Dude, I need to go to bed. I got to be up tomorrow at five to drive down to LA. Something was stuck in my head and I had to get this out there before I got to bed. I came across the Nash equilibrium tonight and on wiki they were explaining it in Layman and formal. I usually hate when shit is explained formally. I'm a break it down barney style first, just to get a basic understanding of shit, then formally, if needed and if interested. But for a majority of the world, we don't need formal.
I know people say this would be considered "dumbing down society" or what have you, but really, when nobody understands what you're talking about, you can lose the point of what you're trying to do: inform. I'm not saying abolish formalities or jargon, but seriously, at the end of the day, who really needs it? Examples below
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Informal definition
Informally, a set of strategies is a Nash equilibrium if no player can do better by unilaterally changing his or her strategy. To see what this means, imagine that each player is told the strategies of the others. Suppose then that each player asks himself or herself: "Knowing the strategies of the other players, and treating the strategies of the other players as set in stone, can I benefit by changing my strategy?"
If any player would answer "Yes", then that set of strategies is not a Nash equilibrium. But if every player prefers not to switch (or is indifferent between switching and not) then the set of strategies is a Nash equilibrium. Thus, each strategy in a Nash equilibrium is a best response to all other strategies in that equilibrium.[3]
The Nash equilibrium may sometimes appear non-rational in a third-person perspective. This is because it may happen that a Nash equilibrium is not Pareto optimal.
The Nash equilibrium may also have non-rational consequences in sequential games because players may "threaten" each other with non-rational moves. For such games the Subgame perfect Nash equilibrium may be more meaningful as a tool of analysis.
[edit] Formal definition
Let (S, f) be a game with n players, where Si is the strategy set for player i, S=S1 X S2 ... X Sn is the set of strategy profiles and f=(f1(x), ..., fn(x)) is the payoff function. Let x i be a strategy profile of all players except for player i. When each player i \in {1, ..., n} chooses strategy xi resulting in strategy profile x = (x1, ..., xn) then player i obtains payoff fi(x). Note that the payoff depends on the strategy profile chosen, i.e. on the strategy chosen by player i as well as the strategies chosen by all the other players. A strategy profile x* \in S is a Nash equilibrium (NE) if no unilateral deviation in strategy by any single player is profitable for that player, that is
\forall i,x_i\in S_i, x_i \neq x^*_{i} : f_i(x^*_{i}, x^*_{-i}) \geq f_i(x_{i},x^*_{-i}).
A game can have either a pure-strategy or a mixed Nash Equilibrium, (in the latter a pure strategy is chosen stochastically with a fixed frequency). Nash proved that if we allow mixed strategies, then every game with a finite number of players in which each player can choose from finitely many pure strategies has at least one Nash equilibrium.
When the inequality above holds strictly (with > instead of \geq) for all players and all feasible alternative strategies, then the equilibrium is classified as a strict Nash equilibrium. If instead, for some player, there is exact equality between x^*_i and some other strategy in the set S, then the equilibrium is classified as a weak Nash equilibrium.
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See what I mean? I think it's cool how they explain it informally and formally, but when looking over it once, I picked up more informally than formally.
Do you know what jargon means in old french? Chatter of birds. Imagine that in your head. Annoying birds squawking at each other and nobody knows what the fuck they're talking about unless you speak bird. That's jargon and "formal" speak.
It's almost like we make learning something more complicated than it is, or has to be, so other feels smarter or, to give people jobs... being subject matter experts and then some! Wowzers!
I think people get intelligence confused with knowledge. Just like there's a difference between being stupid, ignorant and mentally disabled/retarded. I think so anyway. What about you guys?
So yeah... whatever or whatever. I need sleep desperately.
I know people say this would be considered "dumbing down society" or what have you, but really, when nobody understands what you're talking about, you can lose the point of what you're trying to do: inform. I'm not saying abolish formalities or jargon, but seriously, at the end of the day, who really needs it? Examples below
------------
Informal definition
Informally, a set of strategies is a Nash equilibrium if no player can do better by unilaterally changing his or her strategy. To see what this means, imagine that each player is told the strategies of the others. Suppose then that each player asks himself or herself: "Knowing the strategies of the other players, and treating the strategies of the other players as set in stone, can I benefit by changing my strategy?"
If any player would answer "Yes", then that set of strategies is not a Nash equilibrium. But if every player prefers not to switch (or is indifferent between switching and not) then the set of strategies is a Nash equilibrium. Thus, each strategy in a Nash equilibrium is a best response to all other strategies in that equilibrium.[3]
The Nash equilibrium may sometimes appear non-rational in a third-person perspective. This is because it may happen that a Nash equilibrium is not Pareto optimal.
The Nash equilibrium may also have non-rational consequences in sequential games because players may "threaten" each other with non-rational moves. For such games the Subgame perfect Nash equilibrium may be more meaningful as a tool of analysis.
[edit] Formal definition
Let (S, f) be a game with n players, where Si is the strategy set for player i, S=S1 X S2 ... X Sn is the set of strategy profiles and f=(f1(x), ..., fn(x)) is the payoff function. Let x i be a strategy profile of all players except for player i. When each player i \in {1, ..., n} chooses strategy xi resulting in strategy profile x = (x1, ..., xn) then player i obtains payoff fi(x). Note that the payoff depends on the strategy profile chosen, i.e. on the strategy chosen by player i as well as the strategies chosen by all the other players. A strategy profile x* \in S is a Nash equilibrium (NE) if no unilateral deviation in strategy by any single player is profitable for that player, that is
\forall i,x_i\in S_i, x_i \neq x^*_{i} : f_i(x^*_{i}, x^*_{-i}) \geq f_i(x_{i},x^*_{-i}).
A game can have either a pure-strategy or a mixed Nash Equilibrium, (in the latter a pure strategy is chosen stochastically with a fixed frequency). Nash proved that if we allow mixed strategies, then every game with a finite number of players in which each player can choose from finitely many pure strategies has at least one Nash equilibrium.
When the inequality above holds strictly (with > instead of \geq) for all players and all feasible alternative strategies, then the equilibrium is classified as a strict Nash equilibrium. If instead, for some player, there is exact equality between x^*_i and some other strategy in the set S, then the equilibrium is classified as a weak Nash equilibrium.
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See what I mean? I think it's cool how they explain it informally and formally, but when looking over it once, I picked up more informally than formally.
Do you know what jargon means in old french? Chatter of birds. Imagine that in your head. Annoying birds squawking at each other and nobody knows what the fuck they're talking about unless you speak bird. That's jargon and "formal" speak.
It's almost like we make learning something more complicated than it is, or has to be, so other feels smarter or, to give people jobs... being subject matter experts and then some! Wowzers!
I think people get intelligence confused with knowledge. Just like there's a difference between being stupid, ignorant and mentally disabled/retarded. I think so anyway. What about you guys?
So yeah... whatever or whatever. I need sleep desperately.
thescarykid:
Of course none ya'll say anything. 'Cause you suck.