Game Theory - non zero sum outcomes

Hello there,

I am a philosophy graduate and a participant in a Catayst fund project trying to get to grips with game theory at a meta-philosophical level (not a mathematician).

For all a while now I have been browsing through the white papers over at Research papers - IOHK Research and I found a lot of papers that deal with functional, complete systems that typically have a Nash Equilibrium solution that is zero-sum (unambiguous).

This is important work in building the theoretical basis for Cardano’s blockchain roadmap. But I have found no accommodation of cases where parties have the option of mixed strategies (the example in Game Theory of “The Battle of the Sexes”) with no zero sum - which results in ambiguity (more than one favorable outcome).

This subject interests me in the context of what the Philosopher Ken Binmore calls “Decision making in large worlds” - in particular, whether the solution he proposed in “Rational Decisions” (2009) of “Muddled Equilibra” ) could be accommodated within a functional system.


Fascinating topic thanks for bringing it up! I will look over the links you provided.


Hi Stephen,

Very interesting idea. May I ask if you have any specific aspect of Cardano in mind that you think could be modelled by such a non-zero-sum game with possible muddled equilibria?

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Hi Christino,

My intuitive idea is that muddled equilibria could apply to governance issues that involve non zero sum outcomes. In cases where choices (symmetric) are known but a resolution has been left unsettled between the parties (the players). In short : areas of ambiguity, uncertainty and incompleteness.

In such a situation there will be Nash Equilibra (where the players may assume the game is zero sum - either/or) and there will be “Muddled Equilibra” (where the players may decide according to a range of probabilities).

I am at the limits of my knowledge here and more concerned with the philosophical implications. Game Theory provides solutions that can be translated to functional specifications that define closed, trustless systems like blockchains.

But governance is not zero-sum. At the very least it is always a series (a continuum) of equilibrium problems. If I choose one party over another the other party does not go away - what happens is that new equilibrium problems emerge.