Shaking the Tree

Life often results in situations such that no strategy suggests any further moves. We just don’t know what to do next. In a game of perfect information, where each player knows all the previous moves, this can signal stalemate. Take chess: given both sides know everything that has transpired and have no reason to believe that the opponent will make a mistake, there can come a time when both sides will realize that there are […]

An Introduction to the Game Theoretic Semantics view of Scientific Theory

What is a scientific theory?  In an abstract sense, a scientific theory is a group of statements about the world.  For instance the Special Theory of Relativity has, “The speed of light in a vacuum is invariant,” as a core statement, among others, about the world.  This statement is scientific because, in part, it is meant to hold in a ‘law-like’ fashion: it holds across time, space and observer. The Popperian view is that we […]

Risky Kakanomics

Gloria Origgi writes: This is an application of the theory of kakonomics, that is, the study of the rational preferences for lower-quality or mediocre outcomes, to the apparently weird results of Italian elections. The apparent irrationality of 30% of the electorate who decided to vote for Berlusconi again is explained as a perfectly rational strategy of maintaining a system of mediocre exchanges in which politicians don’t do what they have promised to do and citizens […]

Metta World Peace, James Harden and Furbizia

Everyone is saying that Metta World Peace (the basketball player formerly known as Ron Artest) is crazy for elbowing James Harden in the face. I can’t say that I disagree, but I think there is more to the story. Did no one else notice that James Harden walked right into World Peace while he was celebrating? Watch the video. Harden walks directly into MWP. He doesn’t do anything that would cause a foul, but if […]

Trembling Hands

At least since Selten (1975) game theorists have considered that given a series of decisions there is some small probability that the person making the decisions will make a mistake and do something irrational, even if she knows the right thing to do.  This is called the trembling hand approach: although a person rationally knows the right (rational) thing to do, sometimes her hand trembles and she chooses incorrectly. Therefore, given a game defined by […]

Wittgenstein and Sun Tzu (on throwing the ladder away)

Wittgenstein, Tractatus Logico-Philosophicus #6.54 My Propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them — as steps — to climb beyond them.  (He must, so to speak, throw away the ladder after he has climbed up it.) He must overcome these propositions, and then he will see the world aright. Sun Tzu, The Art of War, Chapter XI #38 At the critical […]

Rock Paper Scissors

Rock Paper Scissors is a game in which 2 players each choose one of three options: either rock, paper or scissors.  Then the players simultaneously reveal their choices.  Rock beats scissors but loses to paper (rock smashes scissors); Paper beats rock and loses to scissors (paper covers rock); Scissors beats paper but loses to rock (scissors cut paper).  This cyclical payoff scheme (Rock > Scissors, Scissors > Paper, Paper > Rock) can be represented by […]

Sexual Reproduction

Say you are a single celled organism.  To reproduce you have to double your size and then you need to split yourself in half.  Repeat indefinitely. Now say you are a single celled organism that has the option to reproduce sexually.  To reproduce you need to increase yourself to 3/2 your original size and find a similar mate.  Then you both contribute 1/2 to the new organism and repeat indefinitely. Asexual reproduction requires you to […]

The Deal with ‘Deal or No Deal’

I just saw the hit game show ‘Deal or No Deal‘.  It wasn’t the first time, but this episode had a contestant with folksiness to rival Palin, so I was entertained and kept watching. But is there any gamesmanship to the ‘Deal or No Deal’ gameshow?  The short answer is: No. The show begins with the contestant choosing a briefcase that contains a number that represents a real monetary amount.  The case is chosen from […]

What are Quantifiers?

What are quantifiers?  Quantifiers have been thought of things that ‘range over’ a set of objects.  For example, if I say There are people with blue eyes this statement can be represented as (with the domain restricted to people): ∃x(Bx). This statement says that there is at least one person with property B, blue eyes. So the ‘Ex’ is doing the work of looking at the people in the domain (all people) and picking out […]