Faculty-Student Research Grant Helps Fund Project
For this thesis Gavin Nachbar ’14 developed and conducted a variation of the economics experiment called the “Centipede Game,” a famous paradox of rationality in the field of economics and game theory. Nachbar is the co-recipient of the Robert E. Rubin Award in Mathematical Economics, which is presented to the outstanding senior graduate in mathematical economics.
The Centipede Game is deceptively simple - a group of anonymous players are sequentially given the chance to either end the game for a high personal payoff, or pass to the next player to increase the gains for the group as a whole. However, if a player chooses to pass, he risks receiving a much lower payoff if the next player decides to end the game and take the high payoff for himself.
Nachbar’s thesis, “Experimental Findings and Adaptive Learning in a Five-Person Centipede Game,” looks at what happens to cooperation levels within a group when the size of the group increases.
During the summer of 2013, Nachbar, a Colorado College mathematical economics major from Amherst, Mass., received a faculty-student research grant with Associate Economics Professor Jim Parco to fund the development of the software necessary to run a five-player group decision-making game, as an extension on previously run studies with a three-person group. He spent eight months developing the software program, teaching himself to write computer programs in Python – a massive undertaking in itself. By Block 5 Nachbar and Parco were ready to run the trial sessions.
The experiment was designed to study decision-making behavior in small groups. “The Centipede Game tests the ability of a group of strangers to cooperate and earn more for the group despite each one having the opportunity to end the game and earn more for himself,” Nachbar said. For the experimental economics game to work and to prevent attempts at collusion, it’s important that the players don’t know one another and are unaware of the purpose of the game. Parco had run a similar previous study at the University of Arizona, but conducting it at Colorado College presented unique challenges – with such a small, close campus, many students know each other. Nachbar scoured Facebook friend pages in an attempt to be sure participants did not know one another.
The importance of anonymity also meant going to great lengths to set up the room. Nachbar and Parco spent Super Bowl weekend turning Gates Common Room into an experimental economics lab, carrying cinderblocks and 18 sheets of 8-by-4-foot plywood up the stairs to create privacy cubicles. They moved 16 computers from another room in Palmer Hall and installed them amidst a web of Ethernet cabling in the makeshift lab.
They then ran the experiment, aimed at determining if people cooperate more or less when two additional players are added to an anonymous group of players within a game.
During each trial of the experiment, five players took turns making a decision in sequence. When it was a player’s turn, that participant had to choose between two options: moving right, to the next player in the sequence, thus passing on the money but potentially increasing the eventual payout for all, or moving down, ending the game and taking the money for himself. Each of the three sessions had 60 rounds of play.
“The sessions went very well,” said Nachbar. “The aim of the analysis in the paper was to see what kind of learning took place over 60 rounds of play." The average payoffs to subject participants ranged from $17.68 to $41.40 across the sessions, with the highest payoff to any single player being $265.
Nachbar found that the addition of two players in a high-pay centipede game significantly changes the kind of adaptive learning that takes place. Overall he found a higher level of sustained cooperation among participants within the game. “This was a very interesting result, and left us thinking that the addition of two players to the game may fundamentally change subjects’ belief on cooperation with strangers, Nachbar said.
“Gavin’s performance on his final thesis was far beyond any reasonable expectation of any undergraduate student,” Parco said. “For starters, he had to teach himself to program in Python so that he could write his own customized software to get 16 networked computers to ‘talk’ to one another in real-time. As for the project itself, Gavin formulated a research question that has remained open in the literature for more than a decade, and has come up with a significant piece of research that is likely publishable in a top economics journal.”
“My thesis project has been the single most challenging and rewarding of my time at Colorado College. The chance to do something like this as an undergraduate student all goes back to the unique structure at CC. Both the ability to become completely immersed during thesis blocks and the incredible support of the faculty is what even makes something like this possible at all.
“Writing the software to run the game took countless hours of work, including the time spent learning to program. But it was truly worth every one. I loved the level of independence the thesis project required, and also the ability to set your own direction with help along the way. Having a data set that is unique to my work has made the analysis a lot of fun at the end of this year. It addressed a question in the literature that has been around for a long time and I'm glad that I was able to be a part of that,” he said.
“The scope, magnitude, significance, and difficulty of the work Gavin produced this past year is what would be expected of an advanced graduate student at an ‘R1’ research university,” Parco said. “For me, Gavin serves as a reminder of the quality of students that are in our classes every day. Someone once commented to me that ‘the problem with a liberal arts education is that you don’t train your students to do anything.’ My reply was simple (with Gavin as an exemplar): ‘Actually, the efficacy of a liberal arts education is that we train our students to do anything.’ ”
Following graduation, Nachbar will be working at Dropbox, Inc., a file hosting service headquartered in San Francisco that offers cloud storage, file synchronization, and client software. He will spend the first year in a business rotation program, with placement the following year.