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9084 results in Discrete Mathematics, Information Theory and Coding

Page 54 of 455

  • On the mixing time of coordinate Hit-and-Run

  • Part of
  • Hariharan Narayanan, Piyush Srivastava
  • Journal:
    Combinatorics, Probability and Computing / Volume 31 / Issue 2 / March 2022
    Published online by Cambridge University Press:
    25 August 2021, pp. 320-332

  • We obtain a polynomial upper bound on the mixing time $T_{CHR}(\epsilon)$ of the coordinate Hit-and-Run (CHR) random walk on an $n-$dimensional convex body, where $T_{CHR}(\epsilon)$ is the number of steps needed to reach within $\epsilon$ of the uniform distribution with respect to the total variation distance, starting from a warm start (i.e., a distribution which has a density with respect to the uniform distribution on the convex body that is bounded above by a constant). Our upper bound is polynomial in n, R and $\frac{1}{\epsilon}$, where we assume that the convex body contains the unit $\Vert\cdot\Vert_\infty$-unit ball $B_\infty$ and is contained in its R-dilation $R\cdot B_\infty$. Whether CHR has a polynomial mixing time has been an open question.

  • 10 - Game Trees with Imperfect Information

  • Bernhard von Stengel, London School of Economics and Political Science
  • Book:
    Game Theory Basics
    Published online:
    22 October 2021
    Print publication:
    19 August 2021, pp 263-298

  • Summary

    Although it appears late in this book, this is a core chapter about non-cooperative games. It studies extensive games, which are game trees with imperfect information. Typically, players do not always have full access to all the information which is relevant to their choices.

  • 2 - Congestion Games

  • Bernhard von Stengel, London School of Economics and Political Science
  • Book:
    Game Theory Basics
    Published online:
    22 October 2021
    Print publication:
    19 August 2021, pp 39-52

  • Summary

    Congestion means that a shared resource, such as a road, becomes more costly when more people use it. In a congestion game, multiple players decide on which resource to use, with the aim to minimize their cost. This interaction defines a game because the cost depends on what the other players do.

  • 3 - Games in Strategic Form

  • Bernhard von Stengel, London School of Economics and Political Science
  • Book:
    Game Theory Basics
    Published online:
    22 October 2021
    Print publication:
    19 August 2021, pp 53-76

  • Summary

    In this chapter we start with the systematic development of non-cooperative game theory. Its most basic model is the game in strategic form, the topic of this chapter. The available actions of each player, called strategies, are assumed as given. The players choose their strategies simultaneously and independently, and receive individual payoffs that represent their preferences for strategy profiles (combinations of strategies).

Page 54 of 455