We consider an example of stochastic games withpartial, asymmetric and non-classical information. We obtainrelevant equilibrium policies using a new approach which allowsmanaging the belief updates in a structured manner. Agents haveaccess only to partial information updates, and our approachis to consider optimal open loop control until the informationupdate. The agents continuously control the rates of their Poissonsearch clocks to acquire the locks, the agent to get all the locksbefore others would get reward one. However, the agents have noinformation about the acquisition status of others and will incura cost proportional to their rate process. We solved the problemfor the case with two agents and two locks and conjectured theresults forN-agents. We showed that a pair of (partial) state-dependent time-threshold policies form a Nash equilibrium.