Game Theory 101: Battle of the Sexes

William Spaniel solves the battle of the sexes (sometimes called Bach or Stravinsky), one of the most common strategic form games in game theory.

Category:

Education

Tags:

• game
• theory
• pure
• mixed
• strategy
• nash
• equilibrium
• battle
• of
• the
• sexes
• bach
• or
• stravinsky
• strategic
• matrix
• form

[GelatinGhost]

Wouldn't the best strategy be to flip a coin? If they both flip a coin, the expected payout is 3/4, as opposed to 2/3.

[JimBobJenkins]

@GelatinGhost If you flipped a coin, my best response would be to always go to my preferred form of entertainment. You can do some quick calculations to verify this.

[OnAFirefly]

Good work. I like these slightly longer videos--5 to 10 minutes instead of 2 to 5; I think that helps in understanding the broader context of the individual topics

[JimBobJenkins]

@OnAFirefly I'm not sure which I like better or if I simply need both. =/

[balancedscorecard79]

@JimBobJenkins When he said flipping the coin he meant that both players commit to play according to what the coin toss shows. If they are to do whatever they prefer better not toss the coin at all. Tossing the coin (with comittment) provides a correlating device which strictly increases the payoffs like GelatinGhost correctly has observed.

[GelatinGhost]

@balancedscorecard79 Heh, wow, you're right: I just now googled "correlated equilibrium coin flip" and it brought me to the wikipedia page for battle of the sexes, in which it described using a coin flip as an optimal strategy and an instance of correlated equilibrium. Thanks a lot for the compliment btw, that's a real self-esteem booster right there ;)

[balancedscorecard79]

@GelatinGhost Man ... If you came with the idea of flipping a coin by yourselfthen you are a pure genius ... because it means you understand correlated equilibrium intuitively (flipping a coin is a so called correlated equilibrium mechanism)

[OnAFirefly]

@JimBobJenkins

There's likely a niche for the shorter ones the same as the longer one. So it's probably not such a bad idea to keep both around.