# Browsing by Author "Sadowski, P"

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Item Open Access A Strategic Model of Magical Thinking: Axioms and Analysis(Economic Research Initiatives at Duke (ERID) Working Paper, 2014-09-26) Sadowski, P; Daley, BThis paper seeks to make two contributions. First, we propose and analyze a tractable model of strategic play in which players behave as if their expectations about their opponents' behavior vary with their own choices. We refer to this nonstandard updating as magical thinking. The model provides a unified view of documented behavior in a range of often-studied games, such as the Prisoners' Dilemma, the Battle of the Sexes, Hawk-Dove, and the Stag Hunt. Second, we provide axioms applied to the behavior of the collection of players in symmetric 2x2 games, and a representation theorem that establishes these axioms to be the precise behavioral content of the model. We thereby suggest a novel way to import the axiomatic methodology of individual decision theory to strategic settings and demonstrate the benefits of this approach. In the model, the degree to which players exhibit magical thinking is heterogeneous in the population and is captured by players' types. All players perceive types to be i.i.d. draws from a common distribution. We show that the model's parameters, namely these individual types and the commonly perceived distribution, can be (essentially) identified from behavior in games, allowing for tractable comparative statics. Finally, the model generates novel predictions across games. For example, the ability of a collection of players to coordinate on Pareto superior Nash equilibria in coordination games is positively correlated with their degree of cooperation in Prisoners' Dilemma games. The supplement for this paper are available at the following URL: http://ssrn.com/abstract=2507394Item Open Access A Theory of Subjective Learning(Economic Research Initiatives at Duke (ERID), 2012-08-31) Dillenberger, D; Lleras, J; Sadowski, P; Takeoka, NWe study an individual who faces a dynamic decision problem in which the process of information arrival is unobserved by the analyst. We derive two utility representations of preferences over menus of acts that capture the individual’s uncertainty about his future beliefs. The most general representation identifies a unique probability distribution over the set of posteriors that the decision maker might face at the time of choosing from the menu. We use this representation to characterize a notion of “more preference for flexibility” via a subjective analogue of Blackwell’s (1951, 1953) comparisons of experiments. A more specialized representation uniquely identifies information as a partition of the state space. This result allows us to compare individuals who expect to learn differently, even if they do not agree on their prior beliefs. We conclude by extending the basic model to accommodate an individual who expects to learn gradually over time by means of a subjective filtration.Item Metadata only A theory of subjective learning(Journal of Economic Theory, 2014-01-01) Dillenberger, D; Lleras, JS; Sadowski, P; Takeoka, NWe study an individual who faces a dynamic decision problem in which the process of information arrival is unobserved by the analyst. We elicit subjective information directly from choice behavior by deriving two utility representations of preferences over menus of acts. One representation uniquely identifies information as a probability measure over posteriors and the other identifies information as a partition of the state space. We compare individuals who expect to learn differently in terms of their preference for flexibility. On the extended domain of dated-menus, we show how to accommodate gradual learning over time by means of a subjective filtration. © 2014 Elsevier Inc.Item Open Access Dynamic preference for flexibility(Econometrica, 2014-01-01) Sadowski, P; Krishna, RWe consider a decision maker who faces dynamic decision situations that involve intertemporal trade-offs, as in consumption-savings problems, and who experiences taste shocks that are transient contingent on the state of the world. We axiomatize a recursive representation of choice over state contingent infinite horizon consumption problems, where uncertainty about consumption utilities depends on the observable state and the state follows a subjective Markov process. The parameters of the representation are the subjective process that governs the evolution of beliefs over consumption utilities and the discount factor; they are uniquely identified from behavior. We characterize a natural notion of greater preference for flexibility in terms of a dilation of beliefs. An important special case of our representation is a recursive version of the Anscombe-Aumann model with parameters that include a subjective Markov process over states and state-dependent utilities, all of which are uniquely identified. © 2014 The Econometric Society.Item Open Access Foundations for Cooperation in the Prisoners’ Dilemma(Economic Research Initiatives at Duke (ERID) Working Paper, 2014-05-07) Daley, B; Sadowski, PWe provide axiomatic foundations for a simple model of play in prisoners' dilemma games. The model accommodates cooperation and suggests that players behave as if their expectations about their opponents' behavior vary with their own choice. We refer to this nonstandard updating as magical thinking. The degree to which players exhibit magical thinking may be heterogeneous in the population and is captured by a uniquely identifi ed parameter for each player. Further, it is as if all players perceive these parameters to be i.i.d. draws from a common distribution. The model's identi fication allows for tractable comparative statics. We investigate how our theory extends to all symmetric 2x2 games. The Supplement for this paper are available at the following URL: http://ssrn.com/abstract=2331585Item Open Access Inertial Behavior and Generalized Partition(Economic Research Initiatives at Duke (ERID), 2016-05-01) Dillenberger, D; Sadowski, PWe call behavior inertial if it does not react to the apparent arrival of relevant information. In a context where the precise information content of signals is subjective, we formulate an axiom that captures inertial behavior, and provide a representation that explains such behavior as that of a rational decision maker who perceives a particular type of information structure, which we call a generalized partition. We characterize the learning processes that can be described by a generalized partition. We proceed to assume that there is a true underlying information structure that may not be a generalized partition, and investigate different channels that may lead the decision maker to nonetheless perceive a generalized partition (and thus to display inertial behavior): A cognitive bias referred to as cognitive inertia and a bound on rationality which we term shortsightedness.Item Open Access Preferences with Taste Shock Representations: Price Volatility and the Liquidity Premium(Economic Research Initiatives at Duke (ERID), 2016-06-09) Sadowski, PIf price volatility is caused in some part by taste shocks, then it should be positively correlated with the liquidity premium. Our argument is based on Krishna and Sadowski (2014), who provide foundations for a representation of dynamic choice with taste shocks, and show that volatility in tastes corresponds to a desire to maintain flexibility. To formally connect volatile tastes to price volatility and preference for flexibility to the liquidity premium, we analyze a modified simple Lucas tree economy, where the representative agent is uncertain about his degree of future risk aversion, and where the productive asset cannot be traded in every period, while rights to output can. We show that a representative agent with a higher degree of uncertainty about his future risk aversion implies a higher liquidity premium (i.e., a lower price for the illiquid asset) and more price volatility.Item Open Access Randomly Evolving Tastes and Delayed Commitment(Economic Research Initiatives at Duke (ERID), 2016-06-09) Krishna, R; Sadowski, PWe consider a decision maker with randomly evolving tastes who faces dynamic decision situations that involve intertemporal tradeoffs, such as those in consumption savings problems. We axiomatize a recursive representation of choice that features uncertain consumption utilities, which evolve according to a subjective Markov process. The parameters of the representation, which are the subjective Markov process governing the evolution of utilities, and the discount factor, are uniquely identified from behavior. We relate the correlation of tastes over time and the desire to delay commitment to future consumption.Item Open Access Subjective Dynamic Information Constraints(Economic Research Initiatives at Duke (ERID), 2016-04-03) Dillenberger, D; Krishna, R; Sadowski, PWe axiomatize a new class of recursive dynamic models that capture subjective constraints on the amount of information a decision maker can obtain, pay attention to, or absorb, via a Markov Decision Process for Information Choice (MIC). An MIC is a subjective decision process that specifies what type of information about the payoff-relevant state is feasible in the current period, and how the choice of what to learn now affects what can be learned in the future. The constraint imposed by the MIC is identified from choice behavior up to a recursive extension of Blackwell dominance. All the other parameters of the model, namely the anticipated evolution of the payoff-relevant state, state dependent consumption utilities, and the discount factor are also uniquely identified.Item Open Access Supplement to 'Subjective Dynamic Information Constraints'(Economic Research Initiatives at Duke (ERID), 2016-04-01) Dillenberger, D; Krishna, R; Sadowski, PSupplement to "Subjective Dynamic Information Constraints" (http://ssrn.com/abstract=2774300). All references to definitions and results in this Supplement refer to Dillenberger, Krishna, and Sadowski (2016, henceforth DKS) unless otherwise specified. This supplement is organized as follows. Section 1 establishes the Abstract Static Representation that is the starting point for our derivations in Appendix C of DKS. Section 2 reviews relevant notions from convex analysis. Section 3 provides a preference independent notion of minimality on the space of rics, which is referred to in Section 6 of DKS. Section 4 provides a metric on the space of partitions as referred to in Appendix A.3 of DKS. Section 5 extends the existence of the RAA representation, which is established in Krishna and Sadowski (2014) for finite prize spaces, to our domain with a compact set of prizes, as discussed in Appendix A.7 of DKS. Finally, Section 6 provides a detailed proof of the partitional representation introduced in Appendix C.1 of DKS.Item Open Access Supplement to a Strategic Model of Magical Thinking: Axioms and Analysis(Economic Research Initiatives at Duke (ERID) Working Paper, 2014-09-26) Sadowski, P; Daley, BWe establish that in the Prisoners' Dilemma, the model of Daley and Sadowski (2014) is logically distinct from three models that employ well-known forms of other-regarding preferences: altruism (Ledyard, 1995; Levine, 1998), inequity aversion (Fehr and Schmidt, 1999), and reciprocity (Rabin, 1993). The paper "A Strategic Model of Magical Thinking: Axioms and Analysis" to which this supplement applies is available at the following URL: http://ssrn.com/abstract=2507377Item Open Access Supplement to: 'Foundations for Cooperation in the Prisoners’ Dilemma'(Economic Research Initiatives at Duke (ERID) Working Paper, 2014-05-07) Daley, B; Sadowski, PWe establish that in the Prisoners’ Dilemma, the model of Daley and Sadowski (2014) is logically distinct from three models that employ well-known forms of other regarding preferences: altruism (Ledyard, 1995; Levine, 1998), inequity aversion (Fehr and Schmidt, 1999), and reciprocity (Rabin, 1993). The paper "Foundations for Cooperation in the Prisoners’ Dilemma" to which this Supplement applies is available at the following URL: http://ssrn.com/abstract=2331579