Bi-matrix Decision Making

[Somdeb Lahiri]

Dear Colleagues:

https://drive.google.com/file/d/17yytGFDrUD3fwUVArDdRZrdtFX-CPEZa/view

I am not sure if any of the several solutions discussed here could help in the resolution of "ambiguity" but any other interpretation of non-cooperative game theory except and beyond the framework presented here, appears to face serious "informational challenges" to me. There is a limit to the extent that "as if theories" of human interactions could be useful or worth pursuing even for the sake of entertainment.

Thanks and regards.

Somdeb.

[somdeb...@gmail.com]

Dear All:

The two new papers at the link below contribute to "Bi-matrix Decision Making" and what I had earlier referred to as "Ellsberg solution".

1) The first paper is available the following link:

https://doi.org/10.31224/4741

Theorem 2 in conjunction with proposition 1 in the "Primer" (available at: https://doi.org/10.6084/m9.figshare.29375843.v2) may imply that all bi-matrix games- and not just matrix games- are within the scope of "optimization theory", and more generally "operations research".

2)The second paper available at the link below, shows that all bi-matrix games that are Two-Person Additively Separable Sum (TPASS) games (Time-PASS games 😊) are "equivalent" to a linear programming problem.

https://doi.org/10.31224/4775

Thank you in anticipation of your time and consideration.

Regards.

Somdeb.

[Somdeb Lahiri]

Thank you very much for pointing out the error. I will certainly examine the proof once again and try to retrieve it.

Warmly.

Somdeb.

On Sun, Jul 6, 2025 at 3:21 PM Bernhard von Stengel <bvons...@gmail.com> wrote:

Hi, sorry to say, but your proof 1) of the existence of "symmetric equilibria" in the sense of Nash equilibria is obviously false (and would be too good to be true).
Take the prisoner's dilemma with payoffs to the row player
2 0
3 1
and symmetric payoffs to the column player, so this is a symmetric game.
Suppose the players play symmetrically x=(p,1-p) which maximizes their symmetric payoffs 2p^2+3p(1-p)+(1-p)^2=1+p for p=1.
But both playing p=1 is not a Nash equilibrium. It's only robust against symmetric deviations.

Best regards,
Bernhard von Stengel

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Somdeb Lahiri
https://sites.google.com/view/somdeblahiri

https://independent.academia.edu/LahiriSomdeb/Teaching-Documents 

https://figshare.com/authors/Somdeb_Lahiri/21580622

"Non-violent non-cooperation" is the most powerful weapon against "zulm"

Lecture Notes: Demand, Demand Curves and Consumer's Surplus

[somdeb...@gmail.com]

For the moment I think I have managed to "put off the fire". Naturally, much work is pending for the way ahead. Thanks a lot for pointing out the error.

https://drive.google.com/file/d/1QjzS41_2E7oFgi78cbQ7tWoTz2kTtjoi/view?usp=drive_link

[somdeb...@gmail.com]

Dear All:

An update on TPSERS games.

https://doi.org/10.31224/4834

Thanks and regards.

Somdeb.