Three Lizards
The ancient game of Slug, Frog, Snake or sansukumi-ken (Japan, 1809)
One of the oldest games in town is Rock Paper Scissors, variously known over the years as roshambo, jankenpon, zhot or chifoumi. In the jargon, the game is described as non-transitive - one where strategy A beats B beats C which beats A, loopwise.
Now look at these guys here
Image credit: Barry Sinervo (UCSC)
You will be delighted to learn that there is a species of lizard (Uta Stansburiana) from the Sonoran deserts of California, that likes to play Rock, Paper Scissors too.
It works like this - orange-throated males are sexual predators large enough to fight off blue-throated males. Blue-throats are monogamous, large enough to beat off yellow-throats who are sometime transvestites, who in turn like to nip over in disguise to mate with orange-throated females, while the orange-throated males are away trying to have sex with the blue-throated females. Phew.
In sum, Orange beats Blue beats Yellow beats Orange. An evolutionary stable system has been achieved.
Ordinarily, this would be our cue to pause and marvel awhile at the splendid inventions of Nature, and for some to mumble incoherently about all things requiring Balance.
But we can do better.
Games are everywhere
Enter John Nash, a mathematician.
In 1949, Nash made a major contribution to von Neumann and Morganstern’s pioneering work The Theory of Games & Economic Activity (1944), which sought to cast all economics as games of strategy between buyers and sellers. Where the pioneers only modelled so-called zero-sum games (I win, you lose) Nash went further.
He was able to show that a whole class of games have an equilibrium where all players can achieve (at least an approximation of) some optimal outcome.
Let’s say you want to eat Italian, I want to eat Chinese, and we both want to eat together. So - assuming my desire to pick the restaurant is less important to me than my unwillingness to eat alone - I’ll have pizza with you. The most famous of Nash’s games, the Prisoner’s Dilemma, is similar insofar as both sides must lose a little in order to not lose a lot.
And these trivial cases are highly scalable to bigger, chewier, multistage, many-condition problems with thousands of players, hundreds of preferences and (unfortunately) many equilibria.
Where there was previously no formal, mathematical way to describe these systems before, they could now be rendered - in some sense - tractable at last. Economists, inexorably drawn to simple, abstract-mechanical models of irreducibly complex things (as moths to the flame) happily expanded upon this work.
Thus, if you are trying to work out how to regulate banks, auction off chunks of radio spectrum or just figure out where to have a quiet drink when everyone else wants a quiet drink too, games are serious business.
And the complexity of these systems may rapidly grow to wonderful depth - and often opaque subtlety - as one adds new rules, new conditions, partial awareness of what other players are now doing or have done, or the way in which signals of next-move intent - intSIG - are shared or hidden between players.
Let us play
Game theorists, we think, have a bunch of wildly interesting lenses with which to inspect collective intelligence. And, as you might have guessed, we at Liminal are now working on some top-secret new games to help you do just that.
Stay tuned for more on this topic.
You are not a lizard
Underlying the original framework though, are some serious problems.
The original Nash model presumed that players are rational - and by rational, we mean two distinct things. Homo economicus is a hungry robot: firstly described as ‘utility maximising’ (it wants as much of everything as it can get) and secondly, not subject to the various cognitive blindspots, delightful kinks and deplorable biases lately assembled under the banner of ‘behavioural’ economics.
You - as a robot - simply don’t have these problems: you’re out there efficiently maximising each and every day, and don’t let nobody get in your way. A fairly depressing and unrealistic picture of what people actually do, we think.
But here’s the good news.
You are neither a hungry robot, nor a sex-crazed lizard. Well, not all of the time, anyway. You, a human, are actually quite nice - liable to favour cooperation, and you’re pretty weird too - ie, prone to all kinds of hardwired misapprehensions and glitches. But your weird edges are our weird edges too: it’s why we love you, really.
And remarkably, it turns out that the best tool to understand human weirdness at scale and the very limits of game theory itself might be… more game theory.
One big game
Let’s play the Ultimatum Game (1982).
It works like this - Player A wins some money, but is required to share some amount with Player B. If B declines A’s offer, both get nothing. That’s it.
Seems simple enough, so: how much should A share? How much should B accept?
From one perspective, A should share almost nothing, and B should accept anything. After all, something is better than nothing if you’re B, and less is more if you’re A.
Right? Not quite.
Learning, always learning
Lastly - unlike our pals the lizards - humans change.
The ability to learn new tricks and discard old ones is key. Indeed, what makes humans both splendid and deadly is our ability to adopt, adapt and create entirely new strategies: to improvise and collage behaviours relevant to context.
In this respect, humans at work and humans at play are not so far apart.
Likewise, large groups of humans - organisations, institutions and companies - also have their own favoured strategies for cooperation and competition, from the micro-social to the communal to organisation-wide games. Community-mechanics are how work gets done… even in the least playful of places.
Postscript
We will be sharing more observations and practical applications of social gameplay in our work here in future. In the meantime, if any of this sounds like fun - do drop by and say hello.
Links
B. Sinervo and C. M. Lively (1996). The rock-paper-scissors game and the evolution of alternative male strategies, Nature, 380:240-243
https://www.nature.com/articles/380240a0
Mating strategies of the side-blotched lizard, Uta stansburiana
http://bio.research.ucsc.edu/~barrylab/lizardland/male_lizards.overview.h
Evolutionary Stable Strategies
https://locusofctrl.github.io/blog/posts-output/2019-02-03-male-strategy/
RJ Leonard (1995) From parlor games to social science: von Neumann, Morgenstern, and the creation of game theory 1928-1944, Journal of Economic Literature [PDF]
http://www.sscnet.ucla.edu/polisci/faculty/chwe/austen/leonard1995.pdf
Game theory meets rock, paper scissors
https://www.quantamagazine.org/the-game-theory-math-behind-rock-paper-scissors-20180402/
The Prisoner’s Dilemma
https://plato.stanford.edu/entries/prisoner-dilemma/
Humans considered quite nice
A podcast with historian Rutger Bregman and Liminal founder Roland Harwood.
https://anchor.fm/weareliminal/episodes/017-Rutger-Bregman---Humankind-ees46o
Humans considered far from always nice
The evolutionary interplay of intergroup conflict and altruism in humans: a review of parochial altruism theory
https://royalsocietypublishing.org/doi/10.1098/rspb.2014.1539#d3e942
James Carse, Finite and Infinite Games. A bad book, with some good ideas. https://en.wikipedia.org/wiki/Finite_and_Infinite_Games
The Ultimatum Game
