Rendezvous on the Line with Different Speeds and Markers That Can Be Dropped at Chosen Time

Abstract

In this paper, we introduce a linear program (LP)-based formulation of a rendezvous game with markers on the infinite line and solve it. In this game one player moves at unit speed while the second player moves at a speed bounded by vmax≤1. We observe that in this setting, a slow-moving player may have interest to remain still instead of moving. This shows that in some conditions the wait-for-mummy strategy is optimal. We observe as well that the strategies are completely different if the player that holds the marker is the fast or slow one. Interestingly, the marker is not useful when the player without marker moves slowly, i.e., the fast-moving player holds the marker.

Keywords

• asymmetric rendezvous on the line
• markers
• asymmetric speeds