Game Theory
edyong | March 8, 2010Ever wonder if acts of kindness or malice really do ripple outwards? If you give up a seat on a train to a stranger, do they go onto "pay it forward" to others? Likewise, if you steal someone's seat, does the bad mood you engender topple over to other people like a set of malicious dominoes? We'd all probably assume that the answers to both questions were yes, but James Fowler and Nicholas Christakis think they have found experimental evidence for the contagious nature of cooperation and cheating.
The duo analysed data from an earlier psychological experiment by Ernst Fehr and Simon Gachter…
edyong | December 8, 2009What do you think a group of women would do if they were given a dose of testosterone before playing a game? Our folk wisdom tells us that they would probably become more aggressive, selfish or antisocial. Well, that's true... but only if they think they've been given testosterone.
If they don't know whether they've been given testosterone or placebo, the hormone actually has the opposite effect to the one most people would expect - it promotes fair play. The belligerent behaviour stereotypically linked to testosterone only surfaces if people think they've been given hormone, whether they…
edyong | December 1, 2009Oscar Wilde once said, "One can survive everything nowadays, except death, and live down anything, except a good reputation." All well and witty, but for those of us who aren't Victorian cads, reputation matters. It's the bedrock that our social lives are built upon and people go to great lengths to build and maintain a solid one. A new study shows that our ability to do this involves the right half of our brain, and particularly an area called the lateral prefrontal cortex (PFC).
Disrupting the neurons in this area hampers a person's ability to build a reputation while playing psychological…
edyong | September 3, 2009When it comes to encouraging people to work together for the greater good, carrots work better than sticks. That's the message from a new study showing that rewarding people for good behaviour is better at promoting cooperation than punishing them for offences.
David Rand from Harvard University asked teams of volunteers to play "public goods games", where they could cheat or cooperate with each other for real money. After many rounds of play, the players were more likely to work together if they could reward each other for good behaviour or punish each other for offences. But of these two…
edyong | April 7, 2009Some people go out of their way to help their peers, while others are more selfish. Some lend their trust easily, while others are more suspicious and distrustful. Some dive headlong into risky ventures; others shun risk like visiting in-laws. There's every reason to believe that these differences in behaviour have biological roots, and some studies have suggested that they are influenced by sex hormones, like testosterone and oestrogen.
It's an intriguing idea, not least because men and women have very different levels of these hormones. Could that explain differences in behaviour between…
edyong | April 6, 2009What happens when you remember a good deed, or think of yourself as a stand-up citizen? You might think that your shining self-image would reinforce the value of selflessness and make you more likely to behave morally in the future. But a new study disagrees.
Through three psychological experiments, Sonya Sachdeva from Northwestern University found that people who are primed to think well of themselves behave less altruistically than those whose moral identity is threatened. They donate less to charity and they become less likely to make decisions for the good of the environment.
Sachdeva…
edyong | March 28, 2009
Animals have distinct personalities and temperaments, but why would evolution favour these over more flexible and adaptible mindsets? New game theory models show that animal personalities are a natural progression from the choices they make over how to live and reproduce.
Any pet owner, wildlife photographer or zookeeper will tell you that animals have distinct personalities. Some are aggressive, others are docile; some are bold, others are timid.
In some circles, ascribing personalities to animals is still a cardinal sin of biology and warrants being branded with a scarlet A (for…
edyong | March 2, 2009I live in London. According to Google Analytics, 96% of this blog's readers make their homes in a different city and 91% live in another country altogether. The fact that most of you are reading this post at all is a symptom of the globalised state of the 21st century.
Through telecommunications, the Internet, free trade, air travel and more, the world's population is becoming increasingly connected and dependent on one another. And as this happens, the problems that face us as a species are becoming ever more apparent, from our relentless overuse of natural resources to the threat of…
edyong | January 19, 2009People seem inordinately keen to pit nature and nurture as imagined adversaries, but this naive view glosses over the far more interesting interactions between the two. These interactions between genes and environment lie at the heart of a new study by Rose McDermott from Brown University, which elegantly fuses two of my favourite topics - genetic influences on behaviour and the psychology of punishment.
three previous pieces on punishment. Each was based on a study that used clever psychological games to investigate how people behave when they are given a choice to cooperate with, cheat, or…
edyong | December 4, 2008Is punishment a destructive force that breaks societies or part of the very glue that holds them together? Last year, I blogged about two studies that tried to answer this question using similar psychological games. In both, volunteers played with tokens that were eventually exchanged for money. They had the option to either cooperate with each other so that the group as a whole reaped the greatest benefits, or cheat and freeload off the efforts of their peers.
In both studies, giving the players the option to punish each other soon put a relative end to cheating. Faced with the threat of…
edyong | September 25, 2008The art of auctioning is an ancient one. The concept of competitively bidding for goods has lasted from Roman times, when spoils of war were divvied up around a planted spear, to the 21st century, when the spoils of the loft are sold through eBay. But despite society's familiarity with the concept, people who take part in auctions still behave in a strange way - they tend to overbid, offering more money than what they actually think an object is worth.
Some economists have suggested that people overbid because they are averse to risk. They would rather make spend more money to be sure of a…
edyong | August 27, 2008 Yesterday, I wrote about selfless capuchin monkeys, who find personal reward in the act of giving other monkeys. The results seemed to demonstrate that monkeys are sensitive to the welfare of their peers, and will make choices that benefit others without any material gain for themselves. Today, another study looks at the same processes in a very different sort of cheeky monkey - human children.
Humans are notable among other animals for our vast capacity for cooperation and empathy. Our concern about the experiences of other people, and our natural aversion to unfair play are the bedrocks…
edyong | August 8, 2008
Social lives are delicate things. We've all had situations where friendships and relationships have been dented and broken, and we're reasonably skilled at repairing the damage. This ability to keep our social ties from snapping relies on being able to read other people, and on knowing a thing or two about what's normal in human society.
For instance, we appreciate that cheating fosters ill-will, while generosity can engender trust. So cheaters might try to win back their companions with giving gestures. These little exchanges are the glue that bind groups of people into happy and…
goodmath | July 30, 2008
Moving on from simple zero-sum games, there are a bunch of directions in which
we can go. So far, the games we've looked at are very restrictive. Beyond the
zero-sum property, they're built on a set of fundamental properties which ultimately
reduce to the idea that no player ever has an information advantage over any other
player: the complete payoff matrix is known by all players; no player gets
to see the other players strategy before selecting their own; and so on.
Moving on to more interesting games, we can relax those assumptions, and allow information to be hidden. Perhaps each…
purepedantry | July 21, 2008I suspect that many of you got a chance to see The Dark Knight movie this weekend.
Just as an aside, I will say that I thought that the movie was sweet. Definitely the best Batman movie, maybe one of the best superhero movies ever made. Heath Ledger is terrifyingly good throughout. Aaron Eckhart and Christian Bale give excellent performances as well, and Maggie Gyllenhaal is a hell of lot better than Katie Holmes.
Anyway, there is a scene in the movie that got me thinking about game theory, and that is what I want to talk about. Beware, if you haven't seen the film, this discussion…
goodmath | July 21, 2008 Before we move beyond zero-sum games, it's worth taking a deeper look
at the idea of utilities. As I mentioned before, in a game, the scores in
the matrix are given by something called a utility function.
Utility is an idea for how to mathematically describe preferences in terms
of a game or lottery. For a game to be valid (that is, for a game to have a meaningful analysis and solution), there must be a valid utility function that
describes the players' preferences.
But what do we have to do to make a valid utility function? It's
simple, but as usual, we'll make it all formal and explicit…
goodmath | July 16, 2008 When I last wrote about game theory, we were working up to how to find
the general solution to an iterated two-player zero-sum game. Since it's been
a while, I'll take a moment and refresh your memory a bit.
A zero-sum game is described as a matrix. One player picks a row, and one player picks a column. Those selections are called strategies. The intersection
of the strategies in the game matrix describes what one player pays to the other. The
matrix is generally written from the point of view of one player. So if we call
our two players A and B, and the matrix is written from the viewpoint…
goodmath | June 10, 2008 So, I've finally had some time to get back to the linear programming
followup. You might want to go back and look at the earlier post to remember what I was talking about.
The basic idea is that we've got a system we'd like to optimize. The constraints of the system are defined by a set of linear inequalities, and
we've got a linear expression that we'd like to maximize.
So, for example, we could have a factory which is capable of producing two
different kinds of widgets. The factory has a maximum capacity of what it can
produce of 300 widgets per day. It gets a supply of metal and plastic…
goodmath | May 5, 2008 The games that we've looked at so far are the simplest case of
basic games. In these games, we've got a payoff matrix, and both players
can see the whole matrix - the players have equal information,
and nothing is secret. The players move simultaneously - so neither player can wait to see what his opponent does before making his own decision. Finally, the game is played exactly once - there are no repetitions.
The first complication we can add is to make it an iterative game - that is, instead of each player going once, they'll repeat the game 10 times in sequence. Everything else stays the…
goodmath | April 25, 2008 Last time I wrote about Game Theory, I explained the basic idea of
zero sum games. In their simplest form, a game can be described by a payoff matrix,where each dimension of the matrix is the set of strategies which can be selected by one player, and each entry in the matrix describes the payoffs that result when all players select their strategy. Informally, a game is zero-sum when the total payoff is zero - that is, when any positive payout to one player is balanced by payouts from other players.
We can formalize some of the basic ideas more precisely. What we can say is that each move…