This is a video about (170705) 주간 아이돌 310회 블랙핑크 (BLACKPINK) - Weekly idol ep 310 BLACKPINK
主要支援:已於2009年4月8日到期 延伸支援:已於2014年4月8日到期(仅限Service Pack 3 x86(SP3 x86)及Service Pack 2 x64(SP2 x64)) 新增的功能 移除的功能 版本 开发历史 批評 主题 Windows XP(开发代号:)是微软公司推出供个人电脑使用的操作系统,包括商用及家用的桌上型电脑、笔记本电脑、媒体中心(英语:)和平板电脑等。其RTM版于2001年8月24日发布;零售版于2001年10月25日上市。其名字「」的意思是英文中的「体验」()。Windows ..
Nov 13, 2019- Explore dobdan222's board "교복", followed by 405 people on Pinterest. See more ideas about Asian girl, Korean student and Fashion.
Nov 10, 2019- Explore cutebear36088's board "여고딩", followed by 557 people on Pinterest. See more ideas about School looks, Fashion and School uniform.
Republika obeh narodov Habsburška monarhija Bavarska Saška Franconia Švabska Zaporoški kozaki Velika vojvodina Toskana Drugo obleganje Dunaja je potekalo leta 1683; pričelo se je 14. julija 1683, ko je Osmanski imperij obkolil Dunaj in končalo 11. septembra ..
Robert Henry Goldsborough (January 4, 1779 – October 5, 1836) was an American politician from Talbot County, Maryland. Goldsborough was born at "Myrtle Grove" near Easton, Maryland. He was educated by private tutors and graduated from St. John's College in ..
Anabolic steroids, also known more properly as anabolic–androgenic steroids (AAS), are steroidal androgens that include natural androgens like testosterone as well as synthetic androgens that are structurally related and have similar effects to testosterone. ..
(Normal form) trembling hand perfect equilibrium | |
---|---|
A solution concept in game theory | |
Relationship | |
Subset of | Nash Equilibrium |
Superset of | Proper equilibrium |
Significance | |
Proposed by | Reinhard Selten |
In game theory, trembling hand perfect equilibrium is a refinement of Nash equilibrium due to Reinhard Selten.[1] A trembling hand perfect equilibrium is an equilibrium that takes the possibility of off-the-equilibrium play into account by assuming that the players, through a "slip of the hand" or tremble, may choose unintended strategies, albeit with negligible probability.
First define a perturbed game. A perturbed game is a copy of a base game, with the restriction that only totally mixed strategies are allowed to be played. A totally mixed strategy is a mixed strategy where every strategy (both pure and mixed) is played with non-zero probability. This is the "trembling hands" of the players; they sometimes play a different strategy, other than the one they intended to play. Then define a strategy set S (in a base game) as being trembling hand perfect if there is a sequence of perturbed games that converge to the base game in which there is a series of Nash equilibria that converge to S.
Note: All completely mixed Nash equilibria are perfect.
Note 2: The mixed strategy extension of any finite normal-form game has at least one perfect equilibrium.[2]
The game represented in the following normal form matrix has two pure strategy Nash equilibria, namely and . However, only is trembling-hand perfect.
Left | Right | |
Up | 1, 1 | 2, 0 |
Down | 0, 2 | 2, 2 |
Trembling hand perfect equilibrium |
Assume player 1 (the row player) is playing a mixed strategy , for .
Player 2's expected payoff from playing L is:
Player 2's expected payoff from playing the strategy R is:
For small values of , player 2 maximizes his expected payoff by placing a minimal weight on R and maximal weight on L. By symmetry, player 1 should place a minimal weight on D if player 2 is playing the mixed strategy . Hence is trembling-hand perfect.
However, similar analysis fails for the strategy profile .
Assume player 2 is playing a mixed strategy . Player 1's expected payoff from playing U is:
Player 1's expected payoff from playing D is:
For all positive values of , player 1 maximizes his expected payoff by placing a minimal weight on D and maximal weight on U. Hence is not trembling-hand perfect because player 2 (and, by symmetry, player 1) maximizes his expected payoff by deviating most often to L if there is a small chance of error in the behavior of player 1.
For 2x2 games, the set of trembling-hand perfect equilibria coincides with the set of equilibria consisting of two undominated strategies. In the example above, we see that the equilibrium <Down,Right> is imperfect, as Left (weakly) dominates Right for Player 2 and Up (weakly) dominates Down for Player 1.[3]
Extensive-form trembling hand perfect equilibrium | |
---|---|
A solution concept in game theory | |
Relationship | |
Subset of | Subgame perfect equilibrium, Perfect Bayesian equilibrium, Sequential equilibrium |
Significance | |
Proposed by | Reinhard Selten |
Used for | Extensive form games |
There are two possible ways of extending the definition of trembling hand perfection to extensive form games.
The notions of normal-form and extensive-form trembling hand perfect equilibria are incomparable, i.e., an equilibrium of an extensive-form game may be normal-form trembling hand perfect but not extensive-form trembling hand perfect and vice versa. As an extreme example of this, Jean-François Mertens has given an example of a two-player extensive form game where no extensive-form trembling hand perfect equilibrium is admissible, i.e., the sets of extensive-form and normal-form trembling hand perfect equilibria for this game are disjoint.[citation needed]
An extensive-form trembling hand perfect equilibrium is also a sequential equilibrium. A normal-form trembling hand perfect equilibrium of an extensive form game may be sequential but is not necessarily so. In fact, a normal-form trembling hand perfect equilibrium does not even have to be subgame perfect.
Myerson (1978)[4] pointed out that perfection is sensitive to the addition of a strictly dominated strategy, and instead proposed another refinement, known as proper equilibrium.