Real Sums

With Apologies to Pat Benatar

In a landscape of competitive ideas, nomenclature is often the first battlefield.  I'm not writing this to challenge existing ideas, but to re-frame their default assumptions.  Competitive, non-default, second-class ideas ideas often are forced into prefixes that identify them as such:  Non-.  Anti-.

When we talk about Game Theory, "zero sum" suggests the wrong things about default assumptions.

Positive sum is an interesting construction, but not necessarily true.  It sits in the consciousnesses as a response to, or translation of non-zero and it isn't correct.  Games designed to be positive sum are often forced into that condition artificially.  Results can just as easily, or even more easily, be neutral or negative.

This is usually fine in Game Theory, because positive, negative, and zero-sum don't describe the structure of the game as much as they describe the results of how some iteration of the game was played out.  They describe the outcome of a game.  Any given outcome might be positive or negative or zero, and individual outcomes are necessarily exclusively one of those three things.

If we want to talk about the design of a game overall, these are not adequate words.  If we want to describe the spectrum of possible outcomes of a game, we can say that football is a zero-sum game.  If we want to talk about the Prisoners' Dilemma, we can only describe one of its outcomes as zero-sum — not the game its self.

Getting Real

Real Sum is both a literally correct statement, as well as loaded with implications.  It suggests that other models are false, which they are.  The very idea of zero-sum games is an artificial construction; the reality is that everyone playing towards a zero-sum outcome is losing.  The aggregate results are in fact negative when compared with the wasted potential or opportunity cost of a better outcome.

Games can be played towards a positive sum — but that is not adequate to describe the game either.  The spectrum of possible results is the set of all real numbers.  If the game is played badly, or greedily, the net result across all players is negative.

The best way, the only way,  to describe games which have a spectrum of possible outcomes is that they are Real Sum.

Wherefore

When I write games, I am building imaginary systems that emphasize Real Sum outcomes.  Depending on how they are interacted with, the results can be to the global benefit or global detriment. 

The end result can benefit an individual and may appear zero-sum, but the scope must be set such that the global result can be demonstrated as negative.  Of course individuals might choose to prefer a restricted scope that focuses on themselves alone, and that is fine.  Such examples provide great case studies of failure states that need to be designed around when building real systems.

Danielle Bunten Berry's classic M.U.L.E. is an excellent example of this sort of design, and I'm sure I won't be able to resist writing more about her body of work in the future.