What does Game Theory say about Steem? (Part 1)

Remember Game Theory from your Economics 101 course? Prisoner's Dilemma, Battle of the Sexes, and Chicken? Game Theory is the formal study of people interacting strategically with each other, and for many of us, the first time we were exposed to game theory was an eye-opening experience. My first in-depth exposure to game theory was listening to an audio course, and I remember having an epiphany, thinking "I'm about to start a new life here, now that I see how to make decisions!"

Fast-forward 10 years, and now I'm a PhD student at UCSB working on applying game theory to engineering problems. I still enjoy game theory, but I've come to realize that it's not quite the panacea I thought it was listening to those tapes all those years ago. Nonetheless, perhaps it can tell us something about the wild and wonderful world of Steem. In particular, maybe it can help predict how well the incentive structure of Steem will work - will the network be vulnerable to wealthy individuals coming in to buy influence? Will a newcomer with no cash be sufficiently incentivized to create good content, even though she's up against giants like @stellabelle and @dantheman?

What is Game Theory?

I like to tell people that game theory is the study of optimization against strategy. If I'm playing a game against you, I'm going to optimize my moves to maximize my chance of winning. At the same time, you're going to optimize your moves to maximize your chance of winning; so my optimization problem has to take your optimization into account, and yours has to take mine into account. In other words, we both have to act strategically. There are at least three components to any game: players, actions, and payoffs. The players are the decision-makers who are optimizing against one another. The actions describe what each player is capable of. Finally, each player has a payoff function that describes how each player values each game outcome.  We'll go into more formal detail in future installments, but for now this bird's-eye view should suffice.

Probably the most famous example "game" is called the Prisoner's dilemma. Suppose there are 2 prisoners who were arrested together, and they're locked in two separate cells and can't communicate with each other. In game-theory-speak, the two prisoners are the "players." The detective doesn't have enough evidence to convict them, so he offers them each a deal: "rat out the other guy, and I'll get your sentence reduced." Thus, each player has to decide between two actions: "rat the other guy out," or "keep quiet." We'll call those "rat" and "quiet." Finally, we have to convert the detective's deal into a payoff function. Here's how we'll do it: if both prisoners choose quiet, they each get a payoff of -1 (this represents a year in prison). If both prisoners rat, they both get convicted and each get a payoff of -5 (let's say that's 5 years each in prison). However, if prisoner A rats but prisoner B is quiet, prisoner A gets a payoff of 0 (i.e., he goes free immediately), but prisoner B gets a payoff of -8 (and vice-versa if their roles are reversed). Everybody with me? 

Now let's see if we can figure out what each player should do. The game is symmetric (both players, so let's just analyze prisoner A's choice. First, suppose prisoner B is quiet. Then prisoner A gets -1 if he's quiet, and 0 if he rats. No years in prison are better than 1 year in prison, so his best choice is to rat. Next, suppose prisoner B rats. Then prisoner A gets -5 if he rats, and he gets -8 if he's quiet. Again, his best choice is to rat. And there you go! The game-theoretic prediction is that both players should rat.

So What? Part of the interesting story told by the Prisoner's Dilemma is that in a sense, the best outcome (both prisoners staying quiet) is actually disincentivized and the worst outcome is incentivized. That is, if both are quiet, they spend a total of 2 years in prison, but if both rat, they spend a total of 10 years in prison. They would clearly be better off both staying quiet, but each prisoner individually has a power incentive to throw the other guy under the bus.

What does any of this have to do with Steem? The Prisoner's Dilemma is a cautionary tale: it says that even if people know what's best for the overall system, they may still be incentivized to act against the system's interests. Part of the premise of Steem is that people who power-up their STEEM will have a long-term incentive to grow the network and act in the best interest of the system as a whole. In a broad sense, powering-up to steem power (SP) is a technique that the developers have devised to prevent Steem from becoming a Prisoner's Dilemma. It seems like it should work! Unfortunately, game theory is chock-full of examples where people have hidden incentives to do the wrong thing. I'll go into a few of these in future installments.

How do we model Steem using game theory? Just to give you a sense of how complicated this could be, let me take a quick first crack at building a game theory model of Steem. Remember, any game theory model needs players, actions, and payoffs. To keep things very simple, for now let's forget about the blockchain backend and only consider Steem's end-users. Thus, let the players in our game represent Steemit's content-creators and curators (i.e., upvoters). 

That's simple enough, so now let's move on to the actions. Oh boy. How do you model the actions? Well, you could say that each player has 3 choices per piece of content: downvote, no vote, or upvote. What about the actions that represent creating content? Here, it might be interesting to model the fact that it takes effort to create quality content. One way to do this is just to give creators two actions: Create Good Content, or Create Bad Content; we can then build the effort part into their payoffs. Here, it might be useful to talk about how many pieces of content people can create; but we're trying to keep it simple, remember?

Finally, let's think about how we might model payoffs. A quick-and-dirty way to think about this is to note that each player experiences two types of gains: immediate and long-term. The more SP you have, the more weight you'd put on the long-term portion. For creators, immediate gains might be the thrill of going viral; long-term gains are the growth of your SP. We would have to model Good content as costly in the short-term (due to the effort it takes to create it), but beneficial in the long-term; Bad content might be beneficial in the short-term (if you can get up-votes), but has no long-term value. From the standpoint of the voters, I'm not even sure how you'd model short-term gains; maybe the satisfaction of helping a post go viral. Long-term gains are nice for the curators because the more SP you have, the more your vote counts and the more weight you put on long-term gains. Thus, it appears that the most powerful curators have incentives to push for long-term gains.

I'll stop there for now. See how complicated it got, even though we've made all those simplifications?

Now for some important caveats before we dive into this in Part 2:

1. Game theory tells us clearly what people should do, but it tends to make pretty poor predictions about what people actually do. Put differently, it's very important not to confuse game theory with social psychology. Game theory is probably quite good at modeling the interaction of companies in a marketplace, but it tends to fall short when it tries to model "regular people" interacting in normal social situations. This is because normal humans are not as strategic as it seems like they should be; experiments show that people make decisions in under the influence of all sorts of cognitive biases that game theory has traditionally not modeled.
2. Game theory doesn't tell us anything at all if we don't have a good model of people's decision-making process. This is what my PhD research is all about, incidentally: how can we influence peoples' behavior if our model of their preferences is bad? One of the significant challenges we'll run into in the game-theoretic analysis of steem is that we'll need to explicitly model people's reasons for posting and upvoting; we'll need to model how interpret the long-term consequences of their votes. Sounds hard.

And now, on to Part 2: The Beauty Contest

Or, skip to Part 3: Is Steem Paying for Groupthink?