Incentive strategies dealing with uncertainty about the follower's MCDM behaviour

Abstract

This paper investigates the incentive problem of two-person Stackelberg game where the follower's responses to the leader's strategy are determined based on multiple criteria decision-making (MCDM) and the follower's preference is unknown to the leader. We first focus on the single-stage (or one-shot) game and propose a minimum-deviation incentive strategy that minimizes the influence of the follower's preference upon the leader's objective function. We also present a way to construct such a strategy. Second, we investigate the multistage game where the leader uses a feedback strategy. We explore a process along which the leader extracts information about the follower's preference from the follower's responses and uses the minimum-deviation incentive strategy at each stage until he acquires enough information to know the follower's preference. Finally, we consider the multistage case where the leader can employ a memory strategy. In this case we propose a kind of memory strategy with dual functions that makes the game's outcome irrelevant to the follower's preference and necessarily leads to the leader's most desirable outcome, even though the leader does not possess any a priori knowledge about the follower's preference. We also derive existence conditions and illustrate a construction method for such memory strategies.