Computing the Subgame Perfect Nash Equilibriums in Parallel Allocation Indivisible Items

Abstract

Multi-Agent resource allocation has also become a research hotspot in the field of artificial intelligence in recent years. A lot of related work aims to design a procedural resource allocation system with execution efficiency. This paper Studied a parallel allocation method for allocating indivisible items between agents in which every agent asks for an object among those that re-main in every round, and every reported item will be allocated randomly to an agent reporting it. In order to depicts the entire distribution process, the authors propose a method of constructing a game tree of parallel allocation. Study the corresponding relationship between the total number of branches of the game tree and items. In the last part, prof the parallel allocation mechanism is dynamic game and show that the subgame perfect Nash equilibrium (SPNE) can be found by backward introduction the game trees. Provides a method to compute the unique subgame perfect Nash equilibrium in linear time.