Fwd: Bi-matrix Decision Making

[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.

---------- Forwarded message ---------
From: somdeb...@gmail.com <Unknown>
Date: Monday, March 7, 2022 at 3:51:58 PM UTC+5:30
Subject: Bi-matrix Decision Making
To: decision_t...@googlegroups.com <Unknown>

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]

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

---------- Forwarded message ---------
From: somdeb...@gmail.com <Unknown>

Date: Sunday, July 6, 2025 at 6:02:24 PM UTC+5:30
Subject: Re: [DT_Forum] Fwd: Bi-matrix Decision Making
To: Bernhard von Stengel <Unknown>
Cc: Von-Stengel,B <Unknown>, decision_t...@googlegroups.com <Unknown>

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...@gmail.com]

Dear All:

An update on TPSERS games.

https://doi.org/10.31224/4834

Thanks and regards.

Somdeb.

[somdeb...@gmail.com]

Dear Colleagues:

TPASS games are capable of addressing conflicts between equilibrium/steady-state and cooperation as in Prisoner's Dilemma and several other situations. However, that still leaves open the problem of linking "coordination games" with linear programming. That is the problem, I have tried to address in the paper available at the following link:

https://doi.org/10.31224/5071

It seems that "the set of pure-strategy equilibria" for a simple coordnation game can be reprented as the "set of solutions of an integer linear programming problem".

As always, I will be very happy to hear from you about the paper. 

Regards.

Somdeb.   

---------- Forwarded message ---------
From: somdeb...@gmail.com <somdeb...@gmail.com>
Date: Saturday, July 5, 2025 at 3:05:15 PM UTC+5:30
Subject: Fwd: Bi-matrix Decision Making
To: 

Dear All:

The 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.