optimal per-suasion rule in persuasion problems without time constraints along with the speaker’s strategy in the credible implementation of the rule. The credibility result, as well as the algorithm, is extended to the case where the listener’s decision is not binary under a concavity assumption. Qualitative properties of optimal rules are derived. In particular, in the absence of time constraints there exists an optimal rule that treats equivalent evidence equivalently whereas this may fail with time constraints. All of the results depend on a relation between the persuasion problem and the maximum flow problem, a well-known combinatorial optimization problem. JEL Classification: C61, D82, D83