GAME 1 Claim a Pile of Dimes

Two players Aand B are chosen. The instructor places a dime on the table. Player A can say Stop or Pass. If Stop, then A gets the dime and the game is over. If Pass, then a second dime is added and it is B’s turn to say Stop or Pass. This goes on to the maximum of a dollar (five turns each). The players are told these rules in advance. Play this game five times in succession with different pairs of players for each game. Keep a record of where the game stops for each pair.  but most students will not have read that far ahead at this stage. Our experience is that the simple, theoretical subgame-perfect equilibrium of immediate pickup is never observed. Most games go to 60 or 70 cents, but you do see the students thinking further ahead. Later pairs learn from observing the outcomes of earlier pairs, but the direction of this learning is not always the same. Sometimes they collude better; sometimes they get closer to the subgame-perfect
outcome.

After the five pairs have played, hold a brief discussion. Ask people why they did this or that. Develop the idea of rollback (or backward induction). Investigate why they did not achieve the rollback equilibrium; did they fail t o figure it out, or did they understand it instinctively but have different objective functions? Don’t prolong the discussion too much;
you’ll want time to get a few other games played.

This game could also be played to motivate the ideas of rollback right before they are covered with the material . If you prefer to cover simultaneous-move games first, then you might want to save this game until after you have completed that material. However, if you are following the order of the material in the book, rollback is likely to be the subject of your lectures within the first two weeks; you could use this game to motivate the following week’s lectures.