Is John Baez considering mathematical game theory in mechanics?

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  • #1
I have a great deal of respect for John Baez and This Week's Finds [TWF] and his colleges, David Corfield and Urs Schreiber, at n-Category Cafe [n-CC].

I struggle to understand the mathematics since my perspective is more physiological than mechanical physics. I probably misinterpret much of their work.

The table of contents at TWF reveals only one brief discussion of game theory week 140 in reference to John von Neumann.

I have noticed references to game theory on two recent n-CC posts:

1 - January 31, 2007 Quantization and Cohomology (Week 12)

One of the comments refers to the Hamilton-Jacobi Equation, which with the Isaacs condition, is of primary importance in dynamic noncooperative games.

2 - January 19, 2007 Traces in Ottawa

This links to the WebPages of Paul-André Melliès [Google can translate French into English].

In the section 'Recent and vintage talks' are two that deal with game theory.

a - Functional boxings in string diagrams. Invited talk At CSL 2006; a discussion of game theory semantics beginning slide 64 of 88.

b - Asynchronous games: fully has supplements model of propositional linear logic. Wednesday talk At LiCS 2005; discusses strategies, lambda calculus and tensors in 55 slides.

Game theory looks at the relationships of topological trajectories and control [action] spaces and information structures; with or without stochastic properties.
One primary difference is that dimensions are strategies rather than only spatial or time.
Robotics and biophysics have incorporated game theory successfully into their fields.
For infinite dynamics games, the theory tends to use PDE.
For finite dynamic games, the theory tends to use the bimatrix or extensive form [tree].

Is Baez moving in the direction of von Neuman, Nash and Conway.
The latter three Johns have made significant contributions to both game theory and physics.

Answers and Replies

  • #2
You should repost this in the "Set Theory, Logic, Probability, Statistics" forum.
  • #3
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Game theory is a very powerful analytical tool. It assumes any given outcome is the most probable consequence of initial conditions. While all outcomes are equally improbable [e.g., landscapes], the probability of causal precusor conditions are greatly constrained. Given that John Baez is a mathematician first, his approach is impeccably logical.
  • #4
Hi josh1

I have posted at "Set Theory, Logic, Probability, Statistics" forum:
Game Theory - applied mathematics - how powerful is it?

I think the original post should remain in this forum.

Many professionals who apply physics, particularly engineers, have been using game theory successfully for about 25-30 years.

This situation reminds me that electrical [and electronics] engineers were using Grassmann algebra in the form of phasor equations about 25-30 years before Schroedinger framed his equation in Clifford algebra.

Gabriel Kron demonstrated near equivalence in ‘Electric Ciruit Models of the Schrödinger Equation’ Phys. Rev. 67, 39-43 (1945).

I understand Richard Feynman used phasor analysis to develop his diagrams for all possible paths.

The ArXiv does have a few Physics-Game Theory related papers, but should consider more use of this powerful analytic tool.
  • #5
Hi Chronos:

I agree - "Game theory is a very powerful analytical tool."

In viewing the ArXiv, there are surprisingly few physics-game_theory papers relative to many professions which utilize applied physics and game theory successfully such as various engineers.

I am influenced by this great reference [viewable on Amazon]:
Dynamic No cooperative Game Theory (Classics in Applied Mathematics) (Paperback) by Tamer Basar, Geert Jan Olsder.

I would like to read one such reference that you might recommend.

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