Multi-agents ultimatum game with reinforcement learning

Abstract

The Ultimatum Game is an experimental economics game in which an agent has to propose a sharing partition of a limited amount of resources to other agents who have to accept it or not. If the offer is rejected per consensus, the process of sharing is abandoned. So all agents have to guess what are the best decisions (offer and vote) to optimise their respective gain. We focus on an iterated multi-agent version of Ultimatum Game also known as the Pirate Game, a riddle in which pirates have to share coins according to specific rules. To solve such game, we employ a multi-agent model. In particular, we design a new kind of Artificial Neural Network model able to output an integer partition of discrete finite resources, trained by a Reinforcement Learning agent to identify an acceptable offer to the voting agents. We take an interest in evaluating the performances against several kinds of voting behaviours. The results are close to theoretical optima for all tested scenarios thus demonstrating the flexibility of our method.