Optimal Hiding with Partial Information of the Seeker's Route

A research team from institutions including the University of California, Santa Cruz and the University of Maryland has published a novel game theory framework titled "Optimal Hiding with Partial Information of the Seeker's Route" on arXiv. The paper, submitted in March 2026, models a strategic interaction between two agents: a Hider concealing a stationary treasure and a Seeker searching locations sequentially. The key innovation is that the Hider observes a prefix of the Seeker's route during the search and can pay a cost to relocate the treasure once to an unvisited location. This creates a dynamic where information revelation timing critically impacts optimal strategies.

The researchers analyze two distinct Seeker models. In the first "restricted" model, the Seeker is unaware the Hider can relocate, operating under false assumptions. In the second "feedback" model, the Seeker is strategic and accounts for the Hider's observation and relocation capability. The core finding is that Seeker awareness reduces the overall game value—the expected payoff for the Hider. They quantify this reduction, showing the difference between the two models is bounded by the entry-wise gap between their corresponding payoff matrices. Numerical simulations demonstrate that the Seeker's benefit from awareness decreases as the switching cost for relocation increases or as the information reveal occurs later in the search route.