Competition for the attention of a "problem solver"

We introduce a new type of agent, whom we refer to as a "problem solver" (PS). The PS interacts with conventional players and wishes to respond optimally to their moves. The PS has only partial information about the moves of the other players. Unlike a regular player, the PS does not "put himself in the shoes" of other players and does not form beliefs about their moves. Rather, he treats the data as a logical puzzle: he calculates the set of possible configurations of moves that are consistent with the data he observes and responds to it. We insert such a problem solver into a simple model of competition for attention and analyze its equilibria. We demonstrate a novel feature of equilibrium in the model, whereby even though the PS always succeeds in his task, he may be uncertain that he will do so. The second author acknowledges financial support from ERC grant 269143. Our thanks to Noga Alon, Ayala Arad, Kfir Eliaz, Gil Kalai and Rani Spiegler for helpful conversations. Page: 1 Date: 7/27/2015