Comment on Nash Equilibria and Schelling Points

Fri, 29 Jun 2012 09:04:15 GMT

There is no pure equilibrium, but there is a mixed equilibrium.

A pure strategy is a single move played ad infinitum.

A mixed strategy is a set of moves, with each turn's move randomly selected from this set.

A pure equilibrium is one where every player follows a pure strategy, and a mixd equilibrium is one where at least some players follow a mixed strategy.

Both pure equilibriums and mixed equilibriums are Nash equilibriums. Nash's proof that every game has an equilibrium rests on his previous work where he and von Neumann invented the concept of a mixed equilibrium and proving that it satisfies the criteria.

So this game has no pure equilibrium, but it does have a mixed one. Yvain goes on to describe how you calculate and determine that mixed equilibrium, and shows that it is the attacker playing Podunk 1/11th the time, and Metropolis 10/11th the time.

EDIT: The post explains this at the end:

Some equilibria are simple choices, others involve plans to make choices randomly according to certain criteria.

Yvain: I would strongly recommend including a quick explanation of mixed and pure strategies, and defining equilibriums as either mixed or pure, as a clarification. At the least, move this line up to near the top. Excellent post and excellent sequence.

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