# 经济代写|博弈论代写Game Theory代考|ECON40010

## 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.

# 博弈论代考

## 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

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