Rethinking Game Theory
As we discussed in lecture, the classic prisoner’s dilemma game involves two prisoners, each with two choices. Each player can either confess or not confess, as seen in the matrix below.
| Player 1 Doesn’t Confess | Player 1 Confesses | |
| Player 2 Doesn’t Confess | (-1,-1) | (0,-9) |
| Player 2 Confesses | (-9,0) | (-5, -5) |
In theory, both players will confess since it is the safer of the two options. Even though the lowest punishment is (-1,-1), the chance of receiving a -9 punishment deters that choice. In the long run, however, each player will fear retaliation of the other, which will eventually lead to cooperation. Still, William Press and Freeman Dyson, two physicists, argue that there might be a better option than cooperation, which they call “zero-determinant” strategies. In these strategies, the players make choices based on results from previous rounds.
In the past, one popular strategy, called “tit-for-tat”, was to choose the same option as the other player did from the previous round. In other words, betrayal returns betrayal, and cooperation returns cooperation. Obviously enough, if Player 1 knew that Player 2 was using the “tit-for-tat” strategy, he would be certain of Player 2’s next move. In that case, Player 1 could use his ability to predict Player 2’s moves to his advantage. As an alternative, the “zero-determinant” strategy is safer since the next choice is based on probabilities, which gives the next choice some unpredictability.
The article below does note, however, that this isn’t necessarily the most optimal strategy for all scenarios. When both Player 1 and Player 2 employ the “zero-determinant” strategy, they will do badly. The trick to succeeding with this strategy, it seems, is to first identify the strategy the other player is using and accommodate to that strategy. Of course, that’s not to say the opponent player will not change his or her strategy as well. Admittedly, this new strategy adds a whole new level of complexity to game theory, although its practicality may not be entirely feasible. After all, is it possible to read minds? Not entirely.
-anon-i-mouse
Resources: http://www.nature.com/news/physicists-suggest-selfishness-can-pay-1.11254