Why My Game Theory Stands For Fairness And Equality, A New Answer to The Pennies Game, Plus Implications For Trump, Columbia, and Harvard

           Today’s post is about a new preliminary answer to the “Pennies Game.” Which is a precursor game to the Prisoner’s Dilemma invented by RAND game theorist Merrill Flood. The “Pennies Game” – depicted here by Flood – is an asymmetric game rather than a symmetric game and this is relevant or arguably more relevant to the power dynamics between more powerful players and less powerful players, such as the game between Trump, Columbia, and Harvard (although I previously explained that scenario is an asymmetric, multiplayer game).     The Pennies Game has two players with pennies who have to split the pennies, and can opt between splitting these proceeds, or keeping them with one player having more pennies than the other.


Here, Flood’s answer (1,2) vindicates the game theorist John von Neumann and in real life with two players playing for pennies, the two players choose to have one player earn one penny, and one player earn two pennies rather than having one player earn zero pennies and another player earn one penny (as predicted by John Nash who advocated for (2,1), and who was proven wrong by real life players at least in this context). 

                  Well, I respectfully disagree with Flood’s experimental answer performed by two players at RAND based on other psychological experiments and backed up by studies of monkeys, which show that all beings have an innate sense of fairness that everyone intuitively gets (or should get) even as kindergarteners, which is how I could know as a kindergartener that my teacher collectively punishing the whole class was wrong. 

So what’s my new answer to the Pennies Game? I haven’t done a proof, and this isn’t core to my research agenda, which is about taking on John Nash, but if both players equally split the proceeds there’s an entirely new equilibrium that is located at the point (1.5, 1.5), which is located above the triangle and is higher than the equilibrium displayed there, making it utility maximizing, and maybe even Pareto optimal (though I haven’t checked). 

                  Now, this result might not be physically possible because the game stipulates it is played for pennies, and a penny cannot be divided in half legally if the players are playing for actual coins (destroying U.S. currency is illegal, and the money wouldn’t be worth anything). But I also assume that these days most currency is digital or can be expressed in other ways, i.e., electronically, and therefore the money could under current banking standards be expressed as (1.5, 1.5) and the equilibrium is thus possible.

                  And even if it’s not possible because the game designer insists on literal pennies, the (1,2) answer is still wrong if the game is played repeatedly. If the game is played repeatedly (and it is, as stipulated by the problem), the correct answer would be an alternating equilibrium of one player making two pennies with the other making one penny and going back and forth where both players split the profits over time and the net result is equal, assuming the game is played infinitely. 

                  But, as explained, notably the (1.5, 1.5) equilibrium falls higher on the graph at the mark labeled "I" (I didn't make it, but that's where it falls, how convenient for me), meaning it is more socially optimum, even if the wealthy player has to make a sacrifice, and I still have no idea how to enforce this sacrifice other than relying on the basic moral sense of fairness that all humans and animals share. I also obviously haven’t done a mathematical proof like I have for my new answer to the Prisoner’s Dilemma or to the game Chicken where I have pre-prints I’m working on, but this is my “intuitive” or “gut” answer, and as I explained, intuition is powerful and underlies absolutely all of my game theory work, which is written from a woman’s perspective, and I had my intuition for Chicken four years before I had any math except for the math I'd taken in high school (plus one of the highest grades in my college stats class), and before I could prove it, and I later did.

                  What does this mean for Trump, Harvard, and Columbia? Probably that Trump should cave and stop oppressing these institutions, and that Harvard and Columbia equally need to work on the accusations of antisemitism that have been raised, even while some pro-Palestinian protestors have been wrongfully characterized as violent or antisemitic (which some clearly are, and some clearly are not).


-Cortelyou C. Kenney, 9/20/25 (7:41 am PT).

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