File:Rock-paper-scissors.svg

I’m pretty sure we all know this, but just in case…

We use the term “rock-paper-scissors” (or RPS) to mean any three-state system where every result defeats one and is defeated by another state. Generally, this is in a situation where you’re trying to understand or guess an opponent’s intention and employ the appropriate counter-strategy. The universal wargame RPS example is: infantry beats cavalry, cavalry beats archers, and archers beat infantry. In Agricola it could be said that snatching up the reed another player needed is one state of an RPS system even though it’s turn-based and not simultaneous reveal. We could say that the very concept of strategy is fundamentally linked to RPS, because in a balanced game of skill there should be at least one plan that can beat any given plan. If the game is not broken, there should therefore be a strategy that counters your chosen strategy, and that counter itself should have a counter. With players of exactly equal ability, the result of the game then becomes simply one of “who picked the correct plan.” Where a game includes multiple iterations of an RPS mechanism, a dynamic equilibrium can establish itself, with each strategy coming in and out of use as counter-plays take and lose dominance over the course of each iteration. RPS systems are incredibly popular because they are balanced a-priori. This makes them perfect for game design.

RPS is so fundamental that it even appears in the natural world. An example is the mating habit of the Side-Blotched Lizard (uta stansburiana). The male side-blotched lizard has a coloured throat that is either orange, blue, or has a yellow stripe. The orange throated male is tough, and tries to mate with as many females as possible, defending a large area of territory to do so. The blue-throats are the next most tough, but have taken the evolutionary strategy of (effective) monogamy, defending only the territory enough for one female. Finally, there are the wimps, the yellow stripes, who sneak up on the orange throats while they aren’t looking and mate with the females in the orange throat’s territory. In effect, orange beats blue because he’s tougher, blue beats yellow because he’s more alert, and yellow beats orange because he’s sneaky.

Tough guy, eh?

This is an excellent example of Evolutionary Game Theory.

It just so happens that if you take a large group of actors in any situation where their primary motivation is to derive maximum benefit from a source of energy, the system naturally tends to either a single strategy (a Nash Equilibrium), or a cyclical and dynamic equilibrium of competing strategies. The actors don’t have to be rational, they simply have to develop habits that allow them to derive energy from a system. Over generations, unsuccessful strategies simply die out; successful strategies reproduce. Strategies are evolutionarily whittled down to the minimum number that allows for this dynamic equilibrium to form. In such a contest, the payout over the long term will be the same no matter what strategy you take. This means that RPS is not a strategy or mechanic applied to games, it is actually a naturally-occurring emergent metaphenomenon of certain complex systems.

To take another example from the natural world, in plant succession, there are three main strategies: ruderal, competitor, and stress-tolerator. Ruderals are things like dandelions that focus on immediate payoff with very little attention paid to long-term survival. They put their focus on the now, and go to seed as soon as possible. They make their seeds durable and long-lasting, able to remain in the ground until the opportunity arrives for them to sprout again. Competitors, in contrast, have strong defensive capability and make a point of growing higher, spreading out over the ruderals, poisoning the landscape if necessary with allelopathic strategies, and out-surviving the opportunists. Competitors, in turn, succumb to stress-tolerators, who are typically in it for the long game. They develop resistance to allelopathic attacks, focus on building strong and durable structure, and make highly efficient use of resources. Ruderals are things like grass and dandelions. Competitors tend to be shrubs and perennial plants. Stress-tolerators tend to be trees. They are also, respectively, the Zerg, Terrans, and Protoss in StarCraft. The comparison gets even better, since the Zerg can burrow to regenerate (long-lived seeds), the Terrans use bunkers and mines (defenses and allelopathic strategies), and the Protoss have the largest tech trees – and if used effectively, damage can be easily recovered through judicious use of shield generators – making them highly efficient damage absorbers in the long run.

Terrans forever!

We can accept that there are differences between a literal RPS mechanism, where RPS is used as a method of resolving a contest in game – such as the cavalry-infantry-archer example – and a RPS system, where there are dominant strategies that can be countered by other strategies. A fundamental requirement for a RPS system is that you don’t know for certain which counter to play. In Yomi, the uncertainty exists because you don’t know what card the opponent played that turn. In Agricola, the uncertainty exists because the game is complicated, and you don’t know what cards the opponent has in their hand. If you played a perfect-information game like Navigador with a supercomputer that had solved the game, you would always lose, unless you also played perfectly. You might still beat the supercomputer at Yomi.

They can also be compared to sprinters, middle distance runners, and marathon runners, where the victor is not determined by the strategy but by the length of the race. This is why, when evolutionary game theory gets going, it helps to have a game with an unfixed endpoint such that no strategy is a guaranteed winner. Like plants, the players will have to make the inefficient choice to mix tactics and strategies. Both are required to win a game, but just because player A beats player B with superior tactics doesn’t mean that player B’s strategic plan wasn’t superior… they might have won if only the game had been just a couple turns longer. Rock paper scissors is therefore not a “strategy” – it’s an emergent condition in any complex contest that is adequately long. Putting it in a game isn’t simply the recycling of a tired, old mechanism. It’s the acknowledgement that the inherent balance of the RPS system can be manipulated to make a dynamic and ever-changing strategic landscape in a game if it is used properly.

~ Dylan Kirk

Further Reading:

Robust Adaptive Strategies by Eric D. Beinhocker

Learning, hypothesis testing, and Nash equilibrium by Dean P. Foster and H. Peyton Young

Adaptive game playing using multiplicative weights by Yoav Freund and Robert E. Schapire

A General Class of Adaptive Strategies by Sergiu Hart and Andreu Mas-Colell