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There are variations of the problem that explore the benefits to/of competition when there are more vendors. If there are 3 vendors and the vendors are allowed

There are variations of the problem that explore the benefits to/of competition when there are more vendors. If there are 3 vendors and the vendors are allowed to collaborate, a coalition of 2 vendors will form, they will place there stands at positions 1/4 and 3/4, same as the optimum for consumers with 2 vendors, and the 2-vendor team will get 3/4 the business, which they may share equally by side payments, and the outcast vendor will get only 1/4 of the business, regardless of where he locates. If he locates anywhere other than right next to one of the duopolists, however, the closest duopolist can then relocate closer to the outcast to decrease the outcast's market share. Thus, an unregulated market of 3 vendors with anticompetitive behavior allowed, will only match the optimum (for customers) that is attainable with 2 vendors and centralized planning. The labor and capital of the 3rd vendor produce no benefit to the customers. If you think that this situation is unrealistic, compare it to the market in the USA for steel back when a single firm with its center of production in Pittsburgh was dominant: the dominant pricing model for all firms was 'Pittsburgh plus.' This means that steel customers, regardless of which vendor they chose or where that vendor actually produced the steel, paid shipping charges from Pittsburgh. The customers got no benefit from the geographic diversity of the industry. If there are 3 vendors, and if the beach is regulated so that each vendor must select his/her own location before finding out what locations the others have chosen, with collaboration and moving of locations prohibited, what locations will the 3 vendors choose?

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 ago
  My 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.

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 ago
My 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.