Fair information sharing for treasure hunting

In a search task, a group of agents compete to be the first to find the solution. Each agent has different private information to incorporate into its search. This problem is inspired by settings such as scientific research, Bitcoin hash inversion, or hunting for some buried treasure. A social planner such as a funding agency, mining pool, or pirate captain might like to convince the agents to collaborate, share their information, and greatly reduce the cost of searching. However, this cooperation is in tension with the individuals' competitive desire to each be the first to win the search. The planner's proposal should incentivize truthful information sharing, reduce the total cost of searching, and satisfy fairness properties that preserve the spirit of the competition. We design contract-based mechanisms for information sharing without money. The planner solicits the agents' information and assigns search locations to the agents, who may then search only within their assignments. Truthful reporting of information to the mechanism maximizes an agent's chance to win the search, ε-voluntary participation is satisfied for large search spaces. In order to formalize the planner's goals of fairness and reduced search cost, we propose a simplified, simulated game as a benchmark and quantify fairness and search cost relative to this benchmark scenario. The game is also used to implement our mechanisms. Finally, we extend to the case where coalitions of agents may participate in the mechanism, forming larger coalitions recursively.