California Rapid Alert Narcotics Enforcement Agency
Solution 5: Course Schedule
It's all Game Theory! The grids are set up like a payoff matrix (remember Econ 1?) where the columns represent Dement's strategies and the rows represent Cranea's strategies. Hidden deep inside the introductory paragraph is the phrase "best response", indicating that teams should find a Nash Equilibrium for each 4x3 grid, which will be the "best response" for the two players.

The crossed-out course letters do not appear in the grid, and numbers appear in the place. A quick search of the Stanford Bulletin confirms that the numbers in the grid indeed are course numbers for courses with the crossed-out titles. After searching the Stanford Bulletin some more, teams would find all the course numbers:

A: Advanced Greek:Plato (CLASSGRK 113)
B: Applied Group Theory (MATH 109)
C: Beazley and After (ARTHIST 202)
D: Cancer Epidemiology (HRP 230)
E: Differential Geometry (MATH 143)
F: Ecosystems of California (BIO 125)
G: Hellenistic Poetry (CLASSGEN 301)
H: Human-Centered Design for Aerospace Engineers (AA 238)
I: Introduction to Lighting And Production (DRAMA 31)
J: Introduction to Symmetry Analysis (AA 218)
K: Model Selves: Francis of Assisi (RELIGST 268)
L: Modern Physics (PHYS 70)
M: Path Dependence and Economic Analysis (ECON 168)
N: Philosophy and the Scientific Revolution (PHIL 61)
O: Posture (ATHLETIC 90)
P: Real Estate Development (CEE 248)
Q: Rereading Judaism in Light of Feminism (FEMST 139)
R: Russian Critical Traditions (SLAVLIT 305)
S: Spanish Dialectology (SPANLIT 205)
T: Supply Chain Management (MS&E 262)
U: The Problem of God (RELIGST 32)
V: Tibetan Ritual Life (CASA 127)
W: Utopia and Reality in Modern Urban Planning (URBANST 254)
X: Writing the Honors Thesis (PWR 193)

At a Nash Equilibrium, each player will have nothing to gain by changing their strategy... in other words, a Nash Equilibrium occurs where the number in the top-right is the highest in that row for all three columns, and where the number in the bottom-left is the highest in that column for all four rows.

Completed grid with Nash Equilibria highlighted:


(view larger image)

As indicated by the hint "give us a call when you're done" at the end of the intro paragraph, the Nash Equilibria correspond to a phone code. Many teams had trouble figuring out exactly how this corresponded to a phone code, until they were reminded that their cell phone's buttons were also arranged in a 4x3 grid ("Ohhhhhh....").

When each Nash Equilibrium is mapped onto the corresponding position on a phone keypad, the digits are "94720" (which is, not coincidentally, the zip code for Berkeley, CA). When they enter this code into the phone system (try it!), the oddly enthusiastic voice of Mike Sego directs them to the next location. For teams Ramrod and Think Tank, the next location was Doe Library, at UC Berkeley. After the first two teams, we skipped teams past Berkeley and changed the message to redirect them to the Marin County Civic Center.

A few teams realized that the "best response" for both players was not necessarily at the Nash Equilibria. For instance, in Game 5, the players could beat 205/248 ("0") at the square 268/254 ("9"). If teams pointed this out to us, we added the resulting code into the phone system as a valid solution.

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