Rationality and Reciprocity of Opinion Dynamics in Games

We examine opinion dynamics in repeated multi-agent games. In our model, each agent updates, in continuous time, its opinion about multiple available strategies, in response to payoffs associated with the game and exchanges of opinions with other agents. We show how the model provides a principled and systematic means to investigate behavior of agents that select strategies using rationality and reciprocity, both of which are key features observed in human decision making in social dilemmas. Using bifurcation analysis, we prove conditions for the multistability of equilibria in two-agent two-strategy social dilemmas. For the iterated prisoner's dilemma, we show how, with sufficiently strong reciprocity, the model predicts bistability of mutual cooperation and mutual defection. We illustrate further how the theory predicts important aspects of rational and reciprocal decision making and the sensitivity of behavior to parameters. The results are generalizable to games with more agents and more strategies, and to additional feedback dynamics, e.g., those designed to elicit cooperation.