Tuesday, March 24, 2009

Allocation mechanisms in Scrabble

Earlier this semester Applied Microeconomics students compared the efficiency implications of allocating goods and services through a competitive price mechanism, a random mechanism and a queuing mechansism. Allocations generated by a random mechanism are considered to be generally Pareto-inferior to competitive price based allocations. While not discussed in class, it is important to recognise that random allocations are used widely in games of chance (or those that have a significant element of chance).

Professor Jeff Ely at Northwestern University provides an innovative suggestion with regards to allocation mechanisms in Scrabble! Some background - "Za" and "qi" have recently been added to the game's official word list for its original English-language edition. Given that the traditional high scoring leters are more versatile, should they be revalued?

Let’s kill two birds with one stone. Eliminate the role of chance in scrabble by having players buy their letters rather than draw them at random. Whenever a player needs to replenish his tiles, a tile is turned over and put up for auction. Players bid for the tile with points. A player who already has seven tiles who wins the auction selects one of his tiles to replace and puts that tile up for auction. This continues until all players have seven tiles.

This removes chance from the game and also eliminates the need to revalue the tiles because that will be taken care of endogenously by competitive bidding.

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