Rational Emotions: Orders of Reasoning and Managing Complexity Timo Ehrig and Shyam Sunder Executive Summary How to model expectations, when people anticipate interaction outcomes of large number of people? Rational expectations (RE) solved this problem, but under very tight assumptions that easily break down. Complexity of higher order beliefs explodes when we deviate from RE Emotions may regulate a theory of mind New approach my redefine the relationship between economics and psychology of emotions Emotion no longer opposite of rational behavior, but enabler of rational behavior

How Rational Expectations Solved the Problem of Modeling Expectations A fundamental problem of modelling decisions under risk and uncertainty is too many degrees of freedom in expectations: too many ways of specifying what people believe and what their beliefs about others' beliefs, and so on to higher orders, are. Muth's Rational Expectations (RE) proposal was a major initial step in significantly reducing the degrees of freedom by imposing a consistency (fixed point) condition on expectations. RE is logically compelling, and effective in reducing the degrees of freedom in modelling expectations, and was therefore has been widely adopted in economic models of micro and macro phenomena.

Why we need a new understanding of constraints on higher order expectations The demands of RE on a cognitive apparatus of human individuals proved to be too strong. In macro applications, RE do not advice on equilbrium selection, and break down once there are structural breaks. At higher orders of expectation cognition weakens but logic requires us to consider additional orders or reasoning without bounds . A first order expectation is my expectation about a fundamental state. A second order expectation is my expectation of some else’s expectation. A third order expectation is my expectation of someone else’s expectation of my expectation. And so on. RE posits that everybody knows that everybody knows that everybody knows (and so on) the right distribution. How are higher order expectations formed when there is no common knowledge of distributions? To our knowledge, there is no compelling proposal available. Psychology and neuroscience point to the role of emotions in reasoning and expectation formation by individuals

Our proposal We propose a second type of constraint on human reasoning arising from emotions This conjecture to complement RE should be rooted in observation of individual behaviour and will have important implications for micro as well as macro behaviours under risk or uncertainty. The proposal focuses on functionality of human emotional endowment as an enabler, not a disrupter, of rationality. Key idea: some emotions increase, some decrease the levels of reasoning. Conjecture: Fear increases levels of reasoning, contentment decreases levels of reasoning. Lower levels of reasoning may be functional in some domains (e.g. the two general problem/ Rubinstein’s email game) Levels of reasoning impact important real world problems: bubble formation and bubble bursts, option trading, negotiations, organizational coordination.

Empirics/ Theory A possible experiment: Prime subjects on the emotions of 1. fear/ anxiety 2. contentment/ happiness Let primed subjects play Nagel’s guessing game (a precise device to measure levels of reasoning) Conjecture: Fear will drive levels of reasoning up; Contentment/ Happiness will keep levels of reasoning low. Theory questions: In which games do lower levels of reasoning yield Pareto superior outcomes? In which games does reasoning beyond level 1 or 2 make almost no difference? In which games does a higher level of reasoning always yield advantages a. on individual level b. for all players?