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What Would John Nash Think of Second Life?

The gold standard of MMORPG combatThe gold standard of MMORPG combatSince the 1950s, game theory has been one of the basic ingredients of economic models. Nash’s Nobel-winning mathematical discovery, nowadays known as the Nash equilibrium, opened up a myriad of ways to formally analyze situations where a number of agents try to fare as well as they can in a situation where their interests might be in conflict. Applications range from explaining specialization of animal species to predicting negotiation results between trade unions and industry representatives.

One does not need to be an expert on the workings of virtual environments to notice that most of them seem to thrive on conflict: players are encouraged to fight each other on blood covered battlefields, outbid one another in virtual markets and build alliances, guilds or corporations to get the upper hand on their adversaries. Thus, it is slightly surprising to notice that both game theorists’ interest in virtual worlds as well as virtual world developers’ interest in game theory seem to be nearly nonexistent. In this post I will first try to explain why I think that empirical game theorists and game theoretically oriented econometricians should pay more attention to these hang-outs. After that I will attempt fit myself into a developer’s skin and sketch how understanding game theory might help in designing more enjoyable virtual environments.

Aggregate level theories often have aggregated complexity

There has been much talk about how virtual worlds could serve as living laboratories for economists and other social scientists. In my understanding, however, none of the top 20 economic journals have published any econometric work where economic theory would have been tested using data from a virtual world. There are two reasons why I think that testing game theoretic results might be a good way to break the ice.

First, economic theory resembles physics in the way how it is constructed. One first picks a set of assumptions and then derives results from those assumptions. After that one tries to test these results with empirical experiments. However, controlling the assumptions is much more difficult when the research subjects are people instead of physical particles. Generally, the higher the level of aggregation in the theory one tries to test, the more assumptions there are that need to be controlled. In my understanding, this is one of the core problems of the papers published so far, where researchers have studied economic questions using data from virtual worlds – they all try to test some relatively macro level results, such as the curvature of the demand function or the quantity theory of money. Both of these theories require almost the whole machinery of microeconomics to be fixed to be convincingly tested: consumer preferences must not change, new products should not be added into the product space during the data collection period, relative prices and production conditions should stay constant and so on.

Controlling these variables is of course easier in virtual worlds than in the real world since the worlds operate on computer servers which can practically log all the actions of an avatar. However, none of the few papers I have read do much to counter the so-called missing variable bias, which may arise if some of the ceteris paribus assumptions of a model are not actually controlled. It is altogether surprising to see that the first steps have been taken with theories that remain always difficult to test – however good the data. A caricatured analogy from physics would be that a researcher would decide that a data collected from a rock concert is the best tool for testing theory on wave interference. Though this can probably be done, there are also easier starting points. The pogoing of the lead guitarist can, for example, be used to test Newton’s theory of gravity or the law of motion – and the number of possibly interfering variables will be much smaller than in the wave example.

In contrast to the macro level theory discussed above, game theoretic results are usually derived from only a few core assumptions. They are closer to the fundamentals of economic theory and thus easier to test than the macroeconomic phenomena. Many of the game theoretic results are also used to derive the macroeconomic results. Thus, if we are unable to verify even these low-level results, then any empirical testing of theorems that build on them will be highly contestable.

Second, game theory is often especially difficult to convincingly test in the real world, but the data from virtual worlds seems to be very fitting for this purpose. Macro level data on the real world phenomena is relatively abundant and of good quality compared to, say, people’s behavior in auctions or oligopoly firms’ production and pricing decisions. Both of the latter are usually explained using game theory. For more abstract games, such as the repeated Prisoners’ Dilemma, data on players’ behavior has to be collected by the researchers. The standard way to empirically study such things is to hire thirty undergrads and then organize an experiment where the students play against each other. Such experiments usually suffer from multiple possible biases. Most notably, it is hard to argue how the small sample of undergrads would represent even the student population – not to speak of the players in the actual application field of the theory. Another problem is that the students have to be rewarded for playing the game well, so that one can be sure that the students rank the possible outcomes of the game in the same way as they are ranked in the theoretical model. Ensuring that the rewards are adequate to make the students take the game seriously may become very expensive – especially if one wants to use a convincingly large population of players and play multiple rounds of the game.

As one of the main motivations for people to play online games is to compete with others, virtual worlds are already full of recurrent situations which could be modeled game theoretically. Because of the comprehensive nature of the data, the few core assumptions of these models should be relatively easy to control. Especially the auction houses found in many MMORPGs seem like a perfect source of data for many different game theoretic experiments. Evidently, they can be extremely fruitful for testing results from auction theory and mechanism design. Using a slightly more sophisticated analysis, that data could also be used to study the production decisions of players with an ability to produce relatively scarce items, i.e. to verify oligopoly and monopoly theory. However, the game theoretic use of data from the virtual worlds need not be limited to these fairly obvious scenarios. The competitive nature of virtual worlds breeds a multitude of small subgames that may carry interesting empirical information. Researchers interested in games resembling the Prisoner’s Dilemma, for example, might want to study players’ decisions whether to engage in player vs. player combat or not. In many situations, my personal experience is that players would be better off not fighting, but still one engages the other pre-emptively, as the attacker often has some sort of a first mover advantage compared to the defender. Both end up suffering on the average.

Though the player sample in these situations may still suffer from not being truly randomly taken from the general population, it is definitely more heterogenic compared to the thirty undergrads used in real world experiments. Also, the sample sizes can be thousands of times bigger than in conventional experiments. It is still of course contestable whether the in-game rewards incentivize the players to exercise sufficient effort so that their actions would be comparable to any real-world phenomena. However, if one could show that a game theoretic model works in a virtual world, then it would be quite convincing an argument that in such real-world situations where incentives are even stronger, people should show at least the same amount of rational effort.

Being strategically entertaining

As I mentioned above, many of the entertainment elements of MMORPGs and other virtual worlds build on competition between the players of the game or the inhabitants of the world. When designing these competitive elements, creative use of game theory might help in making this competition more diverse and enjoyable. Nowadays the most popular design pattern seems to be some kind of an elaborate version of rock, paper and scissors. In practice this means that, for example, the character classes or skills of the characters are designed so that every class is strictly weaker than at least one of the other classes but still clearly stronger than at least one of the others. This results in a situation where the competition between the players remains interesting, since no one can beat everybody but everybody can beat somebody.

Though rock, paper and scissors is a good and tried model, it quickly starts to repeat itself. Good knowledge of game theory might help in designing schemes where the gaming dynamic varies from that of the rock, paper and scissors and thus add to the diversity of the world. Actually, the structure where no one is a sure winner is achieved by a multitude of other classic game theoretic structures, and only the imagination of the developer should be limiting their use. The game can be made interesting using very simple means and without increasing the complexity of the game to a level where learning the ropes becomes too big a burden. Game theorists have developed “board games”, such as So Long Sucker or Hex, which are so simple that a three-year-old can understand the rules, but which still remain extremely challenging and entertaining to play. Learning from these examples could be a key to finding alternatives to the rhythmical bashing of the number keys which has become the standard way how MMORPGs are played.

Another reason why virtual world developers might be interested in game theory is that it can be used to design the rules and game mechanics in a way that results in less unwanted or malicious behavior. From a business perspective, the developer wants to create an environment which people find so enjoyable that they are willing to pay for it. As the worlds are complex and competitive environments, it is more a rule than an exception that some players always find a way to abuse the game mechanics in ways that benefit them but harm the great majority of users. When these situations emerge, one can usually identify and repair the mechanics in a way that stops the abuse. This can often be done without any knowledge of game theory. However, better understanding of strategic behavior could help in designing the mechanics so that the detrimental behavior is impossible in the first place. If such broken mechanics emerge despite all the careful planning, there often exists multiple ways to solve these problems. However, the solutions may have different effects on the game-play. Game theory, and mechanism design in particular, could also be used for finding the optimal way to repair the broken mechanic.

Let me give you an example from World of Warcraft. This example might seem a bit too obvious but I wanted to keep it as simple as possible. A part of the competition between players takes place in what is called Battlegrounds (or bgs). In bgs, two teams of 15-40 players battle each other in varying settings. The teams are allocated in such a way that players of approximately the same level are teamed up to fight others in the same level bracket. This way, the designer tries to keep the fights interesting for both, high and low level characters. However, some time ago a trend called twinking became popular among some of the players. It meant that an owner of a high level character would start a low level character. Then he would use his high level character’s money and some help from his high level friends to equip the low level character with as good gear as possible. Then he would take his steroid-pumped midget to the bgs with predictable consequences. The high level player’s low level character had an unfair advantage compared to those who had just started playing the game. This alienated the new players from especially the player vs. player content. The game developer then tried to solve this problem by making the characters collect experience also from the bgs. This meant that the twink could not stay in the low level bracket for a very long time, because he would eventually level up from all the experience gains. As the level of a character also dictates the level of the gear which he can use, the twink’s carefully chosen gear would soon be too weak to make a difference in the higher level brackets.

Obviously, this was not the first best solution to the problem. Now the new players were better off, but the time invested in the twinks was lost and so was the new and entertaining way of fighting with the low level characters. The developer ultimately understood this and introduced a new mechanic where the player can choose whether his character accumulates experience in the bgs. Then the players who choose not to take accumulate experience are teamed with and put against other twinks. This way the twinks have an incentive to reveal their type and they can then be separated from the more casual players. Thus, an ok solution was ultimately found through trial and error. The situation, however, resembles the so called screening and signaling games where a principal tries to separate different types of agents by offering them choices which are designed so that it should be optimal for each agent to choose the option that was meant for her/him. Thinking the example using the signaling framework might yield even better separating solutions. Especially so, as many twinks still choose the easy way and play their bgs among the normal players.

Nice article, but misses one point

Nice research outline. However, all of the theories you pointed out are based on ‘rationality’ that is defined more broadly embracing “common knowledge” problem. To my opinion, if J. Nash were interested in VWs, it is because VWs can tell something about what people in real-world, not in economics, thinks and acts.

VWs would produce more fruitful researches in alliance with experimental economics, behavioral economics, evolutionary game theory and algorithmic game theory. Not probable with traditional rationality-centered game theory that is mostly polished by mainstream economists.