Research Publication!: My Theorem to Aid the Israeli-Palestinian Conflict

 

So, unfortunately, it looks like my P vs. NP proof was incorrect :-(.  That is very disappointing to me.  I probably will not be able to go to graduate school in economics or anything else.  I probably cannot be a professional researcher.  That said, I can still use my economics ideas for myself.


Here is my theorem that I said I would publish if my P vs. NP proof were reviewed, which it was; it is a game theory theorem that I think might help international politics.


Here it is:


Define a "payoff transfer" game to be one where every other move, another set of moves is inserted where each player is allowed to give a finite, integer-valued amount of payoff to any other player, such that after the payoff "gift" is given, the final payoff score of each payoff-transferring player is 0 or above.  I got the idea about payoff transfer from a chat with ChatGPT, but the math, the theorem, and the proof are my own, not the product of AI interaction.

Define a "well-prepared Nash equilibrium" to be a Nash equilibrium where any unilateral strategy change by *one* player other than any fixed arbitrary player P in the strategy profile is such that P has a contingency plan such that if that unilateral defection happens, P will still play a best-response to the new set of strategies by every other player.  Note, every game has a well-prepared Nash equilibrium; we just have to modify an existing Nash equilibrium by ensuring that it is best-response-wise robust under unilateral strategy defections.


Now:  Any perfect information payoff transfer game is such that all well-prepared Nash equilibria are Pareto optimal.


Proof omitted.  Here's a slightly hard to follow quote from my notes, hopefully this proof is not wrong as well :-( :


"The idea is, every player has their best response as a response to any unilateral defection as part of their contingency plan set, so, if the first player “pays” all the other players to change strategies, their automatic contingency plan will activate, and they will “accept the deal” as a contingency, that is, if they receive the money, they will choose a response in that case that optimizes their payoff, that is, they will see that the first player is playing, “offer X payoff units if opponent B changes strategy,” and so they will play, “change to strategy S if opponent A gives me X payoff units.”"


The idea is, if let's say Israel, Egypt, and the Palestinian territories wanted to work to achieve peace, they should do the following to guide their game theory interactions to be like these games (I'm assuming that in real life, strategic actors generally always play a Nash equilibrium):


 - Modify strategies to be "well-prepared Nash equilibria"--modify your current strategic plans to account for wild, possibly irrational unilateral strategy changes by your strategic partners and adversaries, and "be ready for anything" with a plan that constitutes a best response

 - Avoid simultaneous move and "secretive" interactions.  Try to keep interactions in line with perfect information games.

 - Be quantitatively strategic.  Try to put a price on everything that happens in some currency.  If someone is about to do something that might impact you, consider "opening your wallet" and communicating honestly to your opponent or whomever else what you would pay, in money, to get them to do your preferred strategic action.  Try to make utility equivalent to money; be willing to make payments to get things to happen.



I hope this helps Israel and others in the current strategic conflict!  I did my part and published this!  I might publish my other economics ideas too, but sadly, I'm concerned that no one much will care.  I am very disappointed that my P vs. NP proof was wrong, and it means I probably can't go back to school in economics or do anything else with math/STEM in a big way.  I'm not likely to get employed as a programmer.  I suppose I will try to be a manager someday.  Hopefully my court case will be resolved, too!  I think it will...there is probably *some* sort of investigation into how I've been treated.


Good luck, Israel et al.!










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