There are a few tweaks to the Iterated Prisoner’s Dilemma which can affect which strategies tend to be successful. A very common one is to randomize how long the round is, so predicting the end-game doesn’t overwhelm all other strategy factors. A less common one is adding noise, so that what each program tries to do isn’t necessarily what happens.
Does anyone know of any tourneys that have been run where, in addition to Cooperation or Defection, each program also has the choice to End The Game, simulating quitting a business relationship, moving away, shunning, or otherwise ceasing to interact with another program?
Not aware of any tourneys with this tweak, but I use a similar example when I teach.
If the payoff from exiting is zero and the mutual defection payoff is negative, then the game doesn’t change much. Exit on the first round becomes the unique subgame-perfect equilibrium of any finite repetition, and with a random end date, trigger strategies to support cooperation work similarly to the original game.
Life is a more interesting if the mutual defection payoff is sufficiently better than exit. Cooperation can happen in equilibrium even when the end date is known (except on the last round) since exit is a viable threat to punish defection.
What happens when you quit interaction? If this is literally end of the game, you will probably get less points than other players. Well, depending on the payout matrix; because usually the strategies don’t change if you add a constant to all numbers in the matrix, but in this case the constant would influence the cost of quitting the game prematurely.
Perhaps the players who leave their partner should be assigned a random partner in the next turn—chosen randomly those from players who left their partner (or their partner left them) in this turn. Thus everyone would play the same number of turns; you just have an opportunity to replace your partner if you beieve that a random replacement will be better.
Let’s suppose there are so many players that your chance of randomly meeting the same player again is almost zero, so we don’t have to consider with this option.
As an example of the game, let’s say there are two kinds of players: DefectBot always chooses “defect”. OneChanceBot always chooses “cooperate”, but immediately leaves if the opponent defects. At the beginning, DefectBots will gain points, but after a few turns most OneChanceBots will end up in a pair with another OneChanceBot and gain many points, while most DefectBots will end up in a pair with another DefectBot. If the DefectBots also choose to leave if their opponent defects, they will gain some time, but ultimately all OneChanceBots will be removed from the pool of players who change pairs.
In this game the correct strategy would strongly depend on the environment. For example, let’s suppose we have five kinds of RandomBots, each kind in every turn cooperates with some probability (different number for different kind of RandomBot), and each kind in every turn leaves their partner with some probability. You are the only non-random player, and you know about the RandomBot nature in advance, but you don’t know the exact probabilites. To play this game best, you would have to collect a lot of data, make your model of the RandomBot probabilities, and then for every partner you get evaluate the chance the he belongs to one of those kinds, and whether it is better or not to replace them with a random choice. Could be an interesting Bayesian exercise. But you would need many turns (maybe thousands) so that the good strategy would win reliably over another non-random player who made a mistake in their Bayesian equations.
Prisoner’s Dilemma Variant
There are a few tweaks to the Iterated Prisoner’s Dilemma which can affect which strategies tend to be successful. A very common one is to randomize how long the round is, so predicting the end-game doesn’t overwhelm all other strategy factors. A less common one is adding noise, so that what each program tries to do isn’t necessarily what happens.
Does anyone know of any tourneys that have been run where, in addition to Cooperation or Defection, each program also has the choice to End The Game, simulating quitting a business relationship, moving away, shunning, or otherwise ceasing to interact with another program?
Not aware of any tourneys with this tweak, but I use a similar example when I teach.
If the payoff from exiting is zero and the mutual defection payoff is negative, then the game doesn’t change much. Exit on the first round becomes the unique subgame-perfect equilibrium of any finite repetition, and with a random end date, trigger strategies to support cooperation work similarly to the original game.
Life is a more interesting if the mutual defection payoff is sufficiently better than exit. Cooperation can happen in equilibrium even when the end date is known (except on the last round) since exit is a viable threat to punish defection.
Haven’t heard about such version.
What happens when you quit interaction? If this is literally end of the game, you will probably get less points than other players. Well, depending on the payout matrix; because usually the strategies don’t change if you add a constant to all numbers in the matrix, but in this case the constant would influence the cost of quitting the game prematurely.
Perhaps the players who leave their partner should be assigned a random partner in the next turn—chosen randomly those from players who left their partner (or their partner left them) in this turn. Thus everyone would play the same number of turns; you just have an opportunity to replace your partner if you beieve that a random replacement will be better.
Let’s suppose there are so many players that your chance of randomly meeting the same player again is almost zero, so we don’t have to consider with this option.
As an example of the game, let’s say there are two kinds of players: DefectBot always chooses “defect”. OneChanceBot always chooses “cooperate”, but immediately leaves if the opponent defects. At the beginning, DefectBots will gain points, but after a few turns most OneChanceBots will end up in a pair with another OneChanceBot and gain many points, while most DefectBots will end up in a pair with another DefectBot. If the DefectBots also choose to leave if their opponent defects, they will gain some time, but ultimately all OneChanceBots will be removed from the pool of players who change pairs.
In this game the correct strategy would strongly depend on the environment. For example, let’s suppose we have five kinds of RandomBots, each kind in every turn cooperates with some probability (different number for different kind of RandomBot), and each kind in every turn leaves their partner with some probability. You are the only non-random player, and you know about the RandomBot nature in advance, but you don’t know the exact probabilites. To play this game best, you would have to collect a lot of data, make your model of the RandomBot probabilities, and then for every partner you get evaluate the chance the he belongs to one of those kinds, and whether it is better or not to replace them with a random choice. Could be an interesting Bayesian exercise. But you would need many turns (maybe thousands) so that the good strategy would win reliably over another non-random player who made a mistake in their Bayesian equations.