Playing A Risky Game | Stats + Short Stories Episode 46 / by Stats Stories

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David Banks is a statistician at Duke University. He is a fellow of the American Statistical Association and the Institute of Mathematical Statistics, and a former editor of the Journal of the American Statistical Association and Statistics and Public Policy . His major areas of research include risk analysis, syndromic surveillance, agent-based models, dynamic text networks, and computational advertising.

+ Full Transcript

John Bailer : I'd like to welcome you to today's Stats and Short Stories episode. Stats and Short Stories is a partnership between Miami University and the American Statistical Association. Today's guest is David Banks. He's a Professor of Statistics at Duke University. I am John Bailer. I'm Chair of the department of Statistics at Miami University and I'm joined by my colleague Richard Campbell, Chair of the Department of Media, Journalism and Film. We're delighted to have David speaking with us today on the short episode about Adversarial Risk Assessment. David that is quite a mouthful and it's an intriguing topic. Can you just give us a quick sense of what Adversarial Risk Assessment might be?

David Banks : Absolutely. It's a decision theoretic alternative to Classical Game Theory.

Bailer : I'm going to have to stop you David. I looked over and Richard turned a little green.

Banks : Well I hope it will get easier. Game Theory is studied a whole lot in adversarial conflicts such as the prisoner's dilemma or mutually assured destruction. And in these contexts it quickly became apparent that human beings don't make decisions the way Game Theory says they should. Very often they will cooperate in a prisoner's dilemma experiment, where college students are put in that situation. And Game Theory says that should never ever happen. So there's a lot of evidence that Game Theory is not really a good guide for that behavior, an alternative to that is to use Statistical Risk Analysis. And Risk Analysis is an attempt to try to understand what types of threats an opponent might provide, and Classical Risk Analysis assumes that your opponent is non-strategic. So it's like a hurricane. A hurricane doesn't decide to aim for New Orleans and then do a quick faint towards Biloxi because you're off guard. So that type of thing is not useful in strategic games. So Adversarial Risk Analysis proposes that one build a model for the decision making of one's opponent and then make the best choices against that model. And it's actually something that human beings do all the time. Richard, if you were playing chess with Boris Spassky you would think really hard. You'd spend months studying chess openings. You know, in advance, and you'd be looking for the move behind the move behind the move at every single step of the game. On the other hand if you're playing chess with your 8 year old niece you'd probably have a very different mental model for how she approaches the game of chess. And you would adapt your responses accordingly. If you're playing your niece you might look three moves ahead. You're probably not going to look ten moves ahead. And you certainly wouldn't spend months studying chess openings before you play her.

Richard Campbell : And if I was really nice I'd let her win.

Banks : And there is that too, yes. I'm not assuming you're that nice. So my point is, in lots of adversarial situations such as arise in federal regulation when you have the Federal Government trying to regulate the amount of pollution that a company releases into the environment, and there's a third stake-holder, which is sort of the community. There you have three decision-makers all with different interests and they're going to try and come up with a compromise or a solution that will work well for everybody. And in order to do that each has to build a model for the objectives of their opponents. Similarly if I'm Coke and you're Pepsi, well, there's certain things I can invest in. I can invest in trying to open up a Chinese market. I can invest in new products. You can try and invest in opening up India. You might try and invest in buying better shelf-space in the grocery stores. We're going to make our decisions based upon our best guess of what our opponent is going to do. And that involves building a model for what the goals of the opponent are, what the resources of the opponent are, and how the opponent is trying to make decision. Is the opponent working on a five year business plan? Or is the opponent working on a quarterly business plan? And those are all pieces of information that we won't know but we can make shrewd guesses about. And that is what drives an adversarial analyst.

Bailer : Wow. So one of the things that comes to mind is how good is your model? And what do you do in terms of predicting this? How do you check and calibrate such a model for your opponent's behavior?

Banks : This is extremely difficult, and I don't think one should try and minimize the difficulty of that in lots of situations. But remember the short answer is if you have a bad model about your opponent's behavior, then basically you're going to lose. It's no surprise that if you don't know what your opponent is trying to do or you don't know what resources your opponent has, or you don't know how your opponent is weighing the situation, you're at a real disadvantage. And you could try and say, "well, then that's why we should do Game Theory", but Game Theory is going to be a real disadvantage too. Game Theory makes the assumption that all of the opponents have common knowledge and know that that knowledge is held in common. Which is completely unrealistic from most applications. So if you're in a situation where, Richard is a terrorist and I'm a counter terrorist I need to understand what Richard's goals are. I need to understand, does he have a nuclear device? Does he have weaponized smallpox? And I need to understand whether or not he thinks he's got a really good chance of smuggling a bomb on a plane or whether he thinks he's got a really poor chance of smuggling a bomb on a plane. If I don't know these things I'm behind the 8-ball and I have to expect to lose.

Campbell : You talked about guessing at what your opponent might do. Guessing is not something I associate with John and the other statisticians that I know. So you're talking about making best guesses, or are you using "guess" in a particular way here?

Banks : I'm using "guess" in a very particular way, and I apologize, I was trying to be clear. I'm a Bayesian statistician. And a Bayesian is allowed to put their own subjective probabilities on any set of events as long as those probabilities are consistent with each other and as long the Bayesian learns according to Bayes' rule. For example, I can't say that the probability of heads on a coin is 0.7 and the probability of tails on the same coin is 0.8 because those are inconsistent beliefs. But I can say that probability of heads is about 0.8 and the probability of tails therefore is about 0.2 because that is consistent. Then if I observe a series of coin flips in 100 tosses I get 51 heads and 49 tails then I'm going to have to change my mind according to Bayes' rule, so that instead of having an 80/20 coin I now believe that that coin is a lot closer to a 50/50 coin. And there's a formal mathematical procedure for doing that but that's how a Bayesian makes guesses.

Bailer : This is great. Always a pleasure to chat with you David. It's been our pleasure to have David Banks join us on Stats and Short Stories. Stats and Stories is a partnership between Miami University's department of statistics and media journalism and film and the American Statistical Association. Stay tuned and keep following us on Twitter or Apple podcasts, if you'd like to share your thoughts on our program send your email to and be sure to listen for future episodes where we discuss the statistics behind the stories, and the stories behind the statistics.