The advantage of higher-order theory of mind in the game of limited bidding

Higher-order theory of mind is the ability to recursively model mental states of other agents. It is known that adults in general can reason adequately at the second order (covering attributions like "Alice knows that Bob knows that she wrote a novel under pseudonym"), but there are cognitive limits on higher-order theory of mind. For example, children under the age of around 6 cannot correctly apply second-order theory of mind, and it seems to be a uniquely human ability. In this paper, we make use of agent-based models to investigate the advantage of applying a higher-order theory of mind among agents with bounded rationality. We present a model of computational agents in the competitive setting of the limited bidding game, and describe how agents achieve theory of mind by simulating the decision making process of their opponent as if it were their own. Based on the results of a tournament held between these agents, we find diminishing returns on making use of increasingly higher orders of theory of mind