Shoe Stores


Shoe stores and large-footed female customers play a coordination game that can be studied using the Nash equilibrium.[4] Shoe stores want to keep their inventories down so they stock only shoe sizes which customers request.[5] Women with large feet apparently get embarrassed when told that a store doesn’t have anything in their size, so they avoid stores that don’t stock large shoes.[6]

The coordination game played between the shoe customer and the store is shown in Figure 33 and it has two Nash equilibria. In the first, stores stock large sizes and women with big feet get their shoes from normal retail stores.

click to expand
Figure 33

In the second equilibrium, the retailer doesn’t stock large sizes, and the women don’t shop at retail shoe stores. According to an article in Slate.com, this petite equilibrium currently predominates.[7] The no-large-shoe equilibrium is Nash because no one player can do better by deviating. If the store started to stock large sizes, it would just build up an inventory because the big-footed women wouldn’t think to ask for them. If the women started asking for the large sizes, they would feel humiliated because the store wouldn’t have their size in stock.

The shoe stores could break out of the bad equilibrium by advertising. In a Nash equilibrium you assume that your opponent’s strategy is fixed and unalterable. This, of course, isn’t always true. If it’s possible for you to both change your own strategy and alter your opponent’s move, then you could go to a better equilibrium.

In Figure 33 the shoe store and customer can end up in either a good or bad Nash equilibrium. The next chapter considers a class of games where there is only one type of Nash equilibrium, and it’s a nasty one since it results in both players spending life in prison.

[4]Slate (May 10, 2002) provides a non-game theoretic analysis of this issue.

[5]Ibid.

[6]Ibid.

[7]Ibid.




Game Theory at Work(c) How to Use Game Theory to Outthink and Outmaneuver Your Competition
Game Theory at Work(c) How to Use Game Theory to Outthink and Outmaneuver Your Competition
ISBN: N/A
EAN: N/A
Year: 2005
Pages: 260

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