Using iterated reasoning to predict opponent strategies

The field of multiagent decision making is extending its tools from classical game theory by embracing reinforcement learning, statistical analysis, and opponent modeling. For example, behavioral economists conclude from experimental results that people act according to levels of reasoning that form a "cognitive hierarchy" of strategies, rather than merely following the hyper-rational Nash equilibrium solution concept. This paper expands this model of the iterative reasoning process by widening the notion of a level within the hierarchy from one single strategy to a distribution over strategies, leading to a more general framework of multiagent decision making. It provides a measure of sophistication for strategies and can serve as a guide for designing good strategies for multiagent games, drawing it's main strength from predicting opponent strategies. We apply these lessons to the recently introduced Lemonade-stand Game, a simple setting that includes both collaborative and competitive elements, where an agent's score is critically dependent on its responsiveness to opponent behavior. The opening moves are significant to the end result and simple heuristics have achieved faster cooperation than intricate learning schemes. Using results from the past two real-world tournaments, we show how the submitted entries fit naturally into our model and explain why the top agents were successful.