[A Swiftly Tilting City] Prisoner's Dilemma mechanics

[Harlequin]

Since I've never posted here about A Swiftly Tilting City before, I'll start with a little background for context.

Background: ASTC was my winning first-round submission to the in-person Iron Game Chef at Origins 2003.  It is set in a Venice-like renaissance city, a great sprawling metropolis, which is perched literally at the tip of an unbalanced world.  The moral weight of deeds, here, is sufficient to affect the spinning of the planet.  The world will sometimes 'tip' under the accumulated weight, and the stars change their courses in the heavens - astrology is an intricate science, and very real.  The people are proud, accomplished, noble, treacherous.  Players create their character twice; once as the "bleu," essentially good but with character flaws, and once as the "rouge," essentially amoral/immoral but with redeeming qualities.  The outward visage, superficial nature of relationships, etc., is identical in both cases.  The mechanic in the original is that in the center of the table is a bowl full of red and blue stones, plus more of the same stones strewn about the table.  Actions automatically succeed as stated; however, any participant (player/GM) may at any time gauge the narrated deed as morally right (blue) or wrong (red), and add one stone of the corresponding colour to the bowl.  If at any time the bowl overflows, the world tips; all players secretly draw one stone at random from the bowl's contents, most of those contents are put back in, some of it is put on the table again.  The characters switch personae to the opposite nature to the stone drawn; a blue stone pitches them into the rouge, and vice versa.  Play continues with the new (possibly different) motivations in place.

The big thing this design lacked was a resolution mechanic.  I love the mechanic for changing personae, and the idea of two "men behind the mask" with different motives.  But "all actions automatically succeed and are merely judged" is inadequate; it does nothing to propel or meter conflict.

Recently, especially with Ben Lehman's writing about the Great White Game, I've resurrected – among others – A Swiftly Tilting City.  And I had this idea...

The Prisoner's Dilemma as resolution mechanic.

If you've never seen it, the Prisoner's Dilemma comes in a lot of forms; it's a central question in game theory, with some fascinating implications.  In short you have two people, each of whom has the choice to play nice or play nasty (cooperate or defect, in the original).  Neither knows what the other plans to do.  The outcome for each depends on the two choices.  In order of preferability, each player as an individual is best off:[list=1][*]Playing nasty when the other is playing nice.  Let's say this gets you 15 cents.[*]Playing nice when the other is playing nice.  Say this gets each of you a dime.[*]Playing nasty when the other is playing nasty.  Say this gets each of you a nickel.
[*]Playing nice when the other is playing nasty.  Say this gets you nothing.[/list:o]The interesting thing is that for the individual, nasty is always more profitable than nice, no matter what the other guy chooses.  But in the aggregate, nasty costs the total field money.  The biggest pot is the one split by two nice guys.  The game-theoretical question is whether an optimal strategy exists here, and what conditions it depends on.  Douglas Hofstader discusses this well in his book Metamagical Schemas.  He argues that the optimal solution assumes that everyone is just as smart as you are, and will also choose the optimal solution, meaning same as you... therefore nice is actually better.  The game does not pass this judgment... but I'll certainly describe the logic.

As a shorthand I'll use the terms Traitor, Noble, Scoundrel, and Dupe, in order of outcomes by preference.  A given PD (prisoner's dillema event) can have Noble/Noble, Scoundrel/Scoundrel, or Traitor/Dupe.

It fits really well with ASTC.  I'm just not sure how exactly to manage it.  The basic idea is clear.  When executing any task (the sort of thing that one rolls for in most games, and Raises/Sees for in DiTV, etc.), you extend a hand with a stone in it.  Blue means honorable methods, red means treachery/cunning methods.  The opponent (or GM) answers with a stone of his own, you both reveal.  The outcomes follow the Prisoner's Dilemma pattern.  What I'm trying to pin down is how to have those outcomes reflected in play outcomes.  I also want it to function as conflict, not task, resolution... meaning that individual tosses should cumulatively indicate the overall victory in a deterministic way.

What I've got so far looks like this:

You have a number of traits on your character sheet.  (I'm thinking maybe the 'rouge' side is mostly motivations/goals, the 'bleu' side is mostly methods/skills/advantages.)  Someone takes an action; you PD for it.  Traitor/Dupe means one side wins (by in-game duplicity or treachery, etc), one loses.  Noble/Noble means that the narration advantages you both.  Scoundrel/Scoundrel means that you both fail.  Then either player, if unhappy with this outcome, may expend/exhaust a trait to continue the conflict, and we PD again.  This does not override the preceding outcome or narrated events, instead it adds to it.  As in DiTV, whether or not you succeed at X is not in question and based solely on your assertion, but whether it ends the conflict is answered by the system.  If you run out of relevant traits then you'll have to accept things as they stand.

The question here is how the four levels of outcome of the Prisoner's Dilemma get mapped in game-significant terms.  It can't just be win/lose or the whole point of the PD is lost; there have to be other degrees to it.

One option is to use (essentially) fallout for this.  Traitor gets a potential stat gain (experience) and the win.  Noble gets the possible stat gain (experience) OR the conflict win; they can negotiate who chooses which.  Scoundrel suffers fallout (price) OR the conflict loss; again they can negotiate which.  And Dupe gets fallout and the conflict loss.  

We can do this cleanly by using the stones themselves.  Keep the stones that are bid until after the conflict.  Keeping a blue stone is 'glory,' a chance at good things aside from the stakes; keeping a red stone is 'justice,' a chance of bad things apart the stakes.  A Traitor trades stones with his Dupe, plus wins the conflict; a Noble either keeps his own stone (as glory) or trades it for a conflict win; a Scoundrel either keeps his own stone (as justice) or ditches it by losing the conflict.  At the end of the conflict the more glory stones, the better the chance of positive rewards; the more justice stones, the higher the chance of fallout.  (Tentatively, draw once from the bowl per glory; if you draw even one blue you get experience.  Then draw once from the bowl per justice; number of reds drawn is degree of fallout.)  At the end of the conflict all the stones bid or drawn go back into the bowl, possibly causing the world to tip.

A few fillips suggest themselves; for instance, I think that correctly guessing which of their personas your opponent is currently playing should be analogous to expending a trait, or even better.  But this is detail work.

Two things stand out as weaknesses of this as written.  One is the way in which Noble/Noble and Scoundrel/Scoundrel outcomes get negotiated.  Who chooses when?  What happens if consensus is not reached?  The other is how to handle static or inanimate conflicts with this system, when no person is on the other side to betray or be betrayed.

I welcome (of course) general comments on the system.  I think it's pretty cool.  More specifically, however, does anyone have any (a) concerns that this will not be a functional conflict resolution mechanism, or (b) suggestions regarding the weaknesses identified above?

- Eric

[Jason E Leigh]

Eric:

Stunning use of the Prisoner's Delimma!

a) For the background of ASTC, the mechanic is an excellent choice.

b) If concensus is not reached in doling out the rewards, force them to bid traits again - a conflict nested within a conflict - playing inward until one person clearly wins, which then dominoes back out of the nesting to all the nested conflicts.  That's one solution.  Another solution would be a free draw out of the bowl - with the color determining which reward one got.

b again) I wouldn't worry about static conflicts.  I'd say you can trace all conflict back to an actor (character).  If a character is trying to cross a chasm, the questions are For What Purpose?  and Who Would Oppose that Purpose?  That opposition then becomes the controller of any forces that threaten the character's crossing.  If they are just crossing a chasm to get to the other side, where's the conflict?  Just let them do it.

Hope this helps.

Cheers,


Jason

[Bill_White]

This is pretty cool, and while I'm not sure I grasp fully all of the implications of the system as you've stated them, I think the notion of employing a PD-based conflict resolution mechanism has strong possibilities.

How about this:  in any given "round" of conflict, a player of STC has two choices:  the Noble option (blue) or the Scoundrel option (red).  If both choose the Noble option, the conflict is not permanently resolved, but each player gains some immediate benefit, currency, or reward (and/or get to remove stones from the bowl).  If both choose to be Scoundrels, they both lose some in-game currency (and/or have to throw stones into the bowl).  But if one chooses red and the other chooses blue, the Scoundrel gets to narrate what happens--but he has to narrate as the "victor" the one who has the most blue stones in the current conflict.

The benefit or in-game currency is probably red or blue stones, of course.

Really cool mechanics idea!  I had made some notes on this a while back, but never used them.

Bill

[Harlequin]

Thanks, guys.  I appreciate both the praise and the comments.

Some quick notes - Jason, the nested exchanges (not conflicts, terminology note) is basically the same as one end of the above.  Your solution would essentially be the one where in an impasse both players are assumed to opt for "win" rather than "glory" and thus they end up needing to continue.  That's certainly one of the options I'm considering; the opposite assumption (at an impasse you both 'choose' glory rather than victory) is also tempting.  Probably one of the two will go in to the playtest version.  Making them both bid traits to continue in this case is a nice touch, as compared with one player spending a trait to evade an outcome he doesn't like.  Come up with a win/win solution or you both spend to continue.

And yes, I am strongly leaning toward something like your suggestion re: static conflicts.  Again it's terminology - crossing the chasm is not conflict.  Trouble is that there are some statics which can be pretty rewarding to play through - not "can you cross the chasm" but "can you heal the wound," for instance.  What's more I would like, if possible, to have the creation of art and the labours of science be in-game relevant acts, making the PCs true Renaissance men (courtiers, artists, thinkers, duellists, etc.) by default.  And if I want to focus on the work itself, rather than the art as vehicle for the competition between artists, then I need something to handle that.

Hmm... writer/ghostwriter, singer/lipsyncher, scientist/fraud, doctor/quack... maybe there is some potential here for this sort of thing in art and science after all... have to think on that.  An idea of 'investing' stones in the work itself comes to mind, with the quantity being public but not the type.  Hmmm.  Ooh - that could be cool.  Invest your glory/justice stones rather than drawing for stats effects from them.  Trade (possible) stat advancement for improving your art honestly; or evade (possible) stat loss by indulging in fraud.  That has serious potential.

Bill - I had thought through a setup similar to that, even going so far as to use a divorced currency (coins, which goes well with wealth/power) as what you build up over the rounds.  The trouble is that this model (and yours) is a little deterministic.  Even if we use the "or" version of both your and/or currency exchanges, both players either advance at a uniform rate toward (or away from) victory, or knowingly break that pattern by taking the reward option.  I would like the full range of final outcomes (including things like my Noble/Noble split where they agree to give one the victory and the other one a glory stone - a win/win situation such as a duel where the loser gets cosseted by the beautiful courtesan, etc) to be possible, which seems to actually be easier with the "this round is final unless overriden" version.

- Eric

[Jasper]

This is really cool Eric. I love PD, and am glad to see it being used; I wasn't sure about the tipping stuff, but paired with the PD, it's much cooler. Of course, one thing to consider is that the dilemna of PD might not be such a dilemna if the bowl is nearly full, depending on how is works.  You just have to make sure it remains a difficult choice. And of course iterative PD is more complicated than a straight one-shot.

As for the conflict resolution, how about:

If you lose a PD as a Scoundrel, you can extend the conflict with 1 trait. But if you lose as a Dupe, you have to activate 2 instead. This gives the unequal win payoffs PD calls for (via a more or less assailable victory).


Also, with or without the above, you could tie the world-tipping addition of stones to whether a PD with defection is extended. Frex, a stone only gets added if a defector wins the first round and isn't subsequently opposed.  This will depend on something I didn't quite pick up: are you imagining the players wanting to keep the world from flipping? Or do you see it as a kind of inevitable thing, and it's just the timing that matters?

[Harlequin]

Just quick - I see the tipping as inevitable, generally neither very desirable nor very undesirable.  And the way I'm seeing it right now, all of the stones bid during the conflict stay out, and then go back into the bowl en masse at the end after draws for glory/justice are done.

[Bill_White]

I see your point, and you're right that enabling a distinction between experience and fallout (or glory and justice) as part of the conflict system is a desirable feature.  

An aside:  This might be too limiting, but perhaps traits could be quantified in terms of their stone limits--a certain number of red, a certain number of blue.   The value of this would be to provide opponents with a certain amount of information about the other party's possible strategies.

And a function of experience would be to change your stone limits.

Bill

[Jason E Leigh]

Eric:

One other thought I had, and I don't have my refs with me right now or I'd give it to you exact - there's another common model of PD called "Chicken" I think (after the try to crash your cars into each other to see who blinks game), with a different, non-symmetrical pay-off structure.

The point about this being an iterative PD is a good one, and it means, because of the symmetry of the payoff, that there is an optimal solution over time.

I think if you use something like the Chicken payoff model, it makes it harder for one player to find an optimal solution over time that will allow them to dominate the game.

Cheers,


Jason
"Oh, it's you...
deadpanbob"

[Harlequin]

I'd be interested to see that - though I'm not personally convinced that this kind of iterative PD has a truly optimal solution (other than 100% Noble-Noble per Hofstadter's logic).  Or rather, its optimality is very fragile, and easily broken down by the other factors in play.  (The narration of an act inclines you to a certain bid; the changing personas incline you to a certain bid; situational risk-aversion or risk-inclination will affect it, and so forth.)  Also, as Axelrod found, the optimal strategy is in fact a function not only of the strategy itself but also of the strategies it's being used against; an optimal strategy when it is facing copies of itself or true-random functions may not be optimal when facing trust-prone or betrayal-prone environments.

So I'm not sweated about optimization.  A little optimization and game-theory on the part of the players will probably improve play, I betcha.  At most I may need to include a paragraph about the 'Hazards of Optimization' to discourage people from divorcing the bid from the other considerations, pointing out that in addition to being silly it's logically flawed.

Looking on Wikipedia for the 'Chicken' variant, it consists of any situation where (in my terms here) Scoundrel is a worse outcome than Dupe.  Hmm.  I think I don't like it; I think the original one suits my themes better for this game.  Better to live in a world of scoundrels than to be betrayed by one; better yet to be able to trust.

This does make me realize that there will exist incentives for players to actively seek one another out for challenges... because (assuming they can trust one another) they both stand to profit.  Thas' cool.  The temptation to betray will always be there.  One could combat pathologies in this vein by allowing the GM the privilege of forcing a player's bid, in secret, and then instructing the GM not to use it but never to deny having used it.  Its existence as an excuse would be sufficient - can you say 'plausible deniability?'  However, I don't think there's a sufficient likelihood of dysfunctional play that it's worth spending rules on combating it.

Particularly with the ideas about works (of science, art, etc) I mentioned in my earlier post.  I think I will be adopting those; they give a good direction for the game.  You have the option to put your glory or justice stones into your works instead of drawing for them.  In that context, they're almost each as good as the other, save that using justice stones opens you up to being revealed as a fraud down the line.

Oh, and Bill - the idea of having stone limits is an interesting one.  Thank you; I think that right now it's not needed, but it's worth putting in the toolbox for repairs later.  A similar concept came up when discussing it last night with someone, who originally misapprehended it as designed for LARP.  I said no, in a low-trust environment such as LARP it obviously wouldn't work as written.  There, we'd probably give each player a limited pool of stones, and at the end of the night every blue stone you were up from where you started you'd draw for experience, and for every red stone up from where you started you'd draw for fallout.  For the tabletop, however, I think I like the imagery of simply scattering stones all over the table willy-nilly for anyone to use.

Any further ideas on the static challenges thing?  I think I can work past the negotiations thing.  But I would still like to, if possible, have an engine that could handle challenges of the "do you heal him?" sort.  And I'm not really seeing one.  It's possible that "Expertise as a doctor" is a type of Work, and being wounded to degree X chiefly just requires being treated by a doctor whose Work is at least X stones.  Given that I'm having trouble coming up with other setting-appropriate static challenge situations, this one case might suffice.

- Eric

Edited to remove stray BBCode tag.

[Mike Holmes]

I think that you may have to take the next step, and actually learn the math behind game theory. Basically the differences in the different forms of Prisoner Dilemma are in terms of the magnitude of the values of the different results. The original problem is usually stated in terms of years of imprisonment that you get if you narc, or don't narc. Everyone's seen the PD used on cop shows. But it's actually subtly different each time depending on what they offer.

The matrix of results for the standard PD can be seen here: http://pespmc1.vub.ac.be/PRISDIL.html

So the question is what are the values of your options? Let's assume they are all of equal value (with fallout and loss being a -1 to make it zero sum).

Traitor - Stat Gain and win (2)
Noble - Each gets one of stat gain or win (1)
Scoundrel - Fallout or loss (-1)
Dupe - Fallout and loss (-2)

Actually I'm not sure about the value of fallout - isn't it a positive thing, generally? (And what if negotiation doesn't work, roll?) So check the math.

Then you have to consider if, in fact, they actually are all of equal value. Is a stat gain really equal to a win? If the two ends actually have different weights, you'll get skewed results.

The standard looks like:
Traitor - (2)
Noble -  (1)
Scoundrel - (0)
Dupe - (-2)

(Multiply by 5 to get the sample chart results)

So, to get the standard outcome of testing for iterative PD play (and are you sure this is what you want?) you want to make yours match. If fallout is a negative, then co-operating will be much more likely, as the result of being a scoundrel is worse than in the normal PD. OTOH, if it's positive, then being a dupe isn't so bad, so again, agreement is more likely than the standard again.

Mike

[Harlequin]

Mike - I'm not looking to in any way replicate the optimization patterns that you see in analysis of the iterated PD.  Frankly those optimizations are only slightly optimal (other than the Southampton thing where they submitted both "winners" and "losers" which would recognize each other and maximize the winners' score).  As long as T>N>S>D, you get the basic pattern; whether or not you directly replicate those optimization patterns is immaterial to the game.

In addition to outside factors (such as choosing to act in-character per the scene, rather than per any pattern, and also choosing to act based on a cool narration which implies a bid), the situational weighting of preferences throws out the optimization anyway.  Glory stones are a good thing, but (a) they may diminish in value when you already have several in-hand, and (b) the value of a stat gain will depend on your current situation, and the value of the win will depend on the stakes.  Justice stones are a bad thing [the fallout they lead to is negative-only; it's a DiTV uniqueness to conflate this with experience], but again (a) they may diminish in value if you already know you're screwed, and (b) the cost of fallout compared to a loss varies by situation.  Also (c) in some circumstances fallout may actually prove a positive, such as if you're working on a Work such as a really cool opera which is actually written by your daughter (lots of points worth of fraud).  So all of these things mean that the values in the PD matrix are all over the map; they're not fixed at all.

In short, getting the "standard outcome" for the iterated PD is exactly what I don't want.  That would be somewhat akin to reducing Dogs' system to the core math and thereby taking one glance at the dice on the table and announcing the winner.  Perhaps theoretically possible - in fact much easier, in Dogs, than here - but contributes nothing to play.  So I think we're on the same page, except that you may have mistaken my goals.

Let me try to bring this thread back on track.  Optimization strategies are hors de combat except if they lead to a concrete argument about my part (a) in the original post - they cause the system to break down.  What I'm interested in is whether people have any suggestions regarding the weaknesses of the system I identified - negotiations and statics.

With reference to the negotiations, I don't think the original post was clear enough.  Let me reword it.  As originally conceived:
-> If you throw Noble/Noble, then the players have a chance to negotiate a win-win situation of a few types.  Both of you get the stakes (you find a true win-win outcome within the stakes as written).  One of you wins the stakes and the other gets a glory stone.  Or both of you get glory stones and neither achieves the stakes yet; each has the choice of whether to give, or to pay Traits to continue.  If you can agree on one of these outcomes by consensus, it happens.  At an impasse?  Not yet clear.  Probably you default to the last option.
-> Scoundrel/Scoundrel is parallel.  By consensus agree on (a) we both lose the stakes, (b) one loses the stakes and the other takes a justice stone, or (c) we both take a justice stone but pay to continue the conflict.  At an impasse I would guess that again we default to the last option.

My problem with this is that it's not half so elegant as the rest of it.  The opportunity to work out a win/win outcome is very pleasing; I know far too many systems which disallow non-zero-sum win/win thinking.  For a game about moral approaches I think this pattern of thought is very valuable.  But the "requires consensus" is kludgey.  I would rather have something which again promoted win/win and lose/lose thinking patterns, but did not require them, and had the appropriate worths attached (T>N>S>D).

Hmm...

- Eric

[Mike Holmes]

You're coming dangerously close to saying something like System Doesn't Matter. I mean the question of what a system does must be based on "all else being equal" when that's an unknown. No, it won't predict 100% of the results, but it will give you the trend in question that informs the player over time.

Now, if you're saying that the calculations are so complicated by the shifting values, and obscured by other activity...then I think you might be right. That is, it might be "close enough" that any marginal differences in game output will be negligible effects on play (other than intended). I don't even want to do the math to figure that out. At that point it's much easier to just playtest.

So you're probably right.

Looking at the negotiation rules, what happens if they can't agree, and they can't continue (either because they don't want to do so, or because they are out of stuff to burn to do so)? Is that the tie, then? That is, neither get the stakes? What if the stakes are zero sum? That's a problem that I ran into with HQ not too long ago. What if the conflict is attempting to take something away from somebody so that you have it? What's a push there mean? Neither have it, and they can't proceed somehow?

Generally I'm wondering about matching narrations to some of these results. Will that always be possible with all conflicts? Rather, I have a feeling that you may have to have more than a simple statement of stakes in order to ensure that the outcomes can all occur without stretching things.

Mike

[Harlequin]

(That the math would simply be too complicated to perform is exactly where I'm at.  No player will be able to, either.)

Can't agree and can't continue... hmm.  Good question; I don't have a ready answer.  One of my thoughts here is that there will be Traits which are easy to replenish - for the bleu, relationships, and for the rouge, motives - and ones which are quite difficult to get back.  Obviously you'll have more incentive not to use the latter.  This pushes back the question of what happens if you can't continue, by making that point a more extreme one.  Not an answer per se, though.

One thought is the tie rules in - I forget which game - where rather than a tie, what happens is that the conflict is superseded by something else. But I'll have to think about the applicability of that, here.

Your last question is also a good one.  Part of the answer is that because I want to promote the non-zero-sum outcomes wherever possible (because it's the opposite of what so often happens with mechanics); as such, while I agree that not all answers may be available in all cases, I also want to put some pressure/reward into encouraging those solutions.  [For instance I'm considering having Noble/Noble give glory stones not instead of the shared win, but in addition to the shared win, if you can come up with one.  Keep the stone automatically; work out a win/win or pay Traits to continue.  Might need to increase the Traitor's payoff to compensate.]

Another part is that I'm not sure that all outcomes need to be viable for any given stakes.  Not if players know that committing to narrate such an outcome is part of taking that game action.  Like making a statement in Polaris; don't do it if you're not prepared to live with it.

Even put together, this doesn't fully answer your concern, though, and I think you're right that it may require changing how stakes are set; I also think it can only be checked through alpha testing.  I'll do so and post again.

- Eric

[DevP]

Also (c) in some circumstances fallout may actually prove a positive, such as if you're working on a Work such as a really cool opera which is actually written by your daughter (lots of points worth of fraud). So all of these things mean that the values in the PD matrix are all over the map; they're not fixed at all.

So, perhaps is Fallout what is necessary to be used up in order to create that important art via static tests? Pain is necessary to create achievement? More generally, I feel that glory shouldn't be purely negative, because in such cases players may shy away from the Scoundrel/Traitor option, on the grounds of politeness to other characters. If this is padded somehow, then there is still the fundamental feeling of being "screwed over", but there is the consolation that you've somehow awarded the Dupe something worthwhile.