Game Development Reference

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But RPSLS gains nothing in terms of decision interest over RPS. No

Nash equilibrium means no Nash equilibrium. Adding more symbols

does nothing to enrich the mind game of anticipation and deception. More

options may add fictional interest, but it's probably not worth the extra

learning burden.

mixeD stRategies

So far, I've described 1games like rock-paper-scissors as having no Nash

equilibrium. This wasn't entirely accurate. Rock-paper-scissors has no

pure
Nash equilibrium. It does, however, have a
mixed
Nash equilibrium.

A MIXED NASH EQUILIBRIUM is a Nash equilibrium where each player

randomly chooses from a set of strategies with some given set of

probabilities.

In rock-paper-scissors, for example, there is no pure Nash equilib-

rium, but there is one mixed Nash equilibrium. It calls for both players to

throw each move 33.3% of the time. This is a Nash equilibrium since there

is no way one player can gain by deviating from this configuration (since

when the opponent is throwing with perfect randomness, it doesn't matter

what you do; you'll always win half the games).

Other strategy mixes in rock-paper-scissors are not in equilibrium.

For example, imagine you were to choose rock 35% of the time and scissors

and paper 32.5% of the time. Now your opponent can beat you by changing

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