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Non-Dojo Game Theory 1


 

 

There’s a branch of quantitative analysis (nerd math) called Game Theory.  While the word “theory” is in there, I’m not going to pontificate about Hunters under Ossyan’s feat or anything like that.  What I am going to show you is a pretty deep frame work for looking at interactions between two intelligent players.  Oh… and I’ll tie it into Warmachine and Hordes for good measure.

Math needs pictures so let’s get into the examples right away.  One of the most popular Game Theory interactions is called “The Prisoner’s Dilemma”.  You’ve got two guys (A and B) involved in a crime together.  Criminal A is sitting there talking to the cops.  He’s got two choices (snitch, hold out).  Criminal B is facing the mirror scenario.  If they both hold out, they each face minor time in jail (1 year) and beat the system.  If one snitches while the other holds out, the cops we’ll give him a break (zero time for snitch, 10 years to the hold out).  If both snitch on one another they each get five years.  On the surface it seems like the two would hold out, beat the system and get off.

At right is a diagram and the numbers are “years”.

As an example, negative ten means ten years in jail. Criminal A can choose to snitch or hold out on the left side.  B can choose to snitch or hold out on the top.  Let’s look at A’s choices.  No matter what B does, A is better off snitching.  That’s called a dominant strategy.  If you can do one thing that’s ALWAYS better no matter what your opponent does, then you have a pretty easy choice on your hands.  Do that better thing!  It’s rational for A to snitch.  But wait, let’s not ignore B.  B can hope against hope that A’s dumb or hasn’t read this article.  Looking at A’s actions, B will also deduces that he’s better off snitching.  B has the same dominant strategy; snitch.

These poor saps will always snitch on one another.

That’s the rub.  You can play this game in isolated rooms.  You can play it face to face.  It doesn’t matter.  Rational players will always rat one another out.  I probably should have said [Spoiler Alert] for the Law and Order fans out there.  My bad.

If you’re still with me you’ve just digested some heavy stuff.  So how does this relate to Warmachine?  There are three ways to find yourself in a Prisoner’s Dilemma in Warmachine.

1.      List Selection in a Steam Roller Tournament

I reached out to a few high level tourney studs for help on this one.  List Selection and interaction holds a lot of subtly.  So here are two examples of Prisoner’s Dilemma in the Steam Roller environment.

Courtesy of Keith Christianson;

Player A:  Ashphyxious2 (hold out) and Terminus (snitch)

Player B:  Caine2 (hold out) and Haley1

Lich2 doesn’t like Haley1 because Temporal Barrier negates his feat.  Caine2 can’t play against Terminus well because Sacrificial Pawn is a ball buster.  The two players end up playing the miserable grind fest of Terminus vs. Haley1 despite likely preferring the Lich2 vs. Caine2 game.

Courtesy of Michael Chilly Winters (adding a familiar opponent layer);

Winters:  Skarre1 (hold out) and Terminus (snitch)

Pagani:  Kromac (hold out) and Krueger1 (snitch)

Based on personal preference, the match would be Skarre1 vs. Kromac and both players would get to use their favored caster.  Unfortunately for them, Will’s dominant strategy is Krueger1 due to infantry clearing potential and Michael’s dominant strategy is Terminus.  As a result, these two end up playing the Krueger1 vs. Terminus game against their true preference.

As you get to high levels of play in Warmachine, you start realizing that there are a lot intelligent dudes out there.  Use that to your advantage.  Your opponent will typically behave rationally and in their own best interest.  Knowing that, you can strategically react and account for it.

2.      Piece Trading

You’ve got a beat stick.  He’s got a beat stick.  Each of you could avoid one another and be happier.  The outcome payouts can resemble a Prisoner’s Dilemma.  The solution being that you trade and end up slap fighting for eternity.

3.      Pulling a Nick Swardson and showing off your “watch” at a convention.

Don’t show your “watch” to people who don’t want to see it.  This will land you in a different type of Prisoner’s Dilemma.

 

 

There are a number of games out there to identify and really big brains or intuitive ones realize their opponent is equally intelligent, count on it, and select a solution in their best interest.  The top players do it all the time.  I’m going to break down a few more Game Theory frameworks in future articles.  A few particular ones come to mind;

The Hawk-Dove Game:  Aggressive or Defensive posturing. Lot’s of Warmachine application.  Credible threat of force is the name of the game.

Rock/Paper/Scissors:  This screams Yomi.  I love Yomi.  Great game.

Battle of the Sexes:  Two players, two collaborative equilibrium.  One player wins.  Make it you.

Fun fact:  The Mafia figured out the Prisoner’s Dilemma and changed the game so the solution was [hold out, hold out].  How you ask??  Whacking the snitch.  Look at the pay out grid involving that new element.

Fancy that.  Organized crime works!

 

 

 

 

 

The more you know… (hum the little diddy in your head when you read this last part)


I'm a gaming and math enthusiast. I find games that balance strategic interaction with economic principles (delayed option, resource control, etc.) are some of the most rewarding for me as a player. I concentrated in Finance, Analytic Consulting, Decision Sciences and Management Strategy while getting my MBA at Kellogg (Northwestern University) and majored in Chemical Engineering during my undergrad at University of Illinois. I view WM/H through this lens and share my perspective via periodic articles. Thanks for reading!
  1. jaster Reply

    You forgot to also instruct to picture the shooting star icon at the end.

    Otherwise, interesting read, more so for me who’s awful at picking matchups come the start of a game.

  2. Tmage Reply

    You win this round jaster (shakes fist menacingly)… :)

  3. I_Avian Reply

    Psychologist caveat: Game Theory has a huge problem in that people are not rational, self interested beings. Counter-caveat: High Level WMH tournament players mostly are (in the context of an actual tournament).

    I’m constantly trying to figure out a better system to list pairing/selection, that doesn’t come down to an eternal loop of guessing game. One where I can nudge opponents in predictable directions. (Y’know, harness some of that irrationality)

    • Tmage Reply

      I find the Double-Dog and even Triple-Dog Dare are pretty meaningful psychological levers. :) Beyond that you’d probably have to talk to Neutralyze. He’s all flirty blue eyes and Jedi mind-tricks. That next level voodoo is beyond me.

  4. benrislove Reply

    This is an excellent application of the theory, however it’s only a baseline, since terrain and scenario alter the perceived advantage of each list individually.

    It’s actually quite similar to the prisoners dilemma + Mafia involvement. In this case your hold out is the strength of your list in a given scenario. Selecting the “snitch” can result in a weaker scenario game, creating one less avenue for victory. This can enable you to choose the list that your opponent doesn’t expect, based on factors they aren’t considering.

    Occasionally you end up in a VERY favorable situation where you have both scenario advantage and match-up advantage.

    Further application comes in to building your lists. If you build for both sceanrio’s and match-ups. You can cover your match-up weaknesses and scenario weaknesses to cover a far greater number of bases than considering only one of these factors :D This is also HUGE in divide an conquer, since sometimes holding out is 1 year, and snitching is 0 years.

    Simply asserting If your “hold out” penalty is small enough, the potential advantage of having all your lists available to select from in future rounds can be a greater potential gain.

    • Tmage Reply

      Agreed on all points. Thanks for the add and the kind words!

  5. Lamoron Reply

    It’s rare but every once in a while someone brings out an article that opens up a whole new universe… thanks :)

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