A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.
(.pdf download) Subjectivity and correlation, though formally related, are conceptually distinct and independent issues. We start by discussing subjectivity. A mixed strategy in a game involves the selection of a pure strategy by means of a random device. It has usually been assumed that the random device is a coin flip, the spin of a roulette wheel, or something similar; in brief, an ‘objective’ device, one for which everybody agrees on the numerical values of the probabilities involved. Rather oddly, in spite of the long history of the theory of subjective probability, nobody seems to have examined the consequences of basing mixed strategies on ‘subjective’ random devices, i.e. devices on the probabilities of whose outcomes people may disagree (such as horse races, elections, etc.).
For a constant ϵ, we prove a poly(N) lower bound on the (randomized) communication complexity of ϵ-Nash equilibrium in two-player NxN games. For n-player binary-action games we prove an exp(n) lower bound for the (randomized) communication complexity of (ϵ,ϵ)-weak approximate Nash equilibrium, which is a profile of mixed actions such that at least (1−ϵ)-fraction of the players are ϵ-best replying.
John Nash’s notion of equilibrium is ubiquitous in economic theory, but a new study shows that it is often impossible to reach efficiently.
There’s a couple of interesting sounding papers in here that I want to dig up and read. There are some great results that sound like they are crying out for better generalization and classification. Perhaps some overlap with information theory and complexity?
To some extent I also find myself wondering about repeated play as a possible random walk versus larger “jumps” in potential game play and the effects this may have on the “evolution” of a solution by play instead of a simpler closed mathematical solution.
For-profit dialysis companies often maximize their profits at the expense of their patients. John Oliver explores why a medical clinic is nothing like a Taco Bell.
The lack of humanity showed by these corporations is simply horrific. Certainly a market failure which is causing some painful externalities. We need something more significant to fix the inequities that are happening here.
Chapter 2 is a nice piece on the El Farol Problem which is a paradox which “represented a decision problem where expectations (forecasts) that many would attend [the El Farol bar] would lead to few attending, and expectations that few would attend would lead to many attending: expectations would lead to outcomes that would negate these expectations.”
Zhang and Challet generalized this problem into the Minority Game in game theoretic form.
There are two reasons for perfect or deductive rationality to break down under complication. The obvious one is that beyond a certain level of of complexity human logical capacity ceases to cope–human rationality is bounded. The other is that in interactive situations of complication, agents cannot rely upon the other agents they are dealing with to behave under perfect rationality, and so they are forced to guess their behavior. This lands them in a world of subjective beliefs and subjective beliefs about subjective beliefs. Objective, well-defined, shared assumptions then cease to apply. In turn, rational, deductive reasoning (deriving a conclusion by perfect logical processes from well-defined premises) itself cannot apply. The problem becomes ill-defined.
This passage, though in an economics text, seems to be a perfect statement about part of the problem of governing in the United States at the moment. I have a thesis that Donald Trump is a system 1 thinker and is generally incapable of system 2 level thought, thus he has no ability to discern the overall complexity of the situations in which he finds himself (or in which the United States finds itself). As a result, he’s unable to effectively lead. From a complexity and game theoretic standpoint, he feels he’s able to perfectly play and win any game. His problem is that he feels like he’s playing tic-tac-toe, while many see at least a game as complex as checkers. In reality, he’s playing a game far more complex than either chess or go.
The overall problem laid out in this chapter is an interesting one vis-a-vis the issues many restaurant startups face, particularly in large cities. How can they best maximize their attendance not only presently, but in the long term while staying afloat in very crowded market places.
The level at which humans can apply perfect rationality is surprisingly modest. Yet it has not been clear how to deal with imperfect or bounded rationality.
Chapter 3 takes a similar problem as Chapter 2 and ups the complexity of the problem somewhat substantially. While I understand that at the time these problems may have seemed cutting edge and incomprehensible to most, I find myself wondering how they didn’t see it all from the beginning.
This book considers a relatively new metric in complex systems, transfer entropy, derived from a series of measurements, usually a time series. After a qualitative introduction and a chapter that explains the key ideas from statistics required to understand the text, the authors then present information theory and transfer entropy in depth. A key feature of the approach is the authors' work to show the relationship between information flow and complexity. The later chapters demonstrate information transfer in canonical systems, and applications, for example in neuroscience and in finance.
The book will be of value to advanced undergraduate and graduate students and researchers in the areas of computer science, neuroscience, physics, and engineering.
ISBN: 978-3-319-43221-2 (Print), 978-3-319-43222-9 (Online)
The world’s foremost expert on pricing strategy shows how this mysterious process works and how to maximize value through pricing to company and customer.
In all walks of life, we constantly make decisions about whether something is worth our money or our time, or try to convince others to part with their money or their time. Price is the place where value and money meet. From the global release of the latest electronic gadget to the bewildering gyrations of oil futures to markdowns at the bargain store, price is the most powerful and pervasive economic force in our day-to-day lives and one of the least understood.
The recipe for successful pricing often sounds like an exotic cocktail, with equal parts psychology, economics, strategy, tools and incentives stirred up together, usually with just enough math to sour the taste. That leads managers to water down the drink with hunches and rules of thumb, or leave out the parts with which they don’t feel comfortable. While this makes for a sweeter drink, it often lacks the punch to have an impact on the customer or on the business.
It doesn’t have to be that way, though, as Hermann Simon illustrates through dozens of stories collected over four decades in the trenches and behind the scenes. A world-renowned speaker on pricing and a trusted advisor to Fortune 500 executives, Simon’s lifelong journey has taken him from rural farmers’ markets, to a distinguished academic career, to a long second career as an entrepreneur and management consultant to companies large and small throughout the world. Along the way, he has learned from Nobel Prize winners and leading management gurus, and helped countless managers and executives use pricing as a way to create new markets, grow their businesses and gain a sustained competitive advantage. He also learned some tough personal lessons about value, how people perceive it, and how people profit from it.
In this engaging and practical narrative, Simon leaves nothing out of the pricing cocktail, but still makes it go down smoothly and leaves you wanting to learn more and do more―as a consumer or as a business person. You will never look at pricing the same way again.