Heterogeneous facility location game with discrete utility

We study the heterogeneous facility location game model of \(n\) selfish agents on a line, where each agent’s reachable range is a closed subinterval of the line. From two possible facilities, \(f_1\) and \(f_2\), exactly one is chosen to be built on some point of the line, and the agents have their own preferences \(p_1, p_2\in[0,1]\), \(p_1+p_2=1\), over these two facilities. The utility of the agent is \(p_i\) if the placement of the chosen facility \(f_i\) is inside her reachable range, and zero otherwise. The task is to design mechanisms which get the input from the agents and select the type and placement point of the facility to be built, such that it maximizes the social welfare (defined as the total utility of all agents) while ensuring truthfulness, i.e., incentivizing agents to report their preferences (both facility type and placement) honestly as a dominant strategy.

We analyze various scenarios with different setting of privacy of agents’ positional and preference information. When the information is private to the agent, they have the option to misreport it, and hence, we will distinguish between reported information and public information.