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经济代写|微观经济学代考Microeconomics代写|ECON1001 Models of decision under bounded rationality

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经济代写|微观经济学代考Microeconomics代写|ECON1001 Models of decision under bounded rationality

经济代写|微观经济学代考Microeconomics代写|Models of decision under bounded rationality

A first model of choice under bounded rationality is the “satisficing model” proposed by Simon (1982) in opposition to the classic “optimizing” model. The decision-maker judges actions by means of partial criteria $u_k$, to which are attributed the aspiration thresholds $\sigma_k$; he examines the actions in a predefined order and chooses the first one to attain the aspiration thresholds for all the criteria: $s_i$ such that $u_k\left(s_i\right) \geq \sigma_k$. As a particular case, one can consider a unique criterion $u$ (as in the case of optimisation), with its aspiration threshhold $\varepsilon$; the decision-maker chooses the action $s_i$ such that $u\left(s_i\right) \geq \sigma$. At first sight, the $\varepsilon$-rationality model of Radner fits this definition, by considering that the decision-maker chooses the first action that approaches to within $\varepsilon$ of the optimum: $u\left(s_i\right) \geq \max _i u\left(s_i\right)-\varepsilon$, but here the aspiration threshold actually depends on the maximum attainable utility, which is generally unknown to the decision-maker. It can be observed that the satisficing model admits the optimizing model as limiting case when the aspiration thresholds are high enough. However, the satisficing model is directly expressed in terms of bounded instrumental rationality and not bounded cognitive rationality. For this latter to appear, we must examine a process of deliberation by the decision-maker that brings into play cognitive constraints such that he is led to seek a satisfactory action. Such a process, which would have the advantage of endogenising the aspiration thresholds of the decision-maker, has not yet been proposed.
A second model of choice under limited rationality is the “probabilist choice model” (Anderson, de Palma, Thisse, 1992). From a finite set of possible actions, the decision maker chooses the action $i$ with probability $p_i$ such that: $p_i=w_i / \sum_j w_j$, where $w_i$ is a propensity to choose the action $i$ linked to an index of utility $u_i$ of the action $i$. In the linear model, the parameters $w_i$ are proportional to the index of utility: $w_i=u_i$. In the multinomial logit model, the parameters $w_i$ are written in exponential form: $w_i=e^{\mu u_i}$, with the convenient introduction of a parameter $\mu$. Here again, the logit model converges towards the optimising model when the parameter $\mu$ tends to infinity; the decision-maker acts then no more in a stochastic manner, but in a determinist manner (except in the case of indifference between two actions). Conversely, the logit model tends to a purely random choice model when $\mu$ tends to zero. The parameter $\mu$ thus appears to reflect the limited cognitive capacities of the decision maker, but yet again it operates in a model expressing limited instrumental rationality. However, two cognitive justifications of this model, endogenising the parameter $\mu$, have been put forward. In the first, the decision-maker is endowed with a random utility function, but remains optimising to such an extent that he implements each action with the probability that it is the optimising one. When the law of probability of the utility is chosen correctly (doubly exponential), the logit model is obtained. In the second justification (Mattsson-Weibull, 2002), the decision-maker chooses an action by arbitrating between its utility and a control cost in relation to a reference action. When the control cost is chosen correctly (in the form of entropy), the logit model is again obtained.

经济代写|微观经济学代考Microeconomics代写|Models of learning in static situations

The “fictitious play model” assumes that the decision-maker, during a repeated process of decision, is capable of predicting the future states of nature. Moreover, this model essentially expresses exploitation behavior. The decision-maker observes the past frequency of states of nature, deduces from it a distribution of probabilities on future states and chooses, for each period, the action which maximises his expected utility according to this distribution. Exploration behavior can be introduced through voluntary deviation from the above behavior, and this deviation can take two forms. In the ” $\varepsilon$-greedy fictitious play” model, the decision maker can either use the optimum action with the probability $1-\varepsilon$, or use another action drawn uniformly at random with the probability $\varepsilon$. In the “disturbed fictitious play” model, the decision-maker uses the logit (and no longer optimising) choice rule with, as index of utility, the expected utility calculated for each action. For the standard fictitious play, one can easily demonstrate that the decision process will converge towards the optimal action (in the sense of maximisation of expected utility) simply by means of the law of large numbers (the frequency of appearance of each state tends to its probability). For the variations proposed, on the contrary, this convergence is not sure because the random component generated by exploration does not disappear asymptotically.

The “CPR model” (Laslier-Topol-Walliser, 2000) is a model of reinforcement (Roth-Erev, 1995) which assumes that the decision-maker only observes the past performance of his actions and no longer observes the states of nature. It considers that the decision-maker adopts, as index of utility, the cumulative utility obtained for each action and that he chooses his future action with a probability proportional to this index. This model presents good properties as regards the exploration-exploitation dilemma. At the beginning of the process, as the indexes are often initialised uniformly, the decision-maker carries out a systematic exploration of all the actions. At the end of the process, if the index of one action becomes predominant in relation to the others, exploitation becomes very strong, although exploration is never abandoned (every action possesses a residual probability of being chosen). What is more, if one increases (decreases) the parameter $\mu$, one moves the exploration-exploitation compromise towards more exploitation (exploration). For $\mu=0$, there is pure exploration because all the actions are used with the same probability; for $\mu=\infty$, there is pure exploitation because only the action with the maximum index of utility is used. It can be demonstrated that the learning process thus defined converges towards the optimal action (still in the sense of expected utility) because the good actions are played more and more often, due to a retroactive effect of the cumulative utility, whereas exploration tends to zero.

经济代写|微观经济学代考Microeconomics代写|ECON1001 Models of decision under bounded rationality

微观经济学代写

经济代写|微观经济学代考MICROECONOMICS代写|MODELS OF DECISION UNDER BOUNDED RATIONALITY


有限理性下的第一个选择模型是西蒙提出的“满意模型”1982与经典的“优化”模型相反。决策者通过部分标准来判断行动 $u_k$, 归因于吸入嘓值 $\sigma_k$; 他按照预定义的顾 序检育动作,并选择第一个达到所有标准的期望阈值的动作: $s_i$ 这样 $u_k\left(s_i\right) \geq \sigma_k$. 作为一种特殊情况,可以考虑一个独特的标准 $u$ asinthecaseofoptimisation, 及其吸入阈值 $\varepsilon$; 决策者选择行动 $s_i$ 这样 $u\left(s_i\right) \geq \sigma$. 乍一看, $\varepsilon$-Radner 的理性模型符合这个定义,考虑到决策者选择接近内部的第一个行动 $\varepsilon$ 最佳的:
$u\left(s_i\right) \geq \max _i u\left(s_i\right)-\varepsilon$ ,但这里的期望阈值实际上取决于最大可达到的效用,这通常是决策者不知道的。可以观察到,当期望阈值足够高时,满足模型将优化 模型视为极限情况。然而,懑足模型直接用有限的工具理性而不是有限的认知理性来表达。对于后者的出现,我们必须检䝺决策者的深思孰虑过程,该过程使认知 约束发挥作用,从而导致他寻求令人满意的行动。尚末提出这样一个过程,它具有使决策者的愿望阈值内生化的优势。
有限理性下的第二种选择模型是“概率选择模型”Anderson, dePalma, Thisse, 1992. 从一组有限的可能行动中,决策者选择行动 $i$ 有概率 $p_i$ 这样:
$p_i=w_i / \sum_j w_j$ , 在哪里 $w_i$ 是选择行动的倾向 $i$ 与效用指数挂钧 $u_i$ 行动的 $i$. 在线性模型中,参数 $w_i$ 与效用指数成正比: $w_i=u_i$. 在多项式logit模型中,参数 $w_i$ 写 成指数形式: $w_i=e^{\mu u_i}$, 方便地引入一个参数 $\mu$. 同样,当参数 $\mu$ 趋于无穷大; 决策者不再以随机方式行事,而是以确定性方式行事
exceptinthecaseofindifferencebetweentwoactions. 相反, logit 模型在以下情况下趋向于纯随机选择模型 $\mu$ 趋于零。参数 $\mu$ 因此似乎反映了决策者有限的认知 能力,但它又一次在表达有限工具理性的模型中运作。然而,这个模型的两个认知理由,内生参数 $\mu$ ,提出来了。在第一种情况下,决策者被赋予了一个随机的效 用函数,但仍保持优化到这样的程度,即他执行每个动作的概率都是优化的。当效用概率定律选择正确时doublyexponential,得到logit模型。在第二个理由 Mattsson – Weibull, 2002,决策者通过在其效用和与参考行动相关的控制成本之间进行仲裁来选择行动。正确选择控制成本时intheformofentropy,再次 得到logit模型。

经济代写|微观经济学代考MICROECONOMICS代写|MODELS OF LEARNING IN STATIC SITUATIONS


“虚拟游戏模型”假设决策者在重晶决策过程中能够预测末来的自然状态。此外,该模型本质上表达了剥削行为。决策者观察过去的自然状态频率,从中推导出末来 状态的概率分布,并根据该分布为每个时期选择最大化其预期效用的行动。可以通过自愿偏离上述行为来引入探索行为,这种偏离可以有两种形式。在里面 ” $\varepsilon-$ greedy fictitious play”模型,决策者可以使用概率为 $1-\varepsilon$ ,或者使用另一个随机抽取的动作,概率为 $\varepsilon$. 在 “被打扰的虚拟游戏”模型中,决策者使用logit andnolongeroptimising选择规则,作为效用指标,为每个动作计算的预期效用。对于标准的虚构游戏,可以很容易地证明决策过程将收敛于最佳行动 inthesenseofmaximisationofexpectedutility仅仅通过大数定律 the frequencyofappearanceofeachstatetendstoitsprobability. 相反,对于提出的变 体,这种收敛是不确定的,因为探索产生的随机成分不会渐近消失。
“心肺复苏模型” Laslier – Topol – Walliser, 2000是强化模型Roth – Erev, 1995它假定决策者只观崇其行为的过去表现,而不再观察自然状态。它认为决策 者采用每次行动所获得的甸积效用作为效用指标,并以与该指标成正比的概率选择末来的行动。该模型在探索-开发困境方面表现出良好的特性。在过程开始时, 由于指标往往是统一初始化的,决策者对所有的动作进行系统的探索。在这个过程的最后,如果一个行动的指标相对于其他行动变得占主导地位,那么剥削就会变 得非常强烈,尽管探索永远不会被放弃everyactionpossessesaresidualprobabilityofbeingchosen. 更重要的是,如果一个增加decreases参数 $\mu$ ,一个人将勘 探-开发折䖵方䓌转向更多的开发exploration. 为了 $\mu=0$ ,存在纯糉的探索,因为所有的动作都以相同的概率被使用;为了 $\mu=\infty$ ,存在纯粹的剥削,因为只使 用具有最大效用指数的动作。可以证明,如此定义的学习过程收敛于最佳动作stillinthesenseofexpectedutility因为由于甸积效用的追溯效应,好的行为被玩得 越来越频筦,而探索趋于零。

经济代写|微观经济学代考Microeconomics代写

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微观经济学代写

微观经济学是主流经济学的一个分支,研究个人和企业在做出有关稀缺资源分配的决策时的行为以及这些个人和企业之间的相互作用。my-assignmentexpert™ 为您的留学生涯保驾护航 在数学Mathematics作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的数学Mathematics代写服务。我们的专家在图论代写Graph Theory代写方面经验极为丰富,各种图论代写Graph Theory相关的作业也就用不着 说。

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线性代数是数学的一个分支,涉及线性方程,如:线性图,如:以及它们在向量空间和通过矩阵的表示。线性代数是几乎所有数学领域的核心。

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现代博弈论始于约翰-冯-诺伊曼(John von Neumann)提出的两人零和博弈中的混合策略均衡的观点及其证明。冯-诺依曼的原始证明使用了关于连续映射到紧凑凸集的布劳威尔定点定理,这成为博弈论和数学经济学的标准方法。在他的论文之后,1944年,他与奥斯卡-莫根斯特恩(Oskar Morgenstern)共同撰写了《游戏和经济行为理论》一书,该书考虑了几个参与者的合作游戏。这本书的第二版提供了预期效用的公理理论,使数理统计学家和经济学家能够处理不确定性下的决策。

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微积分,最初被称为无穷小微积分或 “无穷小的微积分”,是对连续变化的数学研究,就像几何学是对形状的研究,而代数是对算术运算的概括研究一样。

它有两个主要分支,微分和积分;微分涉及瞬时变化率和曲线的斜率,而积分涉及数量的累积,以及曲线下或曲线之间的面积。这两个分支通过微积分的基本定理相互联系,它们利用了无限序列和无限级数收敛到一个明确定义的极限的基本概念 。

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什么是计量经济学?
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