**2. Literature Rewiev**

A very particular branch of economics literature, only recently developed, is the Economics of Love. It is focused on the household's well-being, marriage and long-term relationships alongside their effects on economic growth (for an exhaustive survey on this literature see [3,4]).

The first work in this new field of Economics appeared in the early 1970s with the theory of marriage by Becker [5]. According to it, all individuals want to find a partner with whom they will maximise their own well-being. The equilibrium in this marriage market is reached when no one can change partner or become single and when nobody can experience a higher well–being (referred to the consumption of household commodities).

Becker´s empirical analysis shows that the gain from marriage is positively dependant on income, on relative difference in wage rates and on the level of intangible variables such as education and beauty. Moreover, individuals choose partners with similar traits such as height, race, social background, etc. Including among the factors which can affect marriages also love (defined as a situation where the utility of one individual depends on the commodity consumption of their partner as well as their own), Becker [6] finds that love raises the likelihood of two people to marry because their well-being is likely to be higher.

After these pioneering works, many other analyses have been focused on understanding how households operate. Outcomes of interest concern consumption, savings, labor supply and other uses of time, household formation and dissolution, demand for health and other forms of human capital, fertility and children outcomes, demand for environmental quality, migration, and household produced goods ([3,4]).

Many papers also investigated the determinants of long-lasting relationships and their effects on economic development. Among them, Brines and Joyner [7] conducted an empirical study on the stability of marriage and cohabiting couples in the United States. They found that inequality in employment and income among the cohabiting couple increased the chances of separation, although the effect was not symmetric since inequality had a larger impact when the female partner earned more than the male partner. Grossbard [4] studied family as a complex decision unit where partners with potentially different objectives made decisions about consumption, work and fertility. He noticed that couples marry and divorce depending upon their ability to coordinate these activities.

More recently Johnson et al. [8] applied a unique longitudinal approach to study the long-term outcomes of relationships among 3405 couples. This paper was concerned on predictors of relationship longevity, from measures of conflict frequency, types of behaviours experienced during times of conflict, satisfaction with the relationship and whether partners believed their relationships would last or not. The German study's findings showed that complacency is perhaps the most significant trap to avoid: a relationship where partners tried not to fall into that same-old routine can be vital and fulfilling for the years to come.

While there are quite a lot of studies on marriage and cohabiting couples see Motz [9] and Houston [10], there are only few papers which study the economic dynamics of romance from a theoretical point of view.

Rinaldi (1998) proposed a mathematical model based on a linear dynamical system where three aspects of love dynamics are taken into account: the forgetting process (oblivion), the pleasure of being loved (return), and the reaction to the appeal of the partner (instinct). The results of the model showed that the equilibrium turns out to be positive if the appeals of the two individuals are positive. Sprott extended those results and discussed various models of love and happiness, like the model of romance between Romeo and Juliet and the one about triangular relationship to analyse how a third part could affect the stability of a relationship, see Sprott J.C. [11].

Wauer et al. [12] studied human romantic relationships via system dynamics methodology where a non-linear modelling was proposed and analysed, showing that there are short-termed and long-termed fluctuations of personal feelings due to, for instance, biological cycles and varying stresses from the daily job. The variability is expected to be more limited for couples of cautious individuals. In Regan [13] individuals behave in order to optimize their net benefit from a given relationship. The desire to maximize their rewards, to minimize their costs and the inequity of the benefits to contributions among the individuals will cause unhappiness in a relationship. It clearly depends on the role of expectations [14] and on the level of effort that is given to the relationship. This commitment then determines whether or not the relationship will be maintained [15]. Ref. [16] added to the initial model of Rinaldi [1] a crossed interactions among partners to analyse the effects and synergies of learning and adapting to live together. According to the results of this model the system is asymptotically stable if the ratio of appeals is greater than the reciprocal of the ratio of mutual intensiveness coefficient.
