Timeline for Is a mixed strategy ever the best response to a pure strategy?
Current License: CC BY-SA 4.0
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| Nov 8, 2019 at 21:17 | comment | added | Giskard | This is definitely a pure strategy in the repeated game. Choosing a strategy/action in a stage game is not entire an strategy in the repeated game, just an element of it. I guess this also means that given the opponent's pure strategy of repeating A or repeating B the 50-50 response is never best, mirroring the opponent is best. | |
| Nov 8, 2019 at 20:26 | comment | added | Steven Jackson | @Giskard, if that does count as a pure strategy, similar options are also available to your opponent (play B 50 times then A 50 times), which means such a strategy does not yield a guaranteed payoff of zero (it can be anywhere from -100 to 100). A mixed strategy will tend towards 0 no matter what your opponents pure strategy is, and the rest of the analysis in the answer holds up (except the part about 50/50 strictly alternating being a certain 0 is invalidated if a "50/50 alternation" is a pure strategy available to the opponent). | |
| Nov 8, 2019 at 19:16 | history | edited | Peteris | CC BY-SA 4.0 |
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| Nov 8, 2019 at 19:16 | comment | added | Peteris | @Giskard yes, equivalent to "you choose a 50/50 mixed strategy that's strictly alternating". I guess it comes down to whether we'd consider that as a mixed or a fixed strategy in this repeated game scenario. | |
| Nov 8, 2019 at 19:06 | comment | added | Giskard | What about the pure strategy of playing A 50 times then playing B 50 times? This guarantues a payoff of zero, so it is even better than your close to zero yielding mixed strategy. | |
| Nov 8, 2019 at 18:40 | history | answered | Peteris | CC BY-SA 4.0 |