We establish a new approach to the modeling of cooperation, and we formulate a new solution concept for cooperative games. We do this by constructing a game of cooperation between individuals who exhibit distaste for relative deprivation, RD, in the sense that they experience stress when their income is lower than that of their comparators. In such a game, the sharing out of the jointly earned income between these individuals when they cooperate, as prescribed by standard solutions of cooperative games, might not be acceptable to the individuals. The stress from RD may have the upper hand. Measuring stress by RD, we thus model a setting in which two individuals who are concerned with being relatively deprived need to decide whether or not to cooperate. We term this setting an RD cooperative game, and we design a rule, the RD solution, for the distribution of the income yielded in this game. The RD solution prescribes cooperation in spite of cooperation-induced stress and preserves the spirit of standardness (an equal sharing of the gain that accrues from cooperation) for two-player games (a property shared by the main solution concepts for cooperative games).

We establish a new approach to the modeling of cooperation, and we formulate a new solution concept for cooperative games. We do this by constructing a game of cooperation between individuals who exhibit distaste for relative deprivation, RD, in the sense that they experience stress when their income is lower than that of their comparators. In such a game, the sharing out of the jointly earned income between these individuals when they cooperate, as prescribed by standard solutions of cooperative games, might not be acceptable to the individuals. The stress from RD may have the upper hand. Measuring stress by RD, we thus model a setting in which two individuals who are concerned with being relatively deprived need to decide whether or not to cooperate. We term this setting an RD cooperative game, and we design a rule, the RD solution, for the distribution of the income yielded in this game. The RD solution prescribes cooperation in spite of cooperation-induced stress and preserves the spirit of standardness (an equal sharing of the gain that accrues from cooperation) for two-player games (a property shared by the main solution concepts for cooperative games).

Governments of countries that attract migrants enact rules, procedures, and policies that constrain migration directly or affect migration indirectly. One such policy is the provision of social welfare benefits. As both intuition and literature lead us to conjecture, a case in point is the provision of social welfare benefits to low-skill workers, which affects the incentive of migration of low-skill workers. This is so because of the assumption that once they join the host country’s workforce, low-skill migrants will be treated like low-skill native workers, in terms not only of wage remuneration and wage taxation but also eligibility for social welfare benefits. For example, this is the practice with regard to migration among European Union countries. A corollary of this perspective is that the more generous are the social welfare benefits in a migrant’s host country, the larger will be the gain awaiting low-skill migrant workers. Our aim in this paper is to draw attention to the possibility that matters do not necessarily unfold in this manner. In a nutshell, our conjecture is as follows. Social welfare benefits for low-skill workers in a country increase the supply of these workers. As a result of the increased supply, the wages of the low-skill workers in the country decline. Consequently, the gain awaiting low-skill migrant workers will diminish, and the incentive of low-skill workers to migrate to the country will be weakened. A policy implication of this conjecture is that governmental concerns over the possibility that, as a result of the enactment of generous social welfare benefits programs, migration pressures will intensify need not apply.

We specify the domain in the income distribution that includes the people to whom income transfers will not increase inequality in that income distribution. Inspired by Sen’s (1973, 1997) characterization of the Gini coefficient as a ratio between a measure of aggregate income-based “depression” (stress) and aggregate income, we inquire as to whether in the wake of an increase of an income or of incomes in a given income distribution, the Gini coefficient does not increase. To this end, we identify the corresponding “safe” domain and show that the pivotal value that demarcates this domain can be elicited from a simple linear function of the Gini coefficient itself. Our rule of demarcation provides for policy interventions that seek to increase a particular income or particular incomes while not exacerbating inequality in the income distribution as measured by the Gini coefficient.

We specify the domain in the income distribution that includes the people to whom income transfers will not increase inequality in that income distribution. Inspired by Sen’s (1973, 1997) characterization of the Gini coefficient as a ratio between a measure of aggregate income-based “depression” (stress) and aggregate income, we inquire as to whether in the wake of an increase of an income or of incomes in a given income distribution, the Gini coefficient does not increase. To this end, we identify the corresponding “safe” domain and show that the pivotal value that demarcates this domain can be elicited from a simple linear function of the Gini coefficient itself. Our rule of demarcation provides for policy interventions that seek to increase a particular income or particular incomes while not exacerbating inequality in the income distribution as measured by the Gini coefficient.

In "Immigration, search and redistribution: A quantitative assessment of native welfare," a paper by Battisti et al. published in the August 2018 issue of the Journal of the European Economic Association, the authors inquire about how migration to 20 Organization for Economic Cooperation and Development (OECD) countries affects the welfare of the countries' native workers. In this comment, we raise several concerns regarding the analytical and the empirical parts of the Battisti et al.'s inquiry that bear on this effect. In particular, when Battisti et al. formulate a rule for the division between a worker and a firm of the surplus that arises from a firm-worker match, Battisti et al. neglect to take into account the fact that wages are taxed. When Battisti et al. formulate the GDP identity, the incorporation of capital is done incorrectly. Calibration of a corrected model undertaken in this comment reveals that these issues affect measurably the empirical results regarding the impacts on the welfare of native workers of skill-neutral migration and of migration by low-skill workers. An additional concern is that our calibration of a corrected model yields estimates of the tax rate on workers' wages that are far too high to be considered feasible. This suggests to us that even when the model of Battisti et al. is corrected, a structural revision is deemed necessary in order to deliver a useful tool for measuring the effect of migration on the welfare of native workers in the 20 OECD countries. As a step in this direction, we calibrate a version of the corrected model, which involves "reasonable" tax rates on wages and a budget deficit. The results yielded by this counterfactual version lend support to the results of the corrected model regarding the negative impact of skill-neutral migration and of migration by low-skill workers on the welfare of native workers.

Following Sen's (1973) characterization of the Gini coefficient as a ratio between a measure of aggregate income-based stress ("depression" in Sen's terminology) and aggregate income, we transform the Gini coefficient into a social welfare function rather than having the Gini coefficient feature as an input in a social welfare function as in Sen (1973 and 1997), Sen (1976), and Sen (1982). The "Gini social welfare function" assigns weights that reflect preferences to aggregate income and to aggregate income-based stress (income inequality), a desirable property that a social welfare function in which the Gini coefficient features as an input does not have. The transformation bears on the formation of public policy and on the welfare analysis of policy interventions.

I study attitudes towards risk taking in cases where a person relates to others positively, namely altruistically. This study is needed because it is unclear how altruism influences the inclination of an altruistic person to take risks. Will this person's risk-taking behavior differ if the utility of another person does not enter his utility function? Does being altruistic cause a person to become more reluctant to take risks because a risky undertaking turning sour will also damage his ability to make altruistic transfers? Or does altruism induce a person to resort to risky behavior because the reward for a successful outcome is amplified by the outcome facilitating a bigger transfer to the beneficiary of the altruistic act? Specifically, holding constant other variables, I ask: is an altruistic person more risk averse or less risk averse than a comparable person who is not altruistic? In response to this question, using a simple model in which preferences are represented by a logarithmic utility function, I show that an altruistic person who is an active donor (benefactor) is less risk averse than a comparable person who is not altruistic: altruism is a cause of greater willingness to take risks. The finding that the altruism trait causes greater willingness to take risks has not previously been noted in the existing literature.

The 1949 study The American Soldier: Combat and Its Aftermath, Volume II, by Stouffer et al. presents detailed accounts of the attitudes of American fighter pilots toward the stress experienced by them and of the policies and practices of the American Air Force command in addressing this stress during WWII. The 2022 study “Killer incentives” by Ager et al. documents an aspect and a repercussion of the stress of German fighter pilots and can be used to identify the response to that stress by the German Air Force command during WWII. Drawing on these two studies, in this paper I construct fighter pilot stress profiles in the two air forces. The picture that emerges is that there is a stark difference between the approaches of the two commands. This diversity leads me to conjecture that the American Air Force command explicitly sought to forestall and curtail fighter pilots’ stress, whereas the German Air Force command implicitly cultivated and engineered fighter pilots’ stress.

A perception at the core of studies that consider the link between social rank and stress (typically measured by the so-called stress hormone cortisol) is that the link is direct. Examples of such studies are Bartolomucci (2007), Beery and Kaufer (2015), and Koolhaas et al. (2017). A recent and stark representation of this body of work is a study by Smith-Osborne et al. (2023), who state that "social hierarchies directly influence stress status" (Smith-Osborne et al. p. 1537, italics added). In the present paper, we reflect on this "direct" perspective. We conjecture that the link between social rank and stress involves an intervening variable: an indirect relationship arises when the loss of rank triggers a behavioral response in the form of risk taking aimed at regaining rank, and it is the engagement in risk-taking behavior that is the cause of an elevated level of cortisol. Smith-Osborne et al., as well as others whose papers are cited by Smith-Osborne et al. and who, like Creel (2001) and Avitsur et al. (2006), conducted comprehensive research on the association between rank (social standing) and stress, do not refer to risk taking at all. We present four strands of research that lend support to our conjecture: evidence that in response to losing rank, individuals are stressed; evidence that in response to losing rank, individuals resort to risk-taking behavior aimed at regaining their lost rank; evidence that there exists a link between engagement in risky activities or exposure to risk and elevated levels of cortisol; and an analytical perspective on incidence and intensity, namely a perspective that shows how the willingness to take risks responds to a change in rank, specifically, how a loss of rank triggers a greater willingness to take risks and how this trigger is stronger for individuals whose rank is higher.

The social stress experienced by an individual from having a low relative income or from having a low income-based rank is a derivative of the individual’s location in social space, and is the outcome of unfavorable comparisons with other individuals in that space. (The term social space stands for the set of individuals with whose incomes or with whose income-based ranks the individual compares his income or his income-based rank.) The stress that arises from unfavorable social comparisons can cause physical and mental harm. Essentially, there are three ways to thwart unfavorable income-related comparisons experienced by an individual: to operate on the individual’s income or on a characteristic (an attribute) of the individual’s income; to operate on the incomes or on a characteristic of the incomes of the individual’s comparators; or to modify the individual’s social space. The first two approaches feature extensively in the existing literature. The third does not. In this communication, I analyze this third approach, keeping in mind its application as a policy tool for lowering social stress.

Sen ( 1973 and 1997) presents the Gini coefficient of income inequality in a population as follows. “In any pair-wise comparison the man with the lower income can be thought to be suffering from some depression on finding his income to be lower. Let this depression be proportional to the difference in income. The sum total of all such depressions in all possible pair-wise comparisons takes us to the Gini coefficient.” (This citation is from Sen 1973 , p. 8.) Sen’s verbal account is accompanied by a formula (Sen 1997, p. 31, eq. 2.8.1), which is replicated in the text of this note as equation (1). The formula yields a coefficient bounded from above by a number smaller than 1. This creates a difficulty, because the “mission” of a measure of inequality defined on the unit interval is to accord 0 to perfect equality (maximal equality) and 1 to perfect inequality (maximal inequality). In this note we show that when the Gini coefficient is elicited from a neat measure of the aggregate income-related depression of the population that consists of the people who experience income-related depression, then the obtained Gini coefficient is “well behaved” in the sense that it is bounded from above by 1. We conjecture a reason for a drawback of Sen’s definition, and we present repercussions of the usage of the “well-behaved” Gini coefficient.

The purpose of this paper is to provide a general proposition of the relationship between altruism and risk taking. As explained in the body of the paper, we diverge from a result reported in Stark et al. (2022) and provide an expansion and a generalization of a preliminary result reported in Stark (2024). In a broad utility framework, we study the risk aversion of an altruistic person who is an active donor (benefactor) and the risk aversion of a beneficiary of an altruistic transfer. In both cases, we find that altruism lowers risk aversion. The specific case in which the utility functions of the benefactor and of the beneficiary are constant relative risk aversion (CRRA) functions constitutes a vivid example of lesser risk aversion characterization. We conclude that in terms of risk-taking behavior, a “population” endowed with altruism is uniformly more willing to take risks than a comparable “population” devoid of altruism.

World Scientific Handbook of Global Migration, pp. 53-82 (2024) No AccessChapter 3: On the Role of Social Comparisons in Shaping Migrants' Remittance Behavior: Theory, and Evidence from ChinaOded Stark and Daniel LaFaveOded Stark and Daniel LaFavehttps://doi.org/10.1142/9789811248139_0003Cited by:0 (Source: Crossref) PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: The following sections are included: Introduction Analytical considerations The empirical approach Data: Chinese rural-to-urban migrants Estimation results Remittances respond to the reference group level Heterogeneity in adherence to the reference group's norm Conclusion References FiguresReferencesRelatedDetails Recommended World Scientific Handbook of Global MigrationMetrics History PDF download

World Scientific Handbook of Global Migration, pp. 179-197 (2024) No AccessChapter 8: Intensity of Migration Need Not Decrease When Migration Cost Increases: The Mitigating Power of Joint Savings AgreementsOded Stark and Marcin JakubekOded Stark and Marcin Jakubekhttps://doi.org/10.1142/9789811248146_0008Cited by:0 (Source: Crossref) PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: The following sections are included: Introduction Formal modeling An increase in the cost of migration and the propensity to form joint saving agreements Examples of empirical implications Discussion and conclusions References FiguresReferencesRelatedDetails Recommended World Scientific Handbook of Global MigrationMetrics History PDF download

World Scientific Handbook of Global Migration, pp. 165-175 (2024) No AccessChapter 7: An Integrated Theory of Relative Deprivation and Risk-Laden MigrationOded Stark and Wiktor BudzinskiOded Stark and Wiktor Budzinskihttps://doi.org/10.1142/9789811248139_0007Cited by:0 (Source: Crossref) PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: The following sections are included: Introduction An integrated model of relative deprivation and risk-laden migration Measures of robustness At destination the individual experiences relative deprivation only when unemployed In the utility representation, relative deprivation is entered non-linearly A numerical illustration Conclusion References FiguresReferencesRelatedDetails Recommended World Scientific Handbook of Global MigrationMetrics History PDF download

We formulate a rule for allocating asylum seekers that is based on the social preferences of the native workers of the receiving countries. To derive the rule, we construct for each country a social welfare function, SWF, where the social welfare of a population is determined both by the population's aggregate absolute income and by the population's aggregate relative income. In a utilitarian manner, we combine the social welfare functions of the countries into a global social welfare function, GSWF. We look for the allocation that yields the highest value of the GSWF. We draw on assumptions that pertain to the manner in which the asylum seekers join the income distribution of the native workers: we consider a case in which the arrival of the asylum seekers has only a minor effect on the absolute income of the native population, and in which following their admission and integration, the asylum seekers join the income distribution of the native population “from below,” namely the incomes of the asylum seekers are lower than the incomes of the low-income native workers. The arrival of asylum seekers can, however, measurably affect the relative incomes of the native population. Our rule states that the share of asylum seekers to be optimally assigned to each country depends only on the aggregate of the income excesses experienced by the native populations in the receiving countries.

The merger of populations expands the comparison space of incomes. As a result, measures of the income-based social stress and of the income inequality of the constituent populations need to be replaced by new measures. To this end, we develop a procedure for calculating the aggregate social stress and the Gini coefficient of the merged population. We show that to calculate the aggregate social stress when the income distributions of the constituent populations do not overlap, it is sufficient to utilize just three characteristics of the constituent populations: their size, the levels of their aggregate income-based social stress, and their mean income. This result carries over to the calculation of the Gini coefficient of the merged population. We also analyze the extent to which the procedure, applied to cases where the constituent populations do not overlap, can be extended to cases where the income distributions of the constituent populations overlap.