Strategies in Competing Subset Selection

We address an optimization problem in which two agents, each with a set of weighted items, compete in order to minimize the total weight of their solution sets. The latter are built according to a sequential procedure consisting in a fixed number of rounds. In every round each agent submits one item that may be included in its solution set. We study two natural rules to decide which item between the two will be included. We address the problem from a strategic point of view, that is finding the best moves for one agent against the opponent, in two distinct scenarios. We consider preventive or minimax strategies, optimizing the objective of the agent in the worst case, and best-response strategies, where the items submitted by the opponent are known in advance in each round.