4-move rock, paper, scissors!

Contrary to baseless speculation, it turns out it is possible to have a four-player, non-degenerate RPS game. The game below is assymetrical: B does better than others, but you don't want to play it all the time because that makes you vulnerable to A. By contrast, D ain't so hot. But if you never play D, then your opponent can get away with A. It's uneven, but the optimal mixed strategy plays everything with non-zero probability.



Notation: the arrow from A to B means that A beats B. Everyone ties themself. No arrow indicates a tie. There is a tie between A and C. The previous analysis indicated there is no non-degenerate 4-RPS with no ties. This has only 1 tie, so it seems to be the best possible.

(This game is just the previous one with the link from A to C removed. This makes it so B no longer dominates C, since C is now invulnerable from A, unlike B.)

Two Middle East politics visualizations

These are both useful summaries. Slate has a chart of relationships between Hamas, Hezbollah, Israel, and Lebanon, versus a number of different actors in the region. NYTimes has something similar on a map, also showing the sizes of ethnic/religious groups. Seems the NYTimes is most interesting as far as visualization/graphic design goes. It also has rich relational information and lots of predicates: does group X have oil wealth? is group X in the government of country Y? Etc. Seems ripe for a relational concept-learning clustering analysis...

[From Metafilter]

neuroscience and economics both ways

I previously posted two neuroeconomics reviews. Here's a new one from this year in Trends in Cognitive Sciences. It's interesting because not only does it look at using psychological knowledge to inform economics, but it also reviews work in the other direction: using economic decision and organizational theory to study brain systems. For example,
here's a paper that analyzes brain reward circuitry using labor supply theory.

The review:
Sanfey, Loewenstein, McClure, Cohen: "Neuroeconomics: cross-currents in research on decision-making"