👓 In Game Theory, No Clear Path to Equilibrium | Quanta Magazine

Read In Game Theory, No Clear Path to Equilibrium by Erica Klarreich (Quanta Magazine)
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.

Published by

Chris Aldrich

I'm a biomedical and electrical engineer with interests in information theory, complexity, evolution, genetics, signal processing, IndieWeb, theoretical mathematics, and big history. I'm also a talent manager-producer-publisher in the entertainment industry with expertise in representation, distribution, finance, production, content delivery, and new media.

3 thoughts on “👓 In Game Theory, No Clear Path to Equilibrium | Quanta Magazine”

  1. Communication complexity of approximate Nash equilibria by Yakov Babichenko, Aviad Rubinstein (arXiv)

    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.

    Suggested by In Game Theory, No Clear Path to Equilibrium by Erica Klarreich (Quanta Magazine)

    <em>Related</em>

    Author: Chris Aldrich

    I'm a biomedical and electrical engineer with interests in information theory, complexity, evolution, genetics, signal processing, theoretical mathematics, and big history.

    I’m also a talent manager-producer-publisher in the entertainment industry with expertise in representation, distribution, finance, production, content delivery, and new media.
    View all posts by Chris Aldrich

    Reply

  2. Subjectivity and Correlation in Randomized Strategies by Robert J. Aumann (Journal of Mathematical Economics 1 (1974) 67-96. North-Holland Publishing Company)

    (.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.).

    Suggested by In Game Theory, No Clear Path to Equilibrium by Erica Klarreich (Quanta Magazine)

    <em>Related</em>

    Author: Chris Aldrich

    I'm a biomedical and electrical engineer with interests in information theory, complexity, evolution, genetics, signal processing, theoretical mathematics, and big history.

    I’m also a talent manager-producer-publisher in the entertainment industry with expertise in representation, distribution, finance, production, content delivery, and new media.
    View all posts by Chris Aldrich

    Reply

  3. A Course in Game Theory by Martin J. Osborne and Ariel Rubinstein (MIT Press)

    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.

    Tangentially suggested after reading In Game Theory, No Clear Path to Equilibrium by Erica Klarreich (Quanta Magazine)
    Free, personal copy is downloadable in .pdf format with registration here.

    Syndicated copies to:

    <em>Related</em>

    Author: Chris Aldrich

    I'm a biomedical and electrical engineer with interests in information theory, complexity, evolution, genetics, signal processing, theoretical mathematics, and big history.

    I’m also a talent manager-producer-publisher in the entertainment industry with expertise in representation, distribution, finance, production, content delivery, and new media.
    View all posts by Chris Aldrich

    Syndicated copies:

    Reply

Likes

Mentions

Reposts

Leave a Reply

Your email address will not be published. Required fields are marked *

To respond to a post on this site using your own website, create your post making sure to include the (target) URL/permalink for my post in your response. Then enter the URL/permalink of your response in the (source) box and click the 'Ping me' button. Your response will appear (possibly after moderation) on my page. Want to update or remove your response? Update or delete your post and re-enter your post's URL again. (Learn More)