Updating Ambiguity Averse Preferences

Dynamic consistency leads to Bayesian updating under expected utility. We ask what it implies for the updating of more general preferences. In this paper, we charac- terize dynamically consistent update rules for preference models satisfying ambiguity aversion. This characterization extends to regret-based models as well. As an appli- cation of our general result, we characterize dynamically consistent updating for two important models of ambiguity averse preferences: the ambiguity averse smooth am- biguity preferences (Klibanoff, Marinacci and Mukerji [Econometrica 73 2005, pp. 1849-1892]) and the variational preferences (Maccheroni, Marinacci and Rustichini [Econometrica 74 2006, pp. 1447-1498]). The latter includes max-min expected utility (Gilboa and Schmeidler [Journal of Mathematical Economics 18 1989, pp. 141-153]) and the multiplier preferences of Hansen and Sargent [American Economic Review 91(2) 2001, pp. 60-66] as special cases. For smooth ambiguity preferences, we also identify a simple rule that is shown to be the unique dynamically consistent rule among a large class of rules that may be expressed as reweightings of Bayes's rule.Updating, Dynamic Consistency, Ambiguity, Regret, Ellsberg, Bayesian, Consequentialism, Smooth Ambiguity

Evolution as Learning Yields Hyperbolic Discounting

Learning is modeled as an infection, which jumps from person to person. The rate of infection mimics individual discount rates and induces savings behavior on its own. It is shown that the apparent discount rate, the combination of the agents' true discount rate and the infection rate, decreases over time and approaches the agents' true discount rate. This decrease, known as hyperbolic discounting, is consistent with what is observed in psychology studies, while the limiting case, exponential discounting, is consistent with market level observations. This model closes the gap between individual and market level observations of discounting behavior without explicitly assuming the two kinds of discounting nor relying on commitment mechanisms.discounting, genetic algorithms, learning

Markov Equilibrium in Models of Dynamic Endogenous Political Institutions

This paper examines existence of Markov equilibria in the class of dynamic political games (DPGs). DPGs are dynamic games in which political institutions are endogenously determined each period. The process of change is both recursive and instrumental: the rules for political aggregation at date t+1 are decided by the rules at date t, and the resulting institutional choices do not affect payoffs or technology directly. Equilibrium existence in dynamic political games requires a resolution to a “political fixed point problem” in which a current political rule (e.g., majority voting) admits a solution only if all feasible political rules in the future admit solutions in all states. If the class of political rules is dynamically consistent, then DPGs are shown to admit political fixed points. This result is used to prove two equilibrium existence theorems, one of which implies that equilibrium strategies, public and private, are smooth functions of the economic state. We discuss practical applications that require existence of smooth equilibria.Recursive, dynamic political games, political fixed points, dynamically consistent rules.

The Dynamic Reform of Political Institutions

This paper formulates a model of dynamic, endogenous reform of political institutions. Specifically, a class of dynamic political games (DPGs) is introduced in which institutional choice is both recursive and instrumental. It is recursive because future political institutions are decided under current ones. The process is instrumental because institutional choices do not affect payoffs or technology directly. DPGs provide a broad framework to address the question: which environments exhibit institutional reform? Which tend toward institutional stability? In any state, private (public) sector decisions are essential if, roughly, they cannot always be replaced by decisions in the public (private) sector. We prove that institutional reform occurs if public sector decisions are not essential. Conversely, private sector decisions are essential if institutional reform occurs. The results suggest that a relatively more effective public sector is conducive to institutional stability, while a more effective private sector is conducive to change. We also show that if the political rules satisfy a dynamic consistency property, then the game admits ``political fixed points" of a recursive map from future (state-contingent) decisions rules to current ones. Since existence of political fixed points is a necessary condition of equilibrium, we apply the result to prove two equilibrium existence theorems, one of which implies that private and public sector decision rules that are smooth functions of the economic state.institutional reform, recursive, instrumental, dynamic political games, political fixed points.