Multi-agent Game Domain: Monopoly

In the previous chapters we have looked at the visual domain and single-agent environments for action domains. In this chapter, we will apply the novelty framework to a multi-agent game environment. As an example of multi-agent game environment, we introduce a simulated version of the Monopoly board game. Monopoly is a multi-agent board game that involves four players taking turns by rolling a pair of unbiased dice and making decisions. The conventional Monopoly board consists of 40 square locations which include 22 real estate locations, 4 railroads, and 2 utility locations that players can buy, sell, or trade. Furthermore, there are squares that correspond to “Go,” a jail location, card locations, and the free parking location. Figure 7.1 shows all assets, their corresponding purchase prices, and color. We setup the Monopoly simulator to have one learning-based agent ( \(\alpha _{\mathcal{T}}\) ) and three fixed-policy agents. These constitute the four players in the game. The objective of the learning-based agent ( \(\alpha _{\mathcal{T}}\) ) is to learn winning strategies for Monopoly. Formally, the task \(\mathcal T\) of the agent, \(\alpha _{\mathcal{T}}\) , is defined as: given the observation space \(x_t \in \mathcal O\) at time t, select an action \(a_t \in \mathcal A\) to maximize the overall reward resulting in a higher win rate.