Rationality and Reciprocity of Opinion Dynamics in Games

We examine opinion dynamics in multi-agent games. Each agent forms an opinion describing its preferences among multiple available strategies and exchanges its opinion with other agents. We explain how the model allows the agents to make rational and reciprocal decisions on strategy selection, both of which are key features observed in human decision making. Using bifurcation analysis, we establish how the agents switch between rational and reciprocal decision making, and we use the results to explain how cooperation emerges in the prisoner's dilemma. Using numerical examples, we illustrate the results of the bifurcation analysis and identify important aspects of rational and reciprocal decision making.