Abstract
This paper considers resource allocation among producers (agents) in the case where the Principal knows nothing about their cost functions while the agents have Markovian awareness about his/her strategies. We use a dynamic setup of the stochastic inverse Stackelberg game as the model. We suggest an algorithm for solving this game based on Q-learning. The associated Bellman equations contain functions of one variable for the Principal and also for the agents. The new results are illustrated by numerical examples.
Highlights
Stackelberg games date back to the monograph [1]
Proportional allocation is the most natural mechanism to distribute resources, which has been approved by the practical control of organizational systems
The static proportional resource allocation mechanism was studied in control of organizational systems; a modification of this mechanism that guarantees strategy-proofness was designed there
Summary
Stackelberg games date back to the monograph [1]. The original setup includes two players, Leader (Principal) and Follower (Agent). We suggest a method for solving such problems in the dynamic setup under incomplete information about the agents’ behavior. Q-learning procedure is replaced by a faster one-dimensional maximization algorithm for a concave function of one variable In both setups, the agents involve recursive statistics. The suggested algorithms can be considered as numerical methods for solving the corresponding static inverse Stackelberg game without sufficient information about the payoff functions of the agents. This game-theoretic model has been applied for optimal resource allocation among producers in the case of insufficient information about their cost functions.
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