World's best Pathfinder economic data visualization blog

Month: April, 2014

Efficient design of a self-licking icecream fantasy cone.

You might be wondering where all the pretty figures have been these last few posts.  It isn’t that I have forgotten the aspiration of my blog, its that I couldn’t find a good module in Python for simulating game theory interactions of wizards.  Worse yet, while I fiddled around with 3d visualizations of the predation-cooperation-ignore boundaries,  I could not escape the sense that any particular results of those boundaries are not useful to anyone whose campaign isn’t reflected by the specific parameters. Why implement a generalized solution to wizard competition if the initial conditions (the setting of the campaign) are going to make all the difference? 

In real life, a generalized model’s specific parameters could be compared with empirical results to get meaningful predictions, but sadly (happily?) that isn’t an option here.  The conceit of this blog is to look to the Pathfinder rules and infer about the setting, but sometimes the rules aren’t there to fill in the gaps and the gap is too large to fill in with guesses.  

From a world-building hobbyists’s point of view I am very inspired by the infrastructure  Alexis at Tao of D&D has built, but my skill set urges to me to take a path toward a solution that has more automation, more programming, and less map-building.  I aim for  a modeling engine that would estimate the price effects of a dragon’s hoard being spent in a small kingdom, or the supply limitations caused by kobold’s plaguing an important iron mine.  When I think about getting to that end-state, I know there will be assumptions and code infrastructure to be built, but it is not yet clear how much micro-foundation, such as agent-based modeling, needs to play a role  to get price-level  and macro population effects.  I don’t see myself as using this tool to get specific information about how Smith Brown’s hammer broke today, and I don’t have a server farm to through at world-simulation.  

What needs to be coded to get to a model that can take local events like a dragon slaying or war, and translate them into GM interpretable story results?  If anyone has any insights or suggestions, I am all ears (or all eyes on the comments).

Wizards are just like you and me.

I posted four questions about wizards last time, but it has not been easy to decide where to start. I am starting with the cooperation incentives for wizards because this is a topic that is relevant to setting and roleplaying as well as analysis of wizard economics.

Two wizards who encounter one another face the same kinds of incentives and decisions as you or I:  Avoid the encounter, seek some constructive benefit from the other person, or try to take what you can by fraud, stealth, or force. Just as in the real world, what stops people from robbing everyone they meet depends on the person, but the kinds of obstacles to predation include things like social/moral inhibitions, having something better to do with your time,  fear of losing something in the conflict,  and the limitations of what can be gained by attack.  Qualitatively, none of this is different for wizards.

What is different?

  • Two wizards encountering may not suspect each other of being wizards unless there is a display of wizardly eccentricity (familiar/staff) or magic (mage armor/mount/something flashier).
  • Weak wizards cannot spare magic for display but not all strong wizards will advertise their magic. This is not really a difference from the muggle’s situation if we substitute “wealth” for “magic”.
  • Wizards are smarter than average, but not necessarily any wiser.  The smarter the wizard is, the more magically powerful he is, too.
  • Wizards can reasonably expect another wizard is more dangerous the more valuables he carries.
  • Wizards can reasonably expect that another wizard has more to offer from cooperation the more valuables he carries.

Put differently, there will often be a high uncertainty about the payout of cooperation and predation because each wizard cannot be sure whether he has met a wizard nor how powerful that wizard might be. If the other wizard is advertising his power, a wizard can take that as a sign of foolhardiness, confidence, or security. 

In a situation where a hidden wizard H encounters a showy wizard S, H will have an opportunity to evaluate S’s power before revealing himself for the encounter. This is a big advantage for H and will tend to tilt the balance toward wizards staying hidden when they don’t feel safe. In an environment with lots of stranger-muggles around, like a city, this is going to offer wizards plenty of muggles to hide among. A solitary wizard might reasonably be able to keep a low profile if desired.  Anonymity helps protect wizards, especially weak ones, in every day encounters with strange wizards.

From the point of view of a hidden wizard approaching a possibility of an encounter, such as a settlement or a figure in the distance, here are some of the factors that might shape the payoff numbers:

  1. S is for security. It the cost inflicted by third-party the external punishment for selecting conflict.
  2. P is the power of the wizard evaluating his decision as he approaches.
  3. O is the expected power of the wizard who might be encountered.
  4. C(P,O) is the estimated payout of cooperation is the value of new spells gained in trade minus copy cost. C increases with both P and O. As an equation, it might look something like: C(P,O)=a+bP+cO+dPO where b,c, and d are positive real numbers.
  5. R(P,O,S) is the estimated payout for choosing predation. It is the value of spells gained from conflict minus losses in conflict.  R increases with P, decreases with O, and decreases with S. As an equation, it might look something like: R(P,O,S)=a+bP+cO+dO/P-S where b is a positive real number and c and d are negative real numbers.
  6. I(P) is the value of ignoring the conflict. It represents what better you have to do with the time. I increases with P. As an equation, it might look something like: I(P)=a+bP+cP^2 where a,b, and c are all positive real numbers. This is an important consideration because wizards, like everyone, have other things they do than hunt for people to rob or befriend.

If each wizard (P and O) in the encounter   both have some idea beforehand about how powerful the other might be, both P and O will can make informed choices based on their comparative strength and the prevailing security of the encounter area.  When one party is much stronger than the other, the strong party would be tempted to predate or at least ignore the other because of better uses of time.  Cooperation makes more sense when the parties are near in strength (making combat uncertain).

The security environment would be the controlling factor, which should be no surprise when you think of it.  Encounters in the wilderness are just more dangerous.  When S is large, noone who isn’t desperate chooses predation because some third party force will come down harder than any payout. This will make the encounter space safer to choose to be showy and in turn make the possibility of identifying potential collaborators higher.  For this to happen, S has to be the kind of security who will protect both wizards, or only the protected wizard will feel safe to show himself in public.

When S is low, aggressive wizards choose predation freely when R(P,O,0) is high enough. This raises the incentive for weaker wizards to choose to hide. This makes both cooperation and predation rarer. Only the foolhardiest and most confident wizards will choose to advertise themselves in those situations.

Cooperation is fostered by a secure environment for both parties who can trust that predation is generally off the table.  This might come from law enforcement that respects the rights of both wizards and will enforce against predation credibly. This could also arise in a situation where the weaker wizard has the benefit of local support and the stronger wizard, while unsupported, stays hidden until reaching out for cooperation. Foolhardy, friendy wizards are more apt to cooperate even if meeting in the wild, alone; but they are also liklier to be killed by bandits or predatory wizards.  Only the luckiest of them will survive to old age and high level.  

Factors favoring cooperation:

  • Fair strong law enforcement or institutions providing that sort of effect in the context
  • Strong party has reputation to protect against claims of predation
  • Strong security favoring a publicly known, weaker wizard
  • Desperation (very low or negative I(P))
  • Poor judgement (e.g., low wisdom)
  • Both parties have a preference for cooperation

Factors preventing cooperation:

  • Insufficient security prevents both parties from revealing themselves
  • Showy party is judged too strong to take the risk by weaker party
  • Showy party is deemed too weak to be worth the time by stronger party
  • One party has a dispreference for cooperation
  • Rents extracted from being sole provider of specialized service (i.e. only one who knows a special, useful spell), or from being locally dominant caster and jealous of potential loss of revenue from students and local spell casting buyers.

As I said above, security is key for wizardly cooperation and institutions are typically the key to security, whether they be wizardly or other institutions. There are lots of books and blogs on how ordinary muggle institutions arise to provide security, and I think a lot of that would apply to wizards.  The development of a secure cooperating community of wizards was probably not automatic prior to the development of high security settlements, but when chance provides an acorn of security  and cooperation, it might not be hard to grow that acorn into an oak of a strong wizardly institution because a wizardly institution will be credibly quite powerful, wealthy, and potentially able to provide security generally.

The prevailing security of the settlements a player encounters is likely strongly determined by the game’s setting, but there is no reason that great plots cannot be made out of the struggle to build institutions, raise security level, and ultimately make the game a safe place for even for a 1st level diviner to carry his toad familiar in public.