4 ms·

This is cool. I was actually asked for the optimal strategy for player 1 in this game as an interview question for a quant research role; I didn't know anything

by hgibbs 6y ago

This is cool. I was actually asked for the optimal strategy for player 1 in this game as an interview question for a quant research role; I didn't know anything about game/decision theory, other than the basics, and so I only got as far as determining what to do with an Ace and a King, and then figuring out that you should bluff with a certain frequency if you hold the ace. Anyhow, I came up with another question while considering this problem. Player 1 should only bluff at the optimal rate if player 2 punishes them for deviating from this rate by changing the frequency that they call when holding the king. Otherwise, Player 1 gains more on average by bluffing with the queen more frequently. So, how should Player 2 figure out if Player 1 is actually bluffing at the optimal rate (and not higher)? It could happen, with exponentially small probability, that Player 1 decides whether to bluff randomly, and bluffs with the first 10,000 queens before ever folding with a queen. How does Player 2 distinguish this from Player 1 only ever bluffing with the queen? But perhaps this is something that the Nash Theorem deals with? I don't know. Any comments from people who know more than me on this are welcome!

s1t5 6y ago
> Player 1 should only bluff at the optimal rate if player 2 punishes them for deviating from this rate by changing the frequency that they call when holding the king. Otherwise, Player 1 gains more on average by bluffing with the queen more frequently. So, how should Player 2 figure out if Player 1 is actually bluffing at the optimal rate (and not higher)? You're describing exploitative strategies - that's the kind of circular thinking of "if he knows that I know what he knows...". In a Nash equilibrium neither side has an incentive to change their strategy even if they know what their opponent is doing. If you're betting at the optimal frequency, there is nothing that your opponent can do to counterexploit your strategy. If you're deviating from the optimal frequency, your opponent can adjust, you can adjust in return and so on.
xapata 6y ago
Nash equilibrium only exists if all players play optimally. Exploiting a non-optimal strategy is not an equilibrium state.

by hgibbs 6y ago

s1t5 6y ago

> Player 1 should only bluff at the optimal rate if player 2 punishes them for deviating from this rate by changing the frequency that they call when holding the king. Otherwise, Player 1 gains more on average by bluffing with the queen more frequently. So, how should Player 2 figure out if Player 1 is actually bluffing at the optimal rate (and not higher)? You're describing exploitative strategies - that's the kind of circular thinking of "if he knows that I know what he knows...". In a Nash equilibrium neither side has an incentive to change their strategy even if they know what their opponent is doing. If you're betting at the optimal frequency, there is nothing that your opponent can do to counterexploit your strategy. If you're deviating from the optimal frequency, your opponent can adjust, you can adjust in return and so on.

xapata 6y ago

Nash equilibrium only exists if all players play optimally. Exploiting a non-optimal strategy is not an equilibrium state.