Tuesday, February 12, 2013

Settlers of Catan... the monetary version


I've been playing the game of Settlers of Catan for ages. Over time I've gotten less cutthroat and more philosophical about the game. What I've come to realize is that Settlers is a great tool for both thinking about monetary phenomena and building different sorts of monetary economies. In this post I'll assume a basic knowledge of Settlers—if you haven't played the game by now, you're living on the moon.

1. Catan isn't a barter economy

The first thing worth noting is that Catan is not a barter economy—it's a monetary economy. This might seem like an odd thing to say. After all, the trades that we see in a typical Settlers game are all commodity-for-commodity trades.

To see why it's a monetary economy, imagine the case of autarky, or a Catan in which trade is prohibited. Here, players can only build structures using cards earned from tiles on which they have a settlement. The value of a lumber card in an autarkical economy is derived solely from its use-value, or its ability to help build settlements and roads.

The moment autarky is lifted and players are allowed to trade resources amongst each other, resource cards provide their owners with a whole new range of services. Not only is a lumber card valuable for the settlements and roads it yields, but also for its ability to purchase things from others. It has become a medium-of-exchange. Given the unpredictability of dice rolls, owning a stock of readily-tradeable exchange media provides players with wiggle room, or monetary optionality. Because an option is valuable, resources that provide optionality earn liquidity premia. The more liquid the resource card, the broader the option it provides and the larger its premium.

Monetary phenomena like monetary optionality begin to emerge the moment we exit from autarky—we don't have to wait till some hypothetical item called "money" appears on the scene in Catan, nor for so-called barter to disappear. All media-of-exchange, whether they exist in our simple Catan economy or the real economy, have money-like properties. In fact, I'll show later that there is no such thing as "money" in our modern economy, only a universe of media-of-exchange that differ along a spectrum of liquidity.

2. Patterns of resource monetization in a Catan economy

The Catan universe is a well-balanced monetary economy. By well-balanced, I mean that we tend to observe an even distribution of trade. Put differently, since Catan's five resources are all equally marketable, none of them earns a superior liquidity premia.

There are ways to tilt the rules of Settlers so that trade patterns get more skewed. One way to do this is to penalize trade in certain goods. For instance, say we institute a rule that continues to allow for full trade in sheep, brick, ore, and wheat but only permits lumber to be traded when a six has been rolled (limited autarky in lumber markets). This inhibits lumber cards from serving as full media of exchange. As a result, lumber loses some of its optionality and will trade at a discount to its prior price. The distribution of trade will now be skewed away from lumber towards the other four resources. If we penalize all resources but one, we would skew the pattern of trade dramatically in this resource's favor.

Another way to affect the distribution of trade is to endow certain resources with unique properties. Let's say that ore is more storeable than the other commodities. The rule in Settlers is that when a 7 is rolled, any player with eight or more cards must lose half their hand. If ore cards don't count to the total when a 7 is rolled (they are storable, after all) then players will be able to hold larger hands as long as they cushion their hand with ore. Players will begin to trade for ore not because they wish to build a city with it, but to protect their hands from 7s. This could increase the incidence of ore cards in trade relative to other cards. The more liquid ore cards become, the more will their monetary optionality increase, as will their liquidity premium.

There are all sorts of ways to tilt the distribution of monetary trade. Be creative.

3. Let's try Settlers chartalism

The idea behind chartalism is that some external monopolizer, say a gang or a king, sets an obligation upon citizens that can only be discharged with a certain type of settlement media. This media doesn't have to be a commodity. It might be an intrinsically useless token.

Let's imagine that the robber in Settlers requires a bribe from all players whenever a 7 is rolled. If a player doesn't pay the bribe, then they must sacrifice two cards. Say that the bribe must be paid in the form of an intrinsically useless $100 Monopoly bill. Players can only purchase the Monopoly bills from the robber on their turn for one resource card. Presumably players will purchase $100 bills since the 1 card cost exceeds the potential loss of 2 cards.


A player who has already bought enough Monopoly money to satisfy the robber should a 7 come up may wish to sell excess bills to players desperate for protection. Monopoly paper bills thereby join the five existing resources as a media of exchange in Catan. We might be able to tilt the distribution of trade in favour of the chartal medium if we encourage its marketability through rule changes discussed in section two.

4. Credit-based settlers

The existing rules of Settlers prohibit credit transactions. Relaxing these rules allows us to introduce a whole new range of resources that can be used in trade—each player's future earnings power.

There are infinite ways to structure credit transactions in Catan. Informal verbal promises are one way. I tell my trading partner that I'll buy a lumber from them now for an IOU of two sheep in the future. Due to their informality, these promises are unlikely to become liquid.

To really tilt the distribution of trade towards credit, we probably want to create standardized paper credit contracts. Standardization allows for quick appraisal, and this lowers transaction costs. Transcribing the promise onto paper will encourage its negotiability, or exchangeability from player to player. The more we streamline the process, the more likely that credit will become Catan's most liquid traded resource. The simplest IOU I can think of is a one-time paper promise to pay out all production from a 6 or 8 tile. The issuer can easily satisfy this obligation since they don't have to trade away for the media to settle it—they produce the media themselves.

When we allow for credit, players are acting simultaneously as bankers. The player that succeeds in getting his or her credit to circulate from player to player has effectively increased their purchasing power relative to everyone else and will be able to advance through the game much quicker. Players that push too close to the sun will find themselves unable to meet their outstanding promises and will default. They'll lose the trust of fellow players and will find it difficult to issue credit again, their advancement in the game slowing.

5. The social contrivance of a fiat Catan dollar

Paul Samuelson famously described how the contrivance of fiat money would allow members of an economy to efficiently solve the problem of passing on savings over time. Through a "grand consensus," worthless "oblongs of paper" would be accepted into circulation. This sort of paper is different from chartal Monopoly paper since the latter discharges a particular obligation. Samuelson's oblongs are merely bits of paper. They have no non-monetary use whatsoever.

Could we get players to accept mere paper? Our first guinea pig will only do so if they know for sure that the next player will accept it. Absent a significant amount of negotiation and coordination ahead of time, its difficult to imagine why the first player will ever trust the future negotiability of paper. Far safer for him or her to just refuse any fiat paper trades. Might players spontaneously negotiate a set of rules to encourage the circulation of Samuelsonian paper? Perhaps, but if the game already allows people several trading technologies—trade in resources, trade in chartal Monopoly money, and trade in credit—will players want to devote resources negotiating an expensive institution like fiat paper? I doubt it.

6. Catan Money?

Can the rules of Settlers be manipulated so that Catan approximates our modern world in which there seems to be one universal medium-of-exchange called money? Could we get ore to appear in all of Catan's trades, or Monopoly money, or the circulating credit of one trustworthy player?

As I pointed out earlier, we don't have to. In the real world, there's no such thing as a universal medium of exchange. Rather, we have an almost an infinite range of media that vary in terms of liquidity. The "dollar", for instance, refers to a number of different exchange media: paper dollars printed by the Fed, electronic dollars created by the Fed, private savings account dollars, chequing account dollars, eurodollars, traveller's cheques, credit card dollars, and more. Private chequing account dollars can be broken down into Bank of America dollars, Wells Fargo dollars, Citi dollars etc. The fact that these various media are denominated in the same unit should not confuse us into consolidating them into one universal medium-of-exchange. A US paper dollar, for instance, is a far more liquid instrument than a hamburger patty, but it still only appears in a small percentage of total US trades. As long as we can manipulate a game of Settlers to show a skewed distribution of trades, then we've sufficiently approximated the real world.

7. Catan economics vs. modern economics

Setting up a stylized Catan environment in order to explore monetary phenomena is akin to the approach taken by modern monetary economists. Economists realized long ago that exchange media simply had no role to play in a stylized Walrasian environment. In a world with an omniscient auctioneer who calculates the prices and quantities of all trades, and in which all trades are cleared at a central clearing house, there's no room for monetary phenomena like media of exchange or liquidity premia to arise.

To get "money" into an economy, modern economists start by introducing various refinements into a Walrasian environment. Rather than have individuals meet at a centralized market, Kiyotaki and Wright (1993) have traders meeting randomly and pairwise. Wright, Trejos, and Shi (1995) replace the auctioneer with traders who are capable of negotiating prices bilaterally. Our simple Settlers environment easily captures decentralized search and bargaining.

Some environments created by modern monetary economists are downright odd. The modern work-horse Lagos/Wright model sets up an environment with day and night markets. Day markets are bilateral and anonymous while night markets are centralized. Dror Goldberg imagines different cities which specialize in a certain good. Traders must trek between cities to secure a consumption good. Settlers, of course, will appear odd to anyone seeing it for the first time. Manipulating the rules of Settlers to see how we can generate monetary patterns is very much like letting rational agents loose in an Lagos/Wright sci-fi environment. The advantage of the former is that it's fun and real people are testing out the model, not imaginary agents.

Try experimenting with some of these rule changes the next time you play Settlers and tell me what happens. Even if you don't get around to it, hopefully I've convinced you that Settlers provides a great model for thinking about monetary economic phenomena.

6 comments:

  1. Fascinating post, JP. Please update with results.

    Have you played any other economic/business board games? I've read good things about the following:

    Power Grid
    Container
    Age of Industry
    Automobile

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    1. I've played Power Grid but not the other three.

      I prefer Settlers to PG. I like how most of the fun is generated spontaneously through the trading aspect of the game. If I recall, rules in PG restrict trade and resource allocation so the game is less spontaneous.

      I will be sure to update with results. The tough part is recruiting willing participants. Most people think I'm trying to rig the game so that I'll be sure to beat them.

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  2. Hey JP,

    My friends and I play Settlers on occasion, and we do allow for credit-type transactions. We typically have an arrangement like the simple one you described where one player gives a lumber for two sheep in the future, but with the caveat that the sheep must be delivered immediately as they are received.

    We like this for a few reasons:
    1. It shifts potential credit risk to sort of "duration risk" (to borrow a bond market term). In other words, you might be more inclined to give your lumber away to someone who has a 6 or 8 on sheep rather than someone with a 3 or 11, since you are likely to receive your sheep sooner. Basically, counterparty credit risk becomes counterparty duration risk (note that this risk is different for each resource for each player, so basically any trade has to be priced differently).

    2. Overextension of credit doesn't lead to default, rather, players who borrow too much will simply be forced to give away their assets as they come, directly crippling their plans, rather than having to rely on player mistrust to penalize overeager borrowers. Depending on how default is treated in other frameworks, this might lead to more responsible borrowing.

    3. It's simple and pretty natural, a lot like your pay out on the next 6 or 8 example.

    Just wondering what you thought of this, and also what other sorts of borrowing schemes you've used.

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    1. Hi Jim,

      That's interesting. Any plans on introducing credit risk? Has anyone purposefully defaulted near the end of the game in order to win, or is that explicitly against the rules you've devised?

      Have you made your credit negotiable? Can it be passed on across traders, say like a mortgage-backed security can be traded beyond its original owner?

      We've played with full credit risk and are debts have been negotiable, but my friends were very suspicious of credit trades so not many were done. They also think I'm creating this new set of rules to stack the game against them, so they are not willing participants. Maybe I should do what you do and start with term risk only, then introduce credit risk later.

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    2. I don't really see the upside of introducing a real credit risk. It would greatly complicate the game for not too much benefit past the simple term risk. Why? Default is a complex event. Even in the real world, with very intricate contracts describing credit agreements, there are always lawyers involved in the event of default. This is a level of unneeded complexity in my view, since Settlers is supposed to take about 90 minutes. Also, our method of delivering immediately on production leaves no choice to the borrower or lender. You must give as soon as you receive, so there can be no purposeful defaulting.

      As far as credit being passed around, we don't have standardized contracts that can be passed across traders, but you can always hedge your credit position to someone else. Say you gave a sheep for player 2's next wheat. You can do another deal with player 3 promising him/her your next wheat for something currently. This isn't totally ideal, but it's basically akin to hedging a swap by doing the opposite swap with someone else. The main problem here is most likely liquidity in a 4 player game.

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  3. I've tried using money in Settlers before. We just made it against the rules to engage in any trade without using money, ie. no direct trade of resources was allowed. With four players we gave everyone $25 at the start and never increased the money supply. It worked pretty well, and made the game a bit faster, because it was easier for parties to negotiate.

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