A ‘Dual’-Improved Shortcut to the Long Run

I use the theories of duality and optimal branchings to find a necessary and sufficient characterization of stochastically stable limit sets (SSLS) that helps improve the radius -- modified coradius test of Ellison (2000). The improved shortcut I offer may permit the identification of SSLS when Ellison’s radius -- modified coradius test fails to identify any, or may be able to pinpoint the true SSLS in cases where Ellison’s test identifies only a superset. I also demonstrate precisely why the radius -- modified coradius test is not universally applicable and illuminate the connection between the modified coradius and the Lagrange multipliers of the optimal branching problem.Evolutionary games, Stochastic stability, Optimal branchings, Extended radius, Extended coradius, Modified coradius

Conflict Leads to Cooperation in Nash Bargaining

We consider a multilateral Nash demand game where short-sighted players come to the bargaining table with requests for both coalition partners and the potentially generated resource. We prove that group learning leads with probability one to complete cooperation and a strictly self-enforcing allocation (i.e., in the interior of the core). Highlighting group dynamics, we demonstrate that behaviors which appear destructive can themselves lead to beneficial and strictly self-enforcing cooperation.Nash bargaining, Learning, Core, Group conflict

History-Dependent Risk Attitude

We propose a model of history-dependent risk attitude (HDRA), allowing the attitude of a decision-maker (DM) towards risk at each stage of a T-stage lottery to evolve as a function of his history of disappointments and elations in prior stages. We establish an equivalence between the existence of an HDRA representation and two documented cognitive biases. First, the DM’s risk attitudes are reinforced by prior experiences: he becomes more risk averse after suffering a disappointment and less risk averse after being elated. Second, the DM displays a primacy effect: early outcomes have the strongest effect on risk attitude. Furthermore, the DM lowers his threshold for elation after a disappointing outcome and raises it after an elating outcome; this makes disappointment more likely after elation and vice-versa, leading to statistically reversing risk attitudes. “Gray areas” in the elation-disappointment assignment are connected to optimism and pessimism in determining endogenous reference points.history-dependent risk attitude, statistically reversing risk attitudes, reinforcement effect, primacy effect, endogenous reference dependence, betweenness, optimism, pessimism

Disappointment Cycles

We propose a model of history dependent disappointment aversion (HDDA), allowing the attitude of a decision-maker (DM) towards disappointment at each stage of a T-stage lottery to evolve as a function of his history of disappointments and elations in prior stages. We establish an equivalence between the existence of an HDDA representation and two documented cognitive biases. First, the DM overreacts to news: after suffering a disappointment, the DM lowers his threshold for elation and becomes more risk averse; similarly, after an elating outcome, the DM raises his threshold for elation and becomes less risk averse. This makes disappointment more likely after elation and vice-versa, leading to statistically cycling risk attitudes. Second, the DM displays a primacy effect: early outcomes have the strongest effect on risk attitude. “Gray areas” in the elation-disappointment assignment are connected to optimism and pessimism in determining endogenous reference points.history dependent disappointment aversion, disappointment cycles, overreaction to news, primacy effect, endogenous reference dependence, optimism, pessimism

History-Dependent Risk Attitude

We propose a model of history-dependent risk attitude, allowing a decision maker’s risk attitude to be affected by his history of disappointments and elations. The decision maker recursively evaluates compound risks, classifying realizations as disappointing or elating using a threshold rule. We establish equivalence between the model and two cognitive biases: risk attitudes are reinforced by experiences (one is more risk averse after disappointment than after elation) and there is a primacy effect (early outcomes have the greatest impact on risk attitude). In dynamic asset pricing, the model yields volatile, path-dependent prices.History-dependent risk attitude, Reinforcement effect, Primacy effect, Dynamic reference dependence

Rationalizing Choice with Multi-Self Models

This paper studies a class of multi-self decision-making models proposed in economics, psychology, and marketing. In this class, choices arise from the set-dependent aggregation of a collection of utility functions, where the aggregation procedure satisfies some simple properties. We propose a method for characterizing the extent of irrationality in a choice behavior, and use this measure to provide a lower bound on the set of choice behaviors that can be rationalized with n utility functions. Under an additional assumption (scale-invariance), we show that generically at most five "reasons" are needed for every "mistake."Multi-self models, Index of irrationality, IIA violations, Rationalizability

Foundations of Intrinsic Habit Formation

We provide theoretical foundations for several common (nested) representations of intrinsic linear habit formation. These representations are dynamically consistent and additive, with geometrically decaying coefficients of habit formation. Our axiomatization introduces a revealed preference theory of weaning a decision-maker from her habits using the device of compensation. We characterize linear habit formation in terms of the ability to wean using uniquely determined compensating streams. Moreover, we distinguish between habits that are responsive to weaning and those that are persistent, develop a simple choice-theoretic measure of the rate of habit decay, and demonstrate how to recover the entire sequence of habit formation coefficients from observed choice behavior. We introduce novel monotonicity and separability axioms that are appropriate for time-nonseparable preferences. Our analysis suggests techniques for eliciting dynamic reference points from choice behavior and obtaining discounted utility representations on endogenously generated auxiliary spaces