Monday, October 1, 2018

Solving the Raygun Problem with Evolutionary Games

by Cathelineau via game-icons.net
I like Evolution: the game, the theory, but in Chapter 13 of "Games of Strategy" I learned about something new -- Evolutionary Games.

An evolutionary game looks at a large population of players -- each using only a single strategy -- to find the balance of strategies that work best together given lots of repeat plays.

Borrowing concepts from natural selection, the mix of how many players use any particular strategy is changed until an equilibrium is found.  At that point, each player will do equally well after playing against every other player and their opponents' strategies.

For instance, 2 backstabbers in a group of 10 cooperators might be a good balance in a prisoner's dilemma game given the right payouts.  In many ways this looks a lot like mixed strategies -- having 2 backstabbers and 8 cooperators is similar to saying that I will backstab 20% of the time.  So having lots of players engaging in different strategies looks a lot like two players using mixed strategies.

An important difference is that each individual player is pursuing a single strategy.  Which is often more analogous to a single play of a board game.

Achieving Polymorphism

This equilibrium might only occur when all players are using the same, obviously dominant strategy (Monomorphism).  But you can end up with a mix of strategies (Polymorphism)... probably in the same situations where mixed strategies would be the best choice.

If Polymorphism is a goal of our game design, the idea of evolutionary games brought two paths to mind.

Rock-Paper-Scissors

The seemingly obvious answer is to make different strategies work best against each other in a daisy chain such that none of them are dominant against a full field of strategies.

I think I've seen this the most in complex TCGs like Magic: the Gathering.  In these games the meta often shift to favor a particular type of deck construction.  In theory as more and more players adopt that strategy, other decks that work well against it in particular will become more effective even if they are not as strong generally in the current meta.

This is easier to conceptualize if you think of a 4 item Rock-Paper-Scissors.  Lets call this game Rock-Paper-Scissors-Raygun.  In this game Rock, Paper, and Scissors interact with each other as you are used to but Raygun beats both Rock and Paper.  Only Scissors beats Raygun.  Raygun is easily the best strategy... except that when a majority of players carry rayguns, scissors is suddenly very effective... which eventually leads to more people playing rocks...

by Lorc via game-icons.net

Raygun Interference

A different way to deal with the raygun problem is to make rayguns interfere with each other.  Maybe each raygun brought to a game of Rock-Paper-Scissors-Raygun reduces the effectiveness of every other raygun.  Rayguns might start out with a relative value twice as high as everything else, but then everyone brings a raygun...

You see this in Railways of the World (Eatern US Map).  Concentrating in the northeast can be hugely efficient and effective in this game... if you are the only person doing it.  Otherwise it becomes cramped and dangerous.  Although, the second person to commit to that plan can be throwing their game away to try to stop a run-away leader.  (See Tragedies of the Game Commons).

In Championship Formula Racing, this can happen differently.  If a track looks to favor a particular over all strategy you can have a glut of cars commit to that strategy.  Since that commitment usually takes place during the simultaneous and private phase of car set-up there is no first mover advantage -- as you see in the Railways of the World example.

What About Monomorphism

Am I going out on a limb to suggest that game designers want Polymorphism?  Would a game ever strive for Monomorphism?  Maybe if something other than strategy contributes to success or failure like dexterity or trivia knowledge?

Something to think about.