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经济代写|博弈论代写Game Theory代考|Commitment

Around $90 \%$ of bird species are socially monogamous over breeding. By this we mean that a pair share parenting duties and remain together during the period of parental care. In many species this bond lasts for a single breeding season and the two individuals pair up with a different partner in the following year. In some long-lived birds the bond is more permanent and lasts for life. Pair-bond formation does occur in some mammal species, but is less common.

So what mental mechanisms are involved in pair-bond formation? Much of the work on this has been on the prairie vole, a mammal species found in the grasslands of North America. In prairie voles individuals have multiple litters with the same partner. Both partners are involved in care, sharing the nest and defending the territory. Pairs show what can be interpreted as affection to one another and appear committed to the partnership in that they sometimes do not take a new partner if their current partner dies. The empirical work on pair-bond formation in the prairie vole is summarized in McGraw and Young (2010). This work has established that receptors for oxytocin and vasopressin in the forebrain play a central role in pair-bond formation, acting through their effect on the dopamine-mediated reward pathways of the brain (Young, 2003; Lim et al., 2004). The hypothesis is that activation of these receptors in the reward centres results in the establishment of an association between the olfactory cues of the partner and the rewarding aspects of copulation. As a result the partner drug addiction where a drug becomes highly rewarding.
Motivated by the above work we build a very basic model of the evolution of commitment in which an inflation factor can bias the reward system in favour of a partner. The model is asexual, and so is a long way from being a realistic model of pair-bond formation in breeding pairs. It may, however, capture a central evolutionary force that acts in a market setting to bring about commitment to a partner. The model is loosely based on that by McNamara et al. (2008).

经济代写|博弈论代写Game Theory代考|A Model of the Co-evolution of Choosiness and Commitment

An asexual population has an annual cycle that has five phases: (i) Pairing, (ii) Resource gain, (iii) Reproduction, (iv) Possible divorce, and (v) Possible death. The details of each phase are as follows:

Pairing. Some individuals are already paired from the previous year, those that are not (i.e. they are single) pair up at random.

Resource gain. During resource gain, in each unit of time each member of a pair has the choice between being selfish by taking an outside option or cooperative by taking an option that helps both its partner and itself. The value of the outside option, $r$, varies with $r$ drawn at random (uniformly) from the range $0\theta$, otherwise it helps the partner. Thus the proportion of time it helps the partner is $\rho=\frac{\theta}{R}$. The rates at which each pair member gains resources as a function of the $\rho$ values of the pair is specified in Exercise 7.9.
Reproduction. Each population member reproduces asexually, where the number of offspring produced is large and is proportional to the mean rate at which resources were gained while paired. These offspring are subject to density-dependent competition before the start of the next pairing phase, with only sufficiently many surviving to compensate for the mortality of adults (see below). Surviving offspring are then adults and are single.

Divorce. Pair members decide whether to split up their pairing (divorce). Each individual has a divorce threshold $d$. Given that the partner commits a proportion of time $\rho$ to helping the individual, then the partner is rejected if $\rho<d$. If either pair member rejects the other the pair divorce and each pair member becomes single, otherwise the partners attempt to stay together until the following year.

Death. The probability that each adult population member dies before the next round of the game is $1 / n$, so that each population member plays an average of $n$ rounds of the game over its lifetime. If an individual dies and its partner survives the partner is single at the beginning of the next pairing phase.

经济代写|博弈论代写Game Theory代考|ECON40010

博弈论代考

经济代写|博弈论代写博弈论代考|承诺


在$90 \%$左右的鸟类是社会一夫一妻制的繁殖。我们的意思是,一对夫妻共同承担抚养孩子的责任,在父母照顾孩子期间一直呆在一起。在许多物种中,这种关系只持续一个繁殖季节,第二年两个个体会与不同的伴侣配对。在一些长寿的鸟类中,这种联系更持久,可以持续一生。配对键的形成在某些哺乳动物物种中确实发生过,但不太常见


那么,什么样的心理机制参与了成对键的形成呢?这方面的大部分研究都是在草原田鼠上进行的,草原田鼠是一种北美洲草原上的哺乳动物。在草原田鼠中,一个个体与同一个伴侣有多个窝。伴侣双方都参与照顾、共享巢穴和保卫领地。情侣之间表现出的情感可以被理解为对彼此的爱,并且表现出对伴侣关系的忠诚,因为如果他们现在的伴侣去世,他们有时不会接受新的伴侣。McGraw和Young(2010)对草原田鼠配对键形成的经验工作进行了总结。这项工作已经证实,前脑中的催产素和抗利尿激素受体在成对结合的形成中发挥着核心作用,通过它们对大脑中多巴胺介导的奖励通路的影响发挥作用(Young, 2003;Lim等人,2004)。该假说认为,激活这些奖赏中枢的受体会导致伴侣的嗅觉线索和交配的奖赏方面之间建立一种联系。结果是伴侣吸毒成瘾,毒品变得非常有价值。基于上述工作,我们建立了一个承诺演化的非常基本的模型,在这个模型中,膨胀因素可以使奖励系统偏向有利于伴侣的一方。这个模型是无性繁殖的,因此要成为一个现实的交配配对形成的模型还有很长的路要走。然而,它可能抓住了一种核心的进化力量,在市场环境中产生了对伴侣的承诺。该模型大致基于McNamara等人(2008)的模型

经济代写|博弈论代写博弈论代考|选择和承诺的共同进化模型


无性繁殖种群的年周期有五个阶段:(i)配对,(ii)资源获取,(iii)繁殖,(iv)可能离婚,(v)可能死亡。每个阶段的详细信息如下:

配对。一些个体已经在前一年配对,那些没有配对(即它们是单身)的随机配对

资源增益。在获取资源的过程中,在每一单位时间内,一对中的每个成员都有两个选择,要么是自私地选择外部选择,要么是合作地选择既能帮助同伴又能帮助自己的选择。外部选项$r$的值随$r$的变化而变化,是从$0\theta$范围中随机(统一)抽取的,否则它将帮助合作伙伴。因此,它帮助伙伴的时间比例是$\rho=\frac{\theta}{R}$。每个pair成员获得资源的速率作为pair $\rho$值的函数在练习7.9中指定。
复制。每个群体成员进行无性繁殖,产生的后代数量很大,与配对时获得资源的平均速率成正比。在下一个配对阶段开始之前,这些后代受到密度依赖性竞争的影响,只有足够多的后代存活下来,以弥补成虫的死亡率(见下文)。存活下来的后代是成年的,并且是单身的

死亡。每个成年人口成员在下一轮游戏之前死亡的概率是$1 / n$,所以每个人口成员在其一生中平均玩了$n$轮游戏。如果一个个体死亡,而它的伴侣存活下来,那么在下一个配对阶段开始时,伴侣是单身的

经济代写|博弈论代写Game Theory代考

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