Two Wrongs

Free Banking Monopoly

Free Banking Monopoly

I while ago I read Kevin Galligan on board games and Markov chains. While the techniques he shares are valuable, I also happen to agree with him that part of the fun of board games is the social aspect of negotiating over a table with your friends about something ultimately inconsequential.

Free banking rules

Here’s an idea to improve the fun level of games that involve some degree of resource management, as e.g. Monopoly does. Like any amazing idea, it could either work out great or be a complete disaster. To be clear, I have not yet had the opportunity to test this myself, but I’d really like to some day.

Under free banking1 Named after the similar historic periods in which a nation’s currency was decentralised and each bank printed their own banknotes. rules, all players are allowed to issue their own currency. Player-issued currencies cannot be used to pay in-game institutions such as the Monopoly bank2 Thus, in the case of Monopoly, purchasing property or plots of land that are not owned by other players is still done with proper Monopoly money., however, they can be used in transactions between players. This is probably clearest with an example: imagine Kevin has landed on my property and now owes me $20.

  • Kevin can pay me $20 in Monopoly dollars, as normal.
  • Kevin can issue $20 in Kevin dollars and try to get me to accept that. If I don’t want to hold Kevin dollars (for whatever reason), I might ask for something like $50 of Kevin dollars to write off a $20 Monopoly dollar debt. If Kevin agrees, we transact in Kevin dollars.
  • If Kevin happens to have $20 in kqr dollars, he can use those. Under the free banking rules, I would be forced to accept my own currency at face value.3 One might think this is what gives player currencies value, but that’s not true. This requirement of accepting one’s own currency at face value is not a strict requirement for free banking to work. However, I think it’s a useful rule to have the first few times one plays to keep things a little simpler.
  • If Kevin does not have kqr dollars, does not want to spend Monopoly dollars, and is worried about printing up more Kevin dollars because they have started inflating beyond his control, he might have some Alice dollars and if we both find a 1:2 exchange rate for Alice dollars reasonable, he could offer up $40 of Alice dollars to cover the rent.

To complicate things further, if Bob thinks highly of Alice’s fiscal policies and would consider 2:3 a fair exchange rate for Alice dollars, Bob can offer to take $35 in Alice dollars from Kevin, and give me $20 Monopoly dollars instead. Bob pockets the profit of $5 Alice dollars. This means that for every transaction between players, a market exchange rate is established by the lowest bidder.

But more importantly, it makes all four people involved happier:

  • Kevin is happier because he only needed to pay $17.5 for rent instead of the nominal $20.
  • I am happier because I get $20 of Monopoly money directly instead of Alice dollars.
  • Bob is happy because he made a $3 profit.4 His profit was $5 Alice dollars, which he judges equal to about $3 Monopoly dollars.
  • Alice is happy because Bob’s intervention gave her currency a more trustworthy exchange rate.

I think this would be a mess, but a highly interesting mess. The quant in me would love to study the exchange rate charts to come out of such a game.

Alas, as a parent of young children with many other competing interests, I’m not sure when I’ll have the opportunity next time. Let me know if you try!

Turning any board game into Diplomacy

How does one get to free banking? There is a middle ground: allowing arbitrary agreements between players, without specifically mentioning free banking.

Monopoly is a game people love to hate, often for the right reasons. But if all our friends want to play Monopoly, what do we think is easier?

  • Convince them to play something else, or
  • Convince them to adopt a few house rules that makes the game more fun?

I’ve always had more luck with the house rules.

In particular, for games like Monopoly where there is an element of resource management, a simple but fun house rule is to allow any players to enter into arbitrary agreements about whatever the heck they want. These agreements are not enforced, but entered on an honour system, which makes them fair.5 If players could invent rules as they went, that would be unfair. But since these agreements are not enforced, they are not rules. It’s just people choosing to promise each other things in a way that looks zero-sum to the outside but presumably is for mutual benefit.

As a concrete example, one simple agreement that almost immediately comes up under this house rule is fractional property ownership. That means Alice pays Bob some of the value Bob is willing to sell the property for, and they split the revenue according to some agreed fraction for the rest of the game or until they agree otherwise. Since this isn’t an enforceable agreement, Bob is still the owner of the property as far as the game cares, and Bob can technically default on the agreement at any time. Bob never has to share even one dollar of revenue with Alice.

From the game’s perspective, what has happened is that Alice has gifted Bob a large sum of money, in exchange for Bob’s promise to keep gifting Alice revenue-dependent small sums of money in the future. But that’s just a promise – it could be empty if Bob is a scoundrel.

This has two consequences:

  • Alice will want a risk premium on the agreement, i.e. if Alice pays half of the property value, she will want more than half of the future revenue. Otherwise Alice is left with all of the risk and no profit to show for it. Finding the appropriate size of this risk premium is part of the fun.
  • There are still social enforcement mechanisms: players that reneg on deals are less likely to get good deals in the future. If Bob breaks the promise and stops paying Alice, Alice might be able to convince others that Bob is a Bad Person and they need to team up (in terms of other agreements) to be stronger and force Bob out of the game.

So basically, it turns any board game into a game of Diplomacy. We get a beautiful explosion of game theory even out of dumb games like Monopoly.

Other agreements

Here are some other ideas for agreements that I have tried that have worked well.

  • Forward contracts: Alice and Bob agrees right now on a price for a sale they will conduct in the future.6 Forward contracts are like futures except not marked to market and not standardised.
  • Options contracts: like the forward contract, except Alice retains the right to back out of the agreement at any time. In exchange, Alice pays Bob a little up front for the potential inconvenience.7 This can be thought of as a first-dibs contract. Alice pay for the right to have first dibs at a future sale for a fixed price.
  • Lease-to-purchase agreements: Alice wants to trade with Bob but can’t afford it right now, so she pays Bob rent for a few turns until she can afford the trade. At that point she can deduct the rent payments as installments going toward the full trade. If Alice changes her mind, these rent payments are still gone.8 This can be thought of as bribing Bob not to trade with someone else – but also as a way to start a big purchase before one is certain it is a good idea, since one has the option to back out but at increasing expense.
  • Variable interest-rate loans: these can be a function of total economic activity, or someone’s revenue, or someone’s wealth, etc.

As is perhaps clear, free banking is really just an extension of these ideas to the very medium of exchange used in transactions between players.

Problems with arbitrary agreements

To be clear, arbitrary agreements are not a panacea to make any game fun. I have noticed two problems when I have tried.

  • If one plays with a new group of people every time, this does not work as well, because the cost of being uncooperative is lower. In other words, these house rules add a prisoner’s dilemma type situation to the game. However, this problem has been smaller than you may think. Sure, I suppose sometimes one might lose to a cheesy backstab, but if one sets appropriate risk premia it ought to even out in the end.
  • One time, the game didn’t seem like it could ever end because everyone was involved in interlocking agreements which would have the effect that if one player got bankrupted, everyone else would come tumbling down too. Somehow I feel like I’ve heard about this somewhere else.