Essays on individual choice

Abstract

This thesis can be divided into two (unrelated) parts. The main part (Chapters 1 and 2) focus on addiction models that entail departures from the classical discounting utility model of Individual Intertemporal Choice: Habit-Formation and Self-Control problems. The other part (Chapter 3) studies the famous p-Beauty Contest Game when we restrict the individual’s choices to integer numbers. In the first part, habit formation is the key feature for a product being addictive: a habit is created when past consumption of the product increases current desire for consumption. An addiction can be either beneficial (when past consumption increases current utility, e.g. jogging) or harmful (when past consumption decreases current utility, e.g. drug consumption). In general one could conceive of harmful addictions as habit-forming activities that imply an immediate reward but generate future costs (negative internalities) whereas beneficial addictions imply an immediate cost but generate future rewards (positive internalities). Self-control problems are understood in terms of time inconsistency: they arise when the individual cannot keep up with an intended intertemporal plan of consumption. In Chapter 1 we analyse a (harmful) addiction model proposed by O'Donoghue and Rabin (O&R) for which they obtain a counterintuitive result: full awareness of selfcontrol problems may exacerbate over-consumption. We show that this result arises from their particular equilibrium selection for the induced intrapersonal game. We provide dominating Markov Perfect equilibria where the paradox vanishes and that seem more ''natural'' since they capture behaviours often observed in the realm of addiction. We also address the issue of why a person could decide to start consuming and possibly develop an addiction: contrary to O&R, and according to the common intuition, we show that naiveté is at the essence. In Chapter 2 we obtain an isomorphism between harmful and beneficial addictions in a discrete-time binary choice context (the model of the first chapter being a particular case of this context). The equivalence thus established allows us to study both phenomena (harmful and beneficial addictions) as two sides of the same coin. Besides the theoretical insight it provides, this dualism is also useful: in particular, it permits to readily translate the results obtained in the first chapter to the domain of beneficial addictions. Once the dualism is established, we analyse addictions under both timeconsistent and time-inconsistent preferences. In Chapter 3, we provide a full characterization of the pure-strategy Nash Equilibria for the p-Beauty Contest Game when we restrict individual's choices to integer numbers. Opposed to the case of real number choices, equilibrium uniqueness may be lost depending on the value of p and the number of players: in particular, as p approaches 1 any symmetric profile constitutes a Nash Equilibrium. We also show that any experimental p-Beauty Contest Game can be associated to a game with the integer restriction and thus multiplicity of equilibria becomes an issue. Finally, we show that in these games the iterated deletion of weakly dominated strategies may not lead to a single outcome while the iterated best-reply process always does (though the outcome obtained depends on the initial conditions).