Sequential Two-Player Games with Ambiguity

If players' beliefs are strictly non-additive, the Dempster-Shafer updating rule can be used to define beliefs off the equilibrium path. We define an equilibrium concept in sequential two-person games where players update their beliefs with the Dempster-Shafer updating rule. We show that in the limit as uncertainty tends to zero, our equilibrium approximates Bayesian Nash equilibrium by imposing context-dependent constraints on beliefs under uncertainty.

Sequential two-player games with ambiguity

If players' beliefs are strictly non-additive, the Dempster-Shafer updating rule can be used to define beliefs off the equilibrium path. We define an equilibrium concept in sequential two-person games where players update their beliefs with the Dempster-Shafer updating rule. We show that in the limit as uncertainty tends to zero, our equilibrium approximates Bayesian Nash equilibrium by imposing context-dependent constraints on beliefs under uncertainty

Learning and Disagreement in an Uncertain World

Most economic analyses presume that there are limited differences in the prior beliefs of individuals, as assumption most often justified by the argument that sufficient common experiences and observations will eliminate disagreements. We investigate this claim using a simple model of Bayesian learning. Two individuals with different priors observe the same infinite sequence of signals about some underlying parameter. Existing results in the literature establish that when individuals are certain about the interpretation of signals, under very mild conditions there will be asymptotic agreement---their assessments will eventually agree. In contrast, we look at an environment in which individuals are uncertain about the interpretation of signals, meaning that they have non-degenerate probability distributions over the conditional distribution of signals given the underlying parameter. When priors on the parameter and the conditional distribution of signals have full support, we prove the following results: (1) Individuals will never agree, even after observing the same infinite sequence of signals. (2) Before observing the signals, they believe with probability 1 that their posteriors about the underlying parameter will fail to converge. (3) Observing the same sequence of signals may lead to a divergence of opinion rather than the typically presumed convergence. We then characterize the conditions for asymptotic agreement under "approximate certainty"---i.e., as we look at the limit where uncertainty about the interpretation of the signals disappears. When the family of probability distributions of signals given the parameter has "rapidly-varying tails" (such as the normal or exponential distributions), approximate certainty restores asymptotic agreement. However, when the family of probability distributions has "regularly-varying tails" (such as the Pareto, the log-normal, and the t-distributions), asymptotic agreement does not obtain even in the limit as the amount of uncertainty disappears. Lack of common priors has important implications for economic behavior in a range of circumstances. We illustrate how the type of learning outlined in this paper interacts with economic behavior in various different situations, including games of common interest, coordination, asset trading and bargaining.

Learning and Disagreement in an Uncertain World

Most economic analyses presume that there are limited differences in the prior beliefs of individuals, an assumption most often justified by the argument that sufficient common experiences and observations will eliminate disagreements. We investigate this claim using a simple model of Bayesian learning. Two individuals with di.erent priors observe the same infinite sequence of signals about some underlying parameter. Existing results in the liter- ature establish that when individuals know the interpretation of signals, under very mild conditions, there will be asymptotic agreementtheir assessments will eventually agree. In contrast, we look at an environment in which individuals are uncertain about the inter- pretation of signals, meaning that they have non-degenerate probability distributions over the conditional distribution of signals given the underlying parameter. When priors on the parameter and the conditional distribution of signals have full support, we show the following: (1) Individuals will never agree, even after observing the same infinite sequence of signals. (2) Before observing the signals, they believe with probability 1 that their posteri- ors about the underlying parameter will fail to converge. (3) Observing the same (infinite) sequence of signals may lead to a divergence of opinion rather than the typically-presumed convergence. We then characterize the conditions for asymptotic agreement under “approx- imate certainty”–i.e., as we look at the limit where uncertainty about the interpretation of the signals disappears. When the family of probability distributions of signals given the parameter has rapidly-varying tails (such as the normal or the exponential distributions), approximate certainty restores asymptotic agreement. However, when the family of proba- bility distributions has regularly-varying tails (such as the Pareto, the log-normal, and the t-distributions), asymptotic agreement does not obtain even in the limit as the amount of uncertainty disappears. We also discuss how lack of common priors implied by the type of learning in this paper interacts with economic behavior in various different situations, including games of common interest, coordination, asset trading and bargaining.asymptotic disagreement, Bayesian learning, merging of opinions.

A Bayesian decision-theoretic framework for studying motivated reasoning

Psychological, political, cultural, and sociological factors shape how people form and revise their beliefs. An established finding across these fields is that people are motivated to hold onto their beliefs even in the face of evidence by ignoring or reinterpreting information in a way that supports what they think. Although these and similar findings are compelling, the predominantly qualitative theories which guide research in this domain, and the often implicit definitions of motivation that accompany these theories, come at the cost of obscuring the cognitive mechanisms that produce motivated reasoning. Here, we introduce a new Bayesian decision-theoretic framework which describes three key factors necessary for distinguishing between cases of practically rational behavior and motivated reasoning. We demonstrate how the framework works in a series of simulations and argue that it provides guidance about what psychologists need to measure to determine where the errors in people's reasoning are occurring when they fail to revise their beliefs in light of new evidence. We then propose that this framework provides guidance for thinking about the development of interventions aimed at correcting misconceptions.<br/

Making Sense of Unexpected Preferences

This dissertation includes three papers using quantitative models to sensibly describe what kinds of preferences political actors will or actually do hold when existing theory offers no insight. The first two papers use evolutionary game theory to predict ways in which politicians, artificially selected on the basis of good performance to remain in office, will in the long run diverge from instrumental rationality as ordinarily assumed in game theory. The first sets out a general principle for producing models of preference evolution in games as political models, namely, that the information about opponent preferences necessary for evolution of non-rational preferences comes from opponents\u27 previous plays, and applies it to two simple games. The second uses the same principles in more detail on a bargaining game that models the plea negotiations between a prosecutor and a defense attorney, leading to a conclusion that failure to learn from setbacks during a trial is an evolutionarily favored trait among prosecutors. The third paper addresses the ideological preferences of Supreme Court justices, which existing statistical models do not effectively compare to those of elected officials since the two groups never vote on the same items, by identifying a set of political actors with whom both groups commonly interact: organized interest groups who vote on Supreme Court cases with amicus curiae briefs and on electoral candidates using campaign donations

On-the-Job Signaling and Self-Confidence

The labour economics literature on signalling assumes workers know their own abilities. Well-settled experimental evidence contradicts that assumption: in the absence of hard facts, subjects are on average overconfident. First we show that in any equilibrium of any signalling model, overconfidence cannot make players better off. In order to obtain more detailed predictions, we then introduce a specific on-the-job signalling model. We show that at fully-separating equilibrium, overconfident workers choose tasks that are too onerous, fail them, and, dejected by such a failure, settle down for a position inferior to their potential. Such a pattern leads to permanent underemployment of workers, and inefficiency of the economy. For the case of unbiased workers uncertain about their own value, we determine a necessary and sufficient condition for the existence of fully-separating equilibrium.

In Honor of Matthew Rabin: Winner of the John Bates Clark Medal

Although there is some evidence that Matthew Rabin existed before 1990, we had the pleasure of discovering him for ourselves when, in the early 1990s, he sent each of us a copy of his manuscript "Incorporating Fairness into Game Theory and Economics" [2]. Matthew was, at this time, an assistant professor in Berkeley's economics department, having recently finished his graduate training at MIT. The paper was remarkable in many ways, and it induced us both to call around and ask: "Who is this guy Rabin?" Now, just a decade later, we find ourselves writing an article in honor of his winning the John Bates Clark award. So, who is this guy

Ambiguity and Social Interaction

We examine the impact of ambiguity on economic behaviour. We present a relatively non-technical account of ambiguity and show how it may be applied in economics. Optimistic and pessimistic responses to ambiguity are formally modelled. We show that pessimism has the effect of increasing (decreasing) equilibrium prices under Cournot (Bertrand) competition. We also examine the effects of ambiguity on peace processes. It is shown that ambiguity can act to select equilibria in coordination games with multiple equilibria. Some comparative statics results are derived for the impact of ambiguity in games with strategic complements.