Two robots are playing a game. Between them is a pile of coins. Each robot, on its turn, can take either one or two coins from the pile. So long as each elects to take one coin, play continues until the pile is exhausted. If either elects to take two, the remaining coins vanish and the game ends.
One might think that the best plan would be always to take a single coin, but if both players are rational and know it, the first player will immediately take two pennies and end the game.
He reasons thus: If there were only two pennies in the pile, I’d benefit most by taking both of them rather than just one. Now suppose there were three pennies. If I took only one, then I would leave my opponent in the position I just imagined, and being rational he’d take both remaining pennies. Therefore I should take two of the three.
And so on backward, up to any arbitrary number of pennies. Paradoxically, it seems, improvident greed is more rational than constructive cooperation. Adapted from Hollis, Martin and Sugden, Robert (1993) “Rationality in action.” Mind 103:1-35, referenced in R.M. Sainsbury, Paradoxes, 2009.
Comments
2 responses to “The Penny Game”
Depends, is your aim “get as many pennies as I can” or “get more than the other guy”? Because one of those is an empty victory, especially when extrapolaed out of the game and into real life.
I’d rather have my life not at the top of modern society than be a medieval monarch at the top of theirs. Because they have two measly coins and some lice…
Concerning the fall, it is indeed my psotiion. However, that’s a psotiion I couldn’t claim to prove in the same way I would claim to be able to prove the existence of God. Notice that while a deist maintains views which are irreligious, their view of God is minimally what a religious theist means by suggesting that God’ exists. Religious people may mean more by God’ but they don’t mean any less, and they don’t mean anything different. Atheism isn’t the same as a denial of religion, Atheism is generally the commitment to the proposition God does not exist . That’s what the post we’re commenting on is about, I take it. Moreover, for somebody to say that atheism is necessary, they must mean that there are problems with Theism which are indissoluble. One problem might be how God doesn’t seem to be evident to people who haven’t reflected on it very much, or even sometimes not evident to those who seem to have reflected on it a lot. I provided a logically possible answer simply as a way to demonstrate that an answer is not only possible, but is a live option offered by a formal religion. Whether one thinks it is plausible or not is sort of besides the point for the argument though the argument merely shows that a solution is not only possible, but also not very difficult. Even if you knew your audience was fully familiar with those arguments, why should they assume you are claiming those particular arguments for support when you didn’t reference them? I’ve heard numerous people make very much the same statements as you have, and many of them have claimed completely different (and sometimes mutually exclusive) support for their psotiions. I wasn’t claiming those particular arguments I was appealing to the existence of such-like arguments which aren’t hard to find. In fact, I only looked those few up in my library once you had asked me for some. Perhaps there are some arguments against the proposition that prayer can be efficacious you are most welcome to provide me those for me to consider as well. Or else, maybe you would care to take issue with any single point I’ve made thus far and we can deal with just that one (one at a time). This is, of course, up to you.Finally, and more importantly, you say: That’s the most disingenuous apology I’ve heard in a long time. Ignoring the fact that you then go on to present the most personal attack I have received in a long time, I am not quite sure what to say I know things can often be lost in translation online, and maybe it would be better if I could speak with you face to face, but for whatever it is worth the apology was sincere. I do feel sorry for any condescension, and I am currently trying to take you seriously, and prepared to field any arguments or points that you may want to present me. I am confident that I can manage to demonstrate, if given the opportunity, that the points I am making are good points, good arguments, and worthy of serious attention. Moreover, I am convinced, and I hope you agree, that the rhetorical tone of the posts, such as the one we’re commenting on, isn’t helpful or intelligent.