13

I strongly suspect that an emerging important area for applications of measure theory will be in approximate dynamic programming techniques. Approximate dynamic programming (aka "reinforcement learning" in the computer science literature) has been the direction of research work in the last ~10-20 years of the dynamic programming literature. Economics is only ...


8

This was too long for comment. "Post 1960" seems an arbitrary and very high bar for an applied field, including micro theory. Most of the topics you name would not be considered contemporary mathematics. For example, measure theory started with Lebesgue's thesis and is over a century old. Topology is even older and started with Poincare, who introduced ...


5

Measure theory is widely used in the problem of fair division (aka "cake-cutting"). See the many papers about fairness in economics journals. For a particular example, see Tatsuro Ichiishi and Adam Idzik, "Equitable allocation of divisible goods", JME 1999.


5

Loeb spaces have been used to model situations with a continuum of agents. See http://eml.berkeley.edu/~anderson/Book.pdf and the chapters by Sun on economic applications in the book Nonstandard Analysis for the Working Mathematician.


5

The term bounded rationality was introduced by Herbert Simon. He wrote "The term, bounded rationality, is used to designate rational choice that takes into account the cognitive limitations of both knowledge and cognitive capacity. Bounded rationality is a central theme in behavioral economics. It is concerned with the ways in which the actual ...


5

I think you're referring to the decoy effect. A popular example of this is the Economist subscription puzzle, popularized in Dan Ariely's TED Talk (starting at 12:22).


4

Perhaps there is some evidence toward your claim, but I would argue that in most situations, people do not use point estimates (although some "smoothing" likely occurs). In particular, there is no doubt that people care about the second movement (variance). The commonly employed, and robustly empirically documented, notion of risk aversion captures exactly ...


4

One recent paper that is being positioned as a very wide-ranging theory of bounded rationality (although certainly it doesn't come close to capturing every insight in the field) is Gabaix's forthcoming QJE, A Sparsity-Based Model of Bounded Rationality. Gabaix formulates a fairly general model where agents can rationally decide to pay limited attention to ...


3

Empirical Evidence on rational inattention: -Title: Attention Discrimination: Theory and Field Experiments with Monitoring Information Acquisition, Authors: Vojtěch Bartoš, Michal Bauer, Julie Chytilová, and Filip Matějka. Source: IZA Discussion Paper No. 8058. Link: Attention Discrimination: Theory and Field Experiments with Monitoring Information ...


2

The following two papers by Andrew Caplin and Mark Dean focus on tests of rational inattention in a lab setting (i.e. with data one could in principle find the field). As BB King said, I won't do it any justice summarizing myself. The second is about Shannon entropy specifically. http://www.econ.brown.edu/fac/Mark_Dean/Pub_Paper_8.pdf http://www.econ.brown....


2

A few quotes from Jessie and Saari (2015) may be of interest. Regarding Luce Choice Axiom (LCA): The effect of LCA is to endow each alternative with an intrinsic level of likelihood that is independent of the particular set from which it is chosen. Mathematically speaking, in Luce’s formulation, the choice axiom implies the existence of a weight ...


2

I'm not sure what capacity allocation games you're applying QRE to. But here's a very stylized example where QRE is applied to an asymmetric game where the strategy spaces of the two players are (nominally) different: \begin{array}{c|cc} &L&R\\\hline T&1,0&0,9\\ D&0,1&1,0 \end{array} This game can be easily represented in the ...


2

I would recommend reading Thaler's Misbehaving, which chronicles the development of behavioral economics as a field and its struggle to gain recognition by mainstream economists. Several of its chapters (particularly, 6, 17-20) would directly answer your question regarding the historical context and partly the "why". I share my own personal view below. I ...


2

Although I still don't understand what these "strengths" are all about, still, mechanically, step $4)$ is now clear. At each point in time, there is a certain allocation of Strengths to actions, $\{S_i(t),\; i=1,2,...,A\}$. This allocation changes through time. The allocation is turned into a relative frequency distribution by dividing each $S_i(t)$ by ...


2

I don't feel these two interpretations are mutually exclusive, they belong to different sides of the same problem - one is empirical the other is theoretical. The conflict you seem to see between these two methods is that the "population" interpretation is individual specific. But the population component is a statistical convenience. It is "everything else" ...


2

This is due to the famous Lucas critique. To make long story short, in the past in the heyday of Keynesian macroeconomics it was quite normal for macroeconomists to just postulate some relationships based on relatively casual empirical observations like for example the Philips curve which says that there is positive relationship between inflation and ...


2

This is not a formal definition, but a useful piece of intuition. I think that the best way to think about it is that when there is uncertainty in a model it arises mainly in two forms either there is information that some agents have, but not every agent has it (private information), or there are truly random events that no one knows (in game theory jargon,...


1

These are many questions. O.k., so let's go step by step: (Q1) What is a mapping actually? A map is just another term for a function. Here, every "law of motion", the actual one (ALM) and the perceived one (PLM), is characterized by its parameters $a$ and $b$. The ALM depends on the PLM, and the function mapping the PLM-parameters to the ALM-parameters is ...


1

What is meant by fixed point reasoning here? Specifically, Nash equilibria. One way to define a Nash equilibrium in words is "a strategy profile from which no player can be made better-off by unilaterally deviating to a different action". In other words, a Nash equilibrium is a "fixed point" because if the game ends up there, play stops because there are ...


1

Very interesting question. To answer the direct question in the title, I'd say I'd have to break the sunk cost fallacy into two arenas. In the first I'd say it is a feature not a bug, but in the second, vice versa. As a means to keep a business from dying before it's been given opportunity to profit. I think that the sunk cost fallacy is still a double ...


1

I think there is a missing concept in your question. If you are discussing simple gambles and not things like the stock market, then the distributions that are involved usually have sufficient statistics. A statistic is sufficient for a parameter if the point estimate could be substituted for the data itself with no loss in information. A statistic, $t$, ...


1

Beside the work of Chichilnisky mentioned by Michael, another interesting use of topology in social choice theory appears in the work of Redekop on Arrow's theorem on economic domains. Redekop, J. (1991). Social welfare functions on restricted economic domains. Journal of Economic Theory, 53, 396–427. Redekop, J. (1993a). Arrow-inconsistent economic domains....


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