Timeline for How to find best strategy for 3 hunters hunting in 2 regions?
Current License: CC BY-SA 4.0
18 events
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| Dec 14, 2022 at 23:24 | comment | added | user7868 | For 3 players, a Nash equilibrium means that no one player can improve their expected reward, holding the other players' strategies constant. That means, for each player whose probability is not 0 or 1, the expected payoffs for the two regions are the same. | |
| Dec 12, 2022 at 14:11 | history | edited | Tita | CC BY-SA 4.0 |
deleted 1032 characters in body
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| Dec 12, 2022 at 13:04 | history | edited | Tita | CC BY-SA 4.0 |
deleted 145 characters in body
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| Dec 12, 2022 at 12:50 | history | edited | Tita | CC BY-SA 4.0 |
Updated question with potential solution and new questions.
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| Dec 12, 2022 at 12:19 | comment | added | Tita | @user7868 I have used Nash equilibrium for when there's 2 hunter, I'm just not familiar with how I should approach it when I have to take into account more than one hunter's choice. I was about to start working on the problem, so I'll try to apply the same logic on the 3 hunter edition! | |
| S Dec 12, 2022 at 10:09 | history | suggested | Stef |
add tag "nash equilibrium"
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| Dec 12, 2022 at 9:45 | review | Suggested edits | |||
| S Dec 12, 2022 at 10:09 | |||||
| Dec 12, 2022 at 5:49 | comment | added | user7868 | Another question to consider is looking for Nash equilibria. A Nash equilibrium is a sets of probabilities of using hunting ground $A$ for each player, such that where no player benefits (in expectation) by changing their strategy. As you've noted, $(0,0,1)$ is a Nash equilibrium - no player benefits from deviating from that strategy. But there are also others. | |
| Dec 11, 2022 at 18:30 | comment | added | Tita | All right! Thanks for the suggestion, I'll try it by myself a bit more tomorrow! | |
| Dec 11, 2022 at 18:27 | comment | added | Stef | Yes. That's my first suggestion. Another, different suggestion, is to look for equilibriums where all three hunters are following the same mixed strategy. This strategy has a single parameter (the probability to go to field A), so it should be easy to compute the expected payoff assuming they all follow it. | |
| Dec 11, 2022 at 18:05 | comment | added | Tita | So, are you suggesting that I find the best strategy in two different cases for hunters 1 and 2, with the cases being what hunter 3 chooses? | |
| Dec 11, 2022 at 18:04 | comment | added | Tita | Yes, they are choosing simultaneously with no prior knowledge or communication. They each want to maximize their rabbits, but they have to take into consideration what the other hunters might do. | |
| Dec 11, 2022 at 17:21 | comment | added | Stef | PS: I assume all hunters are simultaneously choosing which field they go to, and are not allowed prior communication nor able to make an enforceable agreement. | |
| Dec 11, 2022 at 17:16 | comment | added | Stef | Also, the game is completely symmetrical in all three hunters, so you should expect an equilibrium where all hunters have the same mixed strategy. Call p the proba that a given hunter goes to field A under this common mixed strategy, and calculate a hunter's expected payoff as a function of p. | |
| Dec 11, 2022 at 17:14 | comment | added | Stef | Hint: Step 1. "But if hunter 3 chooses region B, the best outcome is when the other two hunters don't choose the same region between themselves." <<< Find the exact best mixed strategy for the first two hunters in this case. | |
| Dec 11, 2022 at 17:10 | comment | added | Stef | Hi. Interesting problem. Could you please explicitly specify whether the hunters are working together, with objective to maximise the expected total rabbits collected, or each for themselves, everyone acting to maximise their own rabbits collected? | |
| Dec 11, 2022 at 16:48 | history | edited | prubin♦ | CC BY-SA 4.0 |
Fixed typo.
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| Dec 11, 2022 at 16:20 | history | asked | Tita | CC BY-SA 4.0 |