Optimal Area Currency with Milton

Friedman and Mario are about the same height.
Friedman and Mario are about the same height.

In hindsight, one of Friedman’s great predictions is the Eurozone crisis. Despite being a huge champion for flexible exchange rates, Friedman never advocated for a common European currency.

Europe exemplifies a situation unfavourable to a common currency. It is composed of separate nations, speaking different languages, with different customs, and having citizens feeling far greater loyalty and attachment to their own country than to a common market or to the idea of Europe.

— Milton Friedman, The Times, November 19, 1997

The crisis of Greece exemplifies many of the problems Friedman points out. In times of economic recession/depression, central banks devalue the domestic currency to return the country to full employment. When economies are similar recessions/depressions move together, if there’s a crisis in Texas it’s probable there’s one in Washington. This makes central bank policy more effective because capital won’t escape from ‘recessed’ areas to one’s with higher returns – there are none. It can be much harder to accomplish this in Europe where every country’s economy is dramatically different and institutional policy fluctuates widely.

What the hell does this have to do with game design?

Why do multiple currencies exist in games to begin with? Why not just have one type of currency rather then four or five?

Simply put, it’s all about segmentation. Once again, Supercell has provided us with a wonderful example, Clash of Clans (CoC). Consider which items cost gold and others elixir, the choice was not an arbitrary one. After a quick scan, you’ll notice only the defensive items (cannons, archer towers, walls) cost gold and only the offensive items (troops, barracks, spells). Why might this be the case? Segmenting these items gives designers greater control over the economy and minimizes the potential for ‘contagion’ effects. Consider a world in which Clash of Clans only contained gold. It’s possible players might have a preference for attacking rather then defending, encapsulating the idea of capital going to its highest return. If this were the case the game could become unbalanced as all players attack and none spend gold to upgrade their base defense. By segmenting base defense into elixir, you remove any opportunity cost from from spending on base defense. This is similar to giving your relatives a gift card, rather then spending it on whatever they fancy, they must now spend it on whatever is from the gift card’s store. A domestic currency is much like a gift card to that country’s ‘store’ just as elixir is a gift card to only CoC’s offense ‘store’.

If Supercell finds players are not creating challenging defenses, it’s very easy increase the rate of gold production without worrying that money will be spent on offense. They can also do this by lowering the cost of items priced in gold. Supercell has toyed more with this strategy in their other title, Boom Beach.

The rules for when segmentation is worthwhile emerge reading Mundell’s famous paper 1 backwards.

Segmentation in games, just like in real world economies, gives game designers and central bankers more control.

There’s more to A/B testing then A and B: I

One of the most powerful features of mobile games is the ability to run simultaneous randomized experiments at no cost. Academics swoon at such a possibility and it’s very real and very spectacular in F2P games.  Decades of running experiments in academic research can lend insight to developer scientists. An example of this is an insight from experimental economics called ‘bending the payoff curve’.

One of the favorite topics of experimental economists concern risk aversion and auction theory, risk aversion due its ability to challenge the neoclassical paradigm (i.e. mainstream economics) and auction theory because it uses fancy mathematics. The first groundbreaking economic experiments employed auctions in lab settings to see if participants diverged from rational behavior. A series of experiments run by Cox, Smith, and Robinson1 appeared to show participants were not doing what we’d expect them to do if they were rational agents (i.e getting the lowest price). The suggestion being participants were acting as risk – averse agents, rather than risk – neutral agents. The key insight, however, came from a challenge in the way these experiments were run from a 1992 AER article called Theory and Misbehavior in First Price Auctions.2

The author, Glenn Harrison, argued that the costs of engaging in non-optimal behavior were incredibly small. In other words, being dumb didn’t cost participants that much, and being smart didn’t earn participants a great deal either. Glenn argued this casts doubt on the suggestion that participants were engaging in non-optimal behavior, but instead participants weighed the expected mental effort of being smart and concluded it wasn’t worth the foregone increase in income.

Each deviation from zero (the optimal bid) costs the participant little.

What researchers need to do, Glenn argued, was bend the payoff curve i.e. increase the reward for being smart. This way researchers can see if the type of behavior they’re testing is a real thing.

What does this mean for A/B testing in my game?

Developers often turn to A/B testing to test even the most minute items; frustration emerges when results are inconclusive. For example, Supercell might test whether or not players prefer reward scheme X or Y in Boom Beach by way of sessions played. An A/B test that presents each scheme after a battle could possibly turn up inconclusive. This is because each reward has a small outcome on player progression. That is itself an insight, but if we’re really interested in whether A or B is better it’d make sense to ‘bend the payoff curve’. That means we’d offer A + 5 or B + 5 to exaggerate the effects of the different reward schemes.

Think of it as amplifying two lights on each side of a room to see where flies gravitate toward. If the lights were dim the effect on the flies would be smaller than it otherwise is.

See? Just like an A/B test.
See? Just like an A/B test.

While not always appropriate, bending the payoff curve is another tool developer scientists should consider when designing experiments.