Game Theory
goodmath | March 31, 2008 In game theory, perhaps the most important category of simple games is
something called zero sum games. It's also one of those mathematical
things that are widely abused by the clueless - you constantly hear
references to the term "zero-sum game" in all sorts of contexts, and they're
almost always wrong.
A zero-sum game is a game in which the players are competing for resources, and the set of resources is fixed. The fixed resources means that any gain by one player is necessarily offset by a loss by another player. The reason that this is called
zero-sum is because you can take any result…
goodmath | March 23, 2008 As an introduction to a mathematical game, and how you
can use a little bit of math to form a description of the game that
allows you to determine the optimal strategy, I'm going to talk a bit about Nim.
Nim is a simple two-player turn-taking game. The idea is you've got a collection of piles of rocks. The standard
terminology calls each pile a heap. Each turn, a player can take any number of rocks from any single heap.
In classic Nim, whoever takes the last rock loses. But we're going to start with an easier to analyze variant, where
whoever takes the last rock wins.
Let's look at an…
goodmath | March 19, 2008 Lots of people wanted game theory, so game theory it is. The logical first question: what is game theory?
Game theory is typical of math. What mathematicians like to do is reduce
things to fundamental abstract structures or systems, and understand them in
terms of the abstraction. So game theory studies an abstraction of games - and
because of the level of abstraction, it turns out be be applicable to a wide
variety of things besides what you might typically think of as games.
Game theory starts with the fundamental idea of a game. What is
a game?
A game consists of a system with at least…
edyong | March 19, 2008Two weeks ago, I wrote about a Science paper which looked at the effects of punishment in different societies across the world. Through a series of fascinating psychological experiments, the paper showed that the ability to punish freeloaders stabilises cooperative behaviour, bringing out the selfless side in people by making things more difficult for cheaters. The paper also showed that 'antisocial punishment', where the punished seek revenge on the punishers, derails the high levels of cooperation that other fairer forms of punishment help to entrench.
Now a new study published in that…
edyong | March 6, 2008
Humans have an extraordinary capacity for selflessness. We often help complete strangers who are unrelated to us, who we may never meet again and who are unlikely to be able to return the favour. More and more, we are being asked to behave in selfless ways to further the common good, not least in the race to tackle climate change.
Given these challenges, it's more important than ever to understand the roots of cooperative behaviour. From an evolutionary point of view, it can be a bit puzzling because any utopic society finds itself vulnerable to slackers, who can prosper at the expense of…
purepedantry | February 29, 2008Jay Cost at RCP uses a prisoner's dilemma game to show why the absense of institutional structures is likely to yield a socially inefficient result in the Democratic primaries. He looks at the super delegates' behavior in terms of what is good for them vs. what is good for the party:
The core problem is that the Democrats have empowered the super delegates to break a tie, but they have not empowered anybody to manage the super delegates. There are no rules that demand the super delegates convene and discuss with one another. There is nobody in charge of regulating the debate. There is…
purepedantry | July 11, 2007One of the ways that scientists study human decision making is through the study of behavior in simple games -- loosely lumped into a field called game theory.
Some of the most interesting and revealing findings involving such games is that human beings are not "strictly rational." Before everyone jumps all over me, let me define that statement. Strictly rational in this sense means that the behavior of human beings during these games does not always maximize expected value of the numerical (usually monetary) reward over the long-term. In laymans terms, if you offer someone $5 with no…
purepedantry | July 3, 2007Rats show a type of "generalized" altruism:
Rats that benefit from the charity of others are more likely to help strangers get a free meal, researchers have found.
This phenomenon, known as 'generalized reciprocity', has only ever been seen before in humans. A good example, says Michael Taborsky of the University of Bern, Switzerland, is what happens when someone finds money in a phone box. In controlled experiments such people have been shown to be much more likely to help out a stranger in need following their good luck.
In humans, such benevolence can be explained by cultural factors as…
purepedantry | May 15, 2007Paul Rubin has an editorial in the Washington Post about how evolution may result in a proclivity towards economic and social conflict:
Conflict was common in the environment in which humans evolved. As primates, which are a very social order, our ancestors lived in relatively small groups in which everyone knew everyone else. Our minds are adapted to deal with populations of that size. Our ancestors made strong distinctions between members of the in-group and outsiders, and we still make such distinctions today -- social psychologists can create in-group and out-group feelings based on…
kcontreary | December 6, 2006A favorite professor of mine once told me that it's always impressive to start with an example from the 18th century. So in deference to him and with a nod to Jonah Lehrer's forthcoming book, I'd like to mention Goethe's anticipation of one of the pillars of auction theory, as elaborated in an article by Moldovanu and Tietzel in JPE 1998.
In 1797, one of the central features of the book market in the (not yet unified) German states was the absence of copyright protection. An author sold his work to a publisher for a set fee, thereby fully relinquishing his rights to it. Publishers could…
purepedantry | June 29, 2006How does cooperation evolve? It is in an organism's best interest to screw its competitors in order to best convey its genes to the next generation, yet we see a variety of human and animals examples of cooperation. The answer falls to a division of mathematics and economics called Game Theory. Game Theory examines the behavior of individuals (or software constructs designed to replicate individual behaviors) as they interact. Generally, this interaction occurs in terms of simple games where the effects of different strategies on the outcome -- cooperation or competition -- can be…