Trust is implicit in many online text conversations-striking up new friendships, or asking for tech support. But trust can be betrayed through deception. We study the language and dynamics of deception in the negotiation-based game Diplomacy, where seven players compete for world domination by forging and breaking alliances with each other. Our study with players from the Diplomacy community gathers 17,289 messages annotated by the sender for their intended truthfulness and by the receiver for their perceived truthfulness.Unlike existing datasets, this captures deception in long-lasting relationships, where the interlocutors strategically combine truth with lies to advance objectives. A model that uses power dynamics and conversational contexts can predict when a lie occurs nearly as well as human players.

In 1955, Arne Pleijel proposed the following problem which remains unsolved to this day: Given a closed plane convex curve C and a point x(2) at a fixed distance )~ above the plane, as the point x(2) varies, characterize the point for which the conical surface with vertex x(2) and base C attains its minimum, and determine the limits as 2 ~ 0 and 2 ~ oo of this minimum point. The purpose of this paper is to solve the cases where 2 approach its extremities and in the course of the solution, we obtain an interesting characterization of the limit points, which we shall call the Pleijel points of C. A consequence is that the inner Pleijel point provides an upper bound for the isoperimetric defect of C. We also generalize the problem to higher dimensional spaces, and obtain the corresponding characterizations of the limiting points for convex surfaces.

No abstract