I recently read an article titled "Do individuals with higher cognitive ability play more strategically?" by Juan Benito-Ostolaza and his colleagues, published in 2016 in the Journal of Behavioral and Experimental Economics. As a strategy board gamer and a psychologist, how could I not take a closer look?
The participants in the study played a perfect information, Nash equilibrium game (the Schelling segregation game) in which they made decisions about where to move in respect to the positions of other players. At the beginning of the game, players were given either a black or white scarf, and a starting place within a circle of other players. The rules of the game indicate that players will be "happiest," and make money at the end of the game, when they are standing next to at least one other player of the same color scarf. Each player gets a single turn in which he or she can decide to move (which may cost money) or stay in place. They played multiple games with various different costs for moving. The starting configuration for the game is on the left side of the picture below, and the optimal equilibrium solution is on the right.
Is it rational to assume that everyone else plays rationally?
All right, this is not going to be the hottest new party game on BGG, but it is easy to teach, equally unfamiliar to everyone, and involves a moderately difficult cognitive challenge that can be studied in the laboratory. As moving costs increase, there is greater incentive to play strategically, i.e. staying in an unhappy location with the assumption that the next player in the circle will be forced to move, thus making the person happy. For example, the most strategic move for the first player is to stay put because the last player (#8 in the diagram) will most likely be compelled to move. Yeah, I had to read the procedure a couple of times before all this made sense.
Now here is the interesting bit. After the participants were finished with the game, they were given a test of fluid intelligence, Raven's Progressive Matrices. This test contains 60 items in increasing difficulty which challenge the participant to identify the missing piece to a puzzle, as shown in the picture below. Raven's test has been around for years and is considered to be a valid, reliable, and relatively culture-fair measure of general cognitive ability.
If you like this kind of puzzle, you should probably be playing SET.
The results of the study showed that the percentage of players acting strategically and making the optimal move for their position is higher among individuals with high values on Raven’s test, particularly for players scoring at or higher than the 50th percentile on the test. The authors concluded that general intelligence has important practical applications, not just in abstract games, but in business settings where strategic planning is important. Critics of IQ tests claim that they don't measure anything meaningful, but here is evidence from game theory that they do.
I'll end with a personal story. My IQ is above average, but definitely short of genius level. This is probably why I had to read over the procedure a couple of times and think it through before I could follow the authors' reasoning about strategic play. On the other hand, I've known several very high IQ people in my life, and I can say anecdotally that they are extremely quick to understand game rules and pick out optimal strategies. Some years ago, I taught one of these friends, a physicist by profession, to play TAMSK. Keep in mind that I'm not a great TAMSK player, but I had played maybe a dozen games previously. Anyway, I won the first game, I barely won the second game, and he won every game after that. Intelligence isn't everything, but it certainly helps people to think efficiently, understand systems, and recognize patterns.
Statistics and Speculations on the Behavioral Science of Board Gaming
- [+] Dice rolls