Convergence : An Experimental Study ∗

One way to define a Nash equilibrium is by positing a set of beliefs (or conjectures) for each player over (about) the actions of their opponents that has the property that, given these beliefs, when each player best responds, the actions taken confirm the initial beliefs. This rational expectations definition leaves open the question of how beliefs and actions get into this self-confirming state. For example, do beliefs converge to their equilibrium state first and drag actions into alignment or is the process action driven with them converging before beliefs. What we find is that the process of convergence is one where actions converge before beliefs. However, after reaching equilibrium in actions, the beliefs of subjects converge to the degenerate beliefs that place all the weight on the partner’s equilibrium action extremely rapidly (within 2 periods on average). We also identify differences between the early converger and the late converger in a group — often it is the case that the early converger plays his part of the Nash action profile long enough to convince his opponent to adhere. Finally, we investigate the process of belief formation and argue that, unlike all of the most common learning models, the belief formation process is one that takes into account not only the payoff of the learner but also those of his opponents.