Computer Game Zenda

This game was invented by James Andreoni and Hal Varian; see their article, "Pre-Play Contracting in the Prisoners 'Dilemma".The paper also contains some code in C. Zenda is a prisoners' dilemma, but this is concealed behind a facade of playing cards and Pull and Push mouse clicks in such a way that students do not easily figure this out. (They could, from thename and word association, but few are sufficiently widelyread or addicts of the right kind of movies.) Nevertheless, the game is best played during an early week of the semester,before you have treated the dilemma in class.

Make sure you have an even number of students. The program matches them randomly in pairs. Each student sees two cards for herself in the bottom half of her screen, and two cards for the player with whom she is matched in thetop half of her screen. For each student, there is a low cardcalled her pull card, and a high card called her push card.She can use her mouse to click on one of these. If she clicks on the low (pull) card, she gets from a central kitty a number of coins (points) equal to the value of that card. If she clicks on the high (push) card, her opponent gets from the same central kitty a number of coins (points) equal to the value of that card. The objective is to get as many coins for yourself as possible. The two matched in a pair make their choices simultaneously. They do not see each other's choice untilboth have clicked, when the actual transfer of coins takes place. Then new random pairings are formed, and the proce- dure is repeated. Depending on the time available, you can typically play up to 10 rounds of this. (Usually most students figure out after 2 or 3 rounds that pull is their dominant strategy.

The values of the low and high cards a player has overher 10 rounds should be alternated in such a way as to alloweach to get the same aggregate payoff if they play the correct strategies. This evenness is important if the exercisecounts toward the course grade.Then a second phase of the game begins. Here each player has the opportunity to bribe the other into playing Push; it shows how the prisoners' dilemma can be overcome if there is some mechanism by which the players can make crediblepromises. Again randomly matched pairs are formed. Againin each pair each player sees her and her opponent's cards. First each chooses how many coins she promises to pay her opponent if (and only if) the opponent plays Push. These bribes come from the player's own kitty (winnings from thefirst phase) and not from the central kitty. The bribes are put in an escrow box. Once both have set the bribes, each can seethe bribe offered by the other.

Then they play the actual gameof clicking on the cards. When both have clicked, each getsthe points from the central kitty depending on the push orpull choices as before. If your opponent plays Push, she gets the bribe you offered from your escrow box; if your oppo-nent plays Pull, your bribe is returned to you from your escrow box. (The fact that the program resolves this disposition ofthe bribes makes the promise credible.) The bribe game is also played a number of times (typically 10 rounds) with freshrandom matching of pairs for each round. Students quite quickly find the optimal bribing strategy.

You can try different variants (treatments) of the game:allow players to talk to one another or forbid talking, keep one pairing for several rounds to see if tacit cooperation develops, and so on. We append for your information the instructionsgiven at the time of playing the game, and a report and analysis circulated later.