4 ms·
If all three vendors know that the others are trustworthy, intelligent and learned in game theory, you might end up with the "everyone cooperates" solution that
by red_admiral 8y ago
If all three vendors know that the others are trustworthy, intelligent and learned in game theory, you might end up with the "everyone cooperates" solution that's optimal for everyone (1/6, 3/6 and 5/6 along the beach) especially if everyone knows the order in which the three are going to have to commit to their preferences.
In practice, base64(solution) =
RXZlcnlvbmUgcGlja3MgdW5pZm9ybWx5IGF0IHJhbmRvbT8gTXkgZmlyc
3QgdGhvdWdodCBpcyB0aGlzIG1pbmltaXplcyB0aGUgcmlzayBvZiBiZW
luZyAic2FuZHdpY2hlZCIgYnkgeW91ciB0d28gY29tcGV0aXRvcnMu
?
- lucas_membrane 8y agoMy analysis long ago was that for this case, the equilibrium mixed strategy with three players was a random choice with uniform probability everywhere within the interval from 1/4 to 3/4 and no probability in the segments at each end. This means that for the people at the ends of the beach, the competitive solution with 3 vendors is not as good as the centrally planned solution with 2 vendors, but for those in the middle of the beach it is very likely to be much better. This lines up with the conclusion for the 2 vendor case that Hotelling found: competition with few vendors for somewhat differentiated products will favor consumers with average preferences.