Strategic posting times over a shared publication medium

We consider a game of timing between advertisers, or similar content creators, who compete for position and exposure over a shared publication medium such as an on-line classified list. Posted items (that may be ads, messages, multimedia, or comments) are ordered according to their posting times, with recent posts displayed at the top positions. The effectiveness of each item depends on its current display position, as well as on a time-dependent exposure function which represents the collective exposure of the publication medium. It is assumed that each of a Poisson-distributed number of advertiser may choose the posting time of his or her item within a finite time interval, with the goal of maximizing the total exposure of this item. We formulate the problem as a non-cooperative game between advertisers, and analyze the Nash equilibrium profile of this game in terms of existence, uniqueness, computation and efficiency. Explicit expressions are derived for the case where the relative importance of the posting positions are geometrically decreasing.