This time right after the spring break (and with no class material additionally covered therefore), I would like to try bringing a very casual topic to the post – a board game about disaster management, more specifically, Pandemic.
It is one of the most popular cooperative board game, published by Z-Man Games in 2007. (I guess many of you might already have played this before.) Four diseases have broken out in the world, and players acting as CDC agents work cooperatively to stop the spread and discover all cures before diseases wipe out the world.
I am bringing this as a topic because the framework of this game is really well-suited to the optimization models. The game board is a world map, which is exactly a network with 48 big cities as nodes and arcs connecting nodes with equal distance, as you can see in the picture. Arrivals of the disease to the city as well as contagion outbreaks are probablistic events, implemented as the frequency in the card deck. Moreover, since this is a co-op game, we can say that there is only one stakeholder, which is a setting welcomed by operation researchers.
There exist many kinds of strategic decisions players can make, and one of the main decision is locating the research centers so that players can access all cities easily from the research centers. This can be considered as either a maximal covering or a p-median facility location problem. Actually, some people already studied this problem using basic network analysis. Quick spoiler: when we locate 3 research centers, Atlanta/Hong Kong/Cairo minimizes average distance. To read more about the list of ‘optimal placement’ decision they figured out, you can view Optimal Placement of Research Centers in Pandemic and Overanalyzing Board Games: Network Analysis and Pandemic.
Some say that there’s no fun if we attempt to break everything down into efficient mathematical equations. But I’d rather claim that it is always interesting to see how our intuitive decisions works compared to a computed ‘optimal’ one, or study why the discrepancy between the model and reality is happening. And we know that we can’t do so without doing the math.
Have fun!
Soovin
Public Sector Operations Research 
Soovin, I love your topic. I do however find it ironic that one of the articles is ‘overanalyzing board games’ since I don’t feel it quite analyzes Pandemic enough.
I wonder if it would be possible to make a more adaptive methodology to siting the research centers. In the game, we tend to cycle through the same group of cities (since they are reshuffled and added to the top of the pile after each outbreak). It would be interesting to weight our placement by where most of the infection is, with a probability of the other cities being drawn before the next outbreak.
Further, since most of the turns are usually spent fighting the infection, this causes research centers to be placed over time rather than all at once; so there is likely a better placement strategy. In other words, when we go to place the third research center it may not make sense to minimize the current distances since we will likely place another in the future. At the same time, we can’t place the research center assuming that the fourth is just about it be put up since it could be many turns yet, if at all.
What do you think would be a good way to handle this uncertainty?
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I think your comment contains a lot of good questions to think about, so thanks! I do agree that what they’ve done is not overanalyzing at all. What they assumed in those postings – that no additional information is available – it’s surely a very restrictive setting that yiels a big discrepancy. In order to make the analysis more suitable to pandemic setting, I may suggest
– As you mentioned research centers are placed over time, so not only the optimal set but also the optimal ordering and timing is needed. We need a sequential decision making. Also, we can make the optimal list dependent on the location of initially-heavily-infected cities.
– After few steps players have better information about the probability of cities than just the frequency in the card deck. So yes, some kind of information update procedure would be certainly helpful. Increasing the weight of cities with most infections/in the cycle sounds like a good and easily implementable idea!
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We should play this the last day of class and put everything we learned into action.
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I would love to.
I can also get additional disaster themed co-op games so that all class members can participate at the same time.
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When looking for examples of public sector OR in board games, I’m not sure there exists a more appropriate example than Pandemic.
This post led me to think about other examples of optimization and stochastic processes in board games. I recently played a game called Panic on Wall Street. “Investors” are able to bid on low, medium, and high risk stocks controlled by “Managers”. After the bidding is over, dice are rolled to determine what happens to the stocks. As you can guess, low risk stocks are very sure and gradual gainers, while high risk stocks are extremely volatile, but offer the largest potential reward. By examining the dice for each stock, my strategy was to calculate the expected profit from each stock, then bid accordingly. This strategy paid off against my greedy rival investors (which included a CEO of a multimillion dollar company).
I’d definitely be interested in playing this game at the end of the semester!
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Sounds good your strategy nicely worked 🙂 I feel board games with bidding are lots of fun. They have plenty of room for mathematical strategy(like yours), but it also depends on what odds and opponents we get so it’s hard to find dominant and deterministic winning tatic!
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