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删除800字节 、 2020年8月6日 (四) 22:10
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在大多数简单的游戏中,进化均衡策略和纳什平衡完全重合。例如,在游戏《囚徒困境Prisoner's Dilemma》中,只有一个纳什平衡,其策略(叛变)也是一种进化均衡策略。
 
在大多数简单的游戏中,进化均衡策略和纳什平衡完全重合。例如,在游戏《囚徒困境Prisoner's Dilemma》中,只有一个纳什平衡,其策略(叛变)也是一种进化均衡策略。
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Some games may have Nash equilibria that are not ESSes. For example, in harm thy neighbor (whose payoff matrix is shown here) both (A, A) and (B, B) are Nash equilibria, since players cannot do better by switching away from either.  However, only B is an ESS (and a strong Nash). A is not an ESS, so B can neutrally invade a population of A strategists and predominate, because B scores higher against B than A does against B.  This dynamic is captured by Maynard Smith's second condition, since E(A, A) = E(B, A), but it is not the case that E(A,B) > E(B,B).
 
Some games may have Nash equilibria that are not ESSes. For example, in harm thy neighbor (whose payoff matrix is shown here) both (A, A) and (B, B) are Nash equilibria, since players cannot do better by switching away from either.  However, only B is an ESS (and a strong Nash). A is not an ESS, so B can neutrally invade a population of A strategists and predominate, because B scores higher against B than A does against B.  This dynamic is captured by Maynard Smith's second condition, since E(A, A) = E(B, A), but it is not the case that E(A,B) > E(B,B).
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有些博弈可能有非雌性的纳什均衡。例如,在伤害你的邻居(其收益矩阵在这里显示)两者(a,a)和(b,b)都是纳什均衡,因为玩家不能通过从其中任何一个切换来做得更好。然而,只有 b 是 ESS (和强 Nash)。不是 ESS,因此 b 可以中立地入侵 a 战略家的人群并占主导地位,因为 b 对 b 的得分高于 a 对 b 的得分。这个动态被 Maynard Smith 的第二个条件所捕获,因为 e (a,a) = e (b,a) ,但是它不是 e (a,b) > e (b,b)的情况。
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还有一些游戏可能具有非进化均衡策略的纳什平衡。例如,在游戏《以邻为壑Harm thy neighbor》中(此处显示为回报矩阵),(A,A)和(B,B)都是纳什平衡,因为玩家无法通过选择放弃任一个来做得更好。但是,只有B是进化均衡策略(也是强纳什)。A不是进化均衡策略,因此B可以中立地入侵A策略的群体并占据优势地位,因为B对B的得分要比A对B的得分高。由于E(A,A)= E(B,A),因此可以通过梅纳德·史密斯的第二个条件来捕获此动态,但是E(A,B)> E(B,B)并非如此。
 
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{|align=block style="clear: right"
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{|align=block style="clear: right"
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{ | align = block style = “ clear: right”
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{| class="wikitable"
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|-
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! 伤害大家Harm everyone !!  !! 
 
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|-
 
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|  || C || D
 
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| C || 2,2 || 1,2
 
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| D || 2,1 || 0,0
|{{Payoff matrix | Name = Harm everyone
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|{{Payoff matrix | Name = Harm everyone
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| {支付矩阵 | 姓名 = 伤害每个人
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                | 2L = C    | 2R = D   |
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                | 2L = C    | 2R = D    |
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2 l = c | 2 r = d |  
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1U = C          | UL = 2, 2  | UR = 1, 2 |
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1U = C          | UL = 2, 2  | UR = 1, 2 |
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1 u = c | UL = 2,2 | UR = 1,2 |
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1D = D          | DL = 2, 1  | DR = 0, 0 }}
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1D = D          | DL = 2, 1  | DR = 0, 0 }}
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1 d = d | DL = 2,1 | DR = 0,0}
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|{{Payoff matrix | Name = Chicken
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|{{Payoff matrix | Name = Chicken
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| {支付矩阵 | 名称 = 鸡
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                | 2L = Swerve    | 2R = Stay      |
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                | 2L = Swerve    | 2R = Stay      |
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2 l = Swerve | 2 r = Stay |
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1U = Swerve    | UL = 0,0        | UR = −1,+1      |
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1U = Swerve    | UL = 0,0        | UR = −1,+1      |
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1U = Swerve    | UL = 0,0        | UR = −1,+1      |
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1D = Stay      | DL = +1,−1      | DR = −20,−20    }}
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1D = Stay      | DL = +1,−1      | DR = −20,−20    }}
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1D = 停留 | DL = + 1,-1 | DR =-20,-20}
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|}
 
|}
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{| class="wikitable"
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! 小鸡博弈The Game of Chicken !!  !! 
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|  || 转身离开Swerve || 留下Stay
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| 转身离开Swerve || 0,0 || -1,+1
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|-
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| 留下Stay || +1,-1 || -20,-20
 
|}
 
|}
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|}
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