By Alexander Zimper, Working Paper 58
Aumann (1976) derives his famous we cannot agree to disagree result under the assumption of rational Bayesian learning. Motivated by psychological evidence against this assumption, we develop formal models of optimistically, resp. pessimistically, biased Bayesian learning within the framework of Choquet expected utility theory.
As a key feature of our approach the posterior subjective beliefs do, in general, not converge to “true” probabilities. Moreover, the posteriors of different people can converge to different beliefs even if these people receive the same information. As our main contribution we show that people may well agree to disagree if their Bayesian learning is psychologically biased in our sense. Remarkably, this finding holds regardless of whether people with identical priors apply the same psychologically biased Bayesian learning rule or not.
A simple example about the possibility of ex-post trading in a financial asset illustrates our formal findings. Finally, our analysis settles a discussion in the no-trade literature (cf. Dow, Madrigal, and Werlang 1990, Halevy 1998) in that it clarifies that ex-post trade between agents with common priors and identical learning rules is only possible under asymmetric information.
Alessio D'Ignazio and Emanuele Giovannetti, Working Paper 102
Is the quality of interconnection between Internet operators affected by their asymmetry? While recent game theoretic literature provides contrasting answers to this question, there is a lack of empirical research.
We introduce a novel dataset based on Internet routing policies, and study the interconnection decisions amongst the Internet Service Providers (ISPs) members of the London Internet Exchange Point (LINX).
Our results show that interconnection quality degradation can be significantly explained by asymmetry between providers. We also show that Competition Authorities should focus more on the role played by the “centrality of an operator”, rather than on its market share.
Sonali Das and Sourish Das, Working Paper 103
We consider the problem of statistical inference of binomial proportions for non-matched, correlated samples, under the Bayesian framework. Such inference can arise when the same group is observed a different number of times on two or more inference occasions, with the aim of testing the proportion of some trait. These scenarios can occur when we are interested to infer the proportion of extreme wave height per year, at a certain measuring station, where measurements are made every hour.
Gaps in measurements, either due to a malfunction of the measuring instrument or another reason, can result in an unequal number of observations in different years. For such scenarios, we develop an adaptive Bayesian method, and suggest a heuristic decision procedure to conduct statistical inference. We use the ΓΈ-divergence measure to quantify the perturbation of the posterior distribution of the proportion in different time points.
We present a simulation study for frequentist power investigation for both the adaptive Bayesian method, as well as the regular frequentist method, using the Monte Carlo technique. Based on the simulation study of frequentist power, as well as theoretical proof, under certain design, the adaptive Bayesian method is shown to outperform the regular frequentist method.
We administer the developed adaptive Bayesian method to two case studies when the total number of observation instances of the same group are unequal, at different time points of interest.
On attitude polarization under Bayesian learning with non-additive beliefs Alexander Zimper and Alexander Ludwig, Working Paper 104
Ample psychological evidence suggests that people’s learning behavior is often prone to a "myside bias" or "irrational belief persistence" in contrast to learning behavior exclusively based on objective data. In the context of Bayesian learning such a bias may result in diverging posterior beliefs and attitude polarization even if agents receive identical information.
Such patterns cannot be explained by the standard model of rational Bayesian learning that implies convergent beliefs. As our key contribution, we therefore develop formal models of Bayesian learning with psychological bias as alternatives to rational Bayesian learning. We derive conditions under which beliefs may diverge in the learning process despite the fact that all agents observe the same - arbitrarily large - sample, which is drawn from an "objective" i.i.d. process. Furthermore, one of our learning scenarios results in attitude polarization even in the case of common priors.
Key to our approach is the assumption of ambiguous beliefs that are formalized as non-additive probability measures arising in Choquet expected utility theory. As a specific feature of our approach, our models of Bayesian learning with psychological bias reduce to rational Bayesian learning in the absence of ambiguity
Loss leader or low margin leader? Advertising and the degree of product differentiation Witness Simbanegavi, Working Paper 105
This paper attempts to isolate the conditions that give rise to loss leader pricing.
I show that for sufficiently low distance between firms, the advertised good is priced below cost irrespective of whether firms advertise the same or different products. Instead, if products are sufficiently differentiated, loss leader pricing may result only if firms advertise the low reservation value product, otherwise the advertised good is a low margin leader. Thus, whether the advertised good is a loss leader or a low margin leader is primarily a function of the extent of differentiation between competing firms.
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