Family ties, incentives and development: a model of coerced altruism

We analyze the effects of family ties on the incentives for production of effort, where family ties are defined as a mixture of true and coerced altruism between family members. We model families as pairs of siblings. Each sibling exerts effort in order to obtain output under uncertainty. A social norm dictates that a sibling with a high output must share a specified amount of this output with his sibling, if the latter's output is low. Siblings may be truly altruistic towards each other, but not to a larger degree than dictated by the social norm. We compare such informal family insurance with actuarially fair formal insurance. We show that coerced family altruism reduces individual efforts in equilibrium. However, individuals always benefit ex ante from living in families with coerced altruism, as compared with living in autarky. We show that a certain degree of coerced family altruism is robust as a social norm in a society of selfish individuals. Finally, we show that if family members are sufficiently altruistic to each other, then informal family insurance by way of coerced altruism may outperform actuarially fair insurance programs.altruism; coerced altruism; family ties; insurance; moral hazard

The Fetters of the Sib: Weber Meets Darwin

We analyze the effects of family ties on the incentives for productive effort. A family is modelled as a pair of altruistic siblings. Each sibling exerts effort to produce output under uncertainty and siblings may transfer output to each other. We show that altruism has a non-monotonic effect on effort. We study how this effect depends on "climate," the magnitude and volatility of returns to effort. We also analyze the evolutionary robustness of family ties and how this robustness depends on climate. We find that family ties will be stronger in milder climates than in harsher climates.altruism; family ties; moral hazard; evolutionary robustness

Kinship, Incentives and Evolution

We analyze how family ties affect incentives, with focus on the strategic interaction between two mutually altruistic siblings. The siblings exert effort to produce output under uncertainty, and they may transfer output to each other. With equally altruistic siblings, their equilibrium effort is non-monotonic in the common degree of altruism, and it depends on the harshness of the environment. We define a notion of local evolutionary stability of degrees of sibling altruism, and show that this degree is lower than the kinship-relatedness factor. Numerical simulations show how family ties vary with the environment, and how this a¤ects economic outcomes.altruism, family ties, free-riding, empathy, Hamilton's rule, evolutionary stability.

The fetters of the sib: Weber meets Darwin

We analyze how family ties affect incentives, with focus on the strategic interaction between a pair of mutually altruistic siblings. Each sibling exerts effort to produce output under uncertainty and the siblings may transfer output to each other. With equally altruistic siblings, their equilibrium effort is nonmonotonic in the common degree of altruism and depends on the harshness of the environment. We define a notion of local evolutionary robustness of degrees of sibling altruism, and show that this degree is less than one half, the kinship relatedness factor. By way of numerical simulations we show that family ties are weaker in harsher environments.altruism, family ties, Hamilton's rule, free-riding, evolutionary robustness

Crime, punishment and social norms

We analyze the interplay between economic incentives and social norms when individuals decide whether or not to engage in criminal activity. More specifically, we assume that there is a social norm against criminal activity and that deviations from the norm result in feelings of guilt or shame. The intensity of these feelings is here endogenous in the sense that they are stronger when the population fraction obeying the norm is larger. As a consequence, a gradual reduction of the sanctions against criminal activity, or of the taxation of legal incomes, may weaken the social norm against crime. Due to the potential multiplicity of equilibria in our model, such a gradual change may even induce a discontinuous increase in the crime rate. We show that law enforcement policies may have dramatic and permanent efects on the crime rate, and lead to hysteresis. We also define political equilibrium under majority rule and show how a majority of individuals, who feel no guilt or shame from violating the law, in political equilibrium can exploit a minority who do have such feelings.crime; punishment; social norm; political equilibrium

Altruism and Climate

Recognizing that individualism, or weak family ties, may be favorable to economic development, we ask how family ties interact with climate to determine individual behavior and whether there is reason to believe that the strength of family ties evolves differently in different climates. For this purpose, we develop a simple model of the interaction between two individuals who are more or less altruistic towards each other. Each individual exerts effort to produce a consumption good under uncertainty. Outputs are observed and each individual chooses how much, if any, of his or her output to share with the other. We analyze how the equilibrium outcome depends on altruism and climate for ex ante identical individuals. We also consider (a) "coerced altruism," that is, situations where a social norm dictates how output be shared, (b) the effects of insurance markets, and (c) the role of institutional quality. The evolutionary robustness of altruism is analyzed and we study how this depends on climate.altruism; family ties; individualism; moral hazard; evolution.

Multiple solutions under quasi-exponential discounting

We consider a group or committee that faces a binary decision under uncertainty. Each member holds some private information. Members agree which decision should be taken in each state of nature, had this been known, but they may attach different values to the two types of mistake that may occur. Most voting rules have a plethora of uninformative equilibria, and informative voting may be incompatible with equilibrium. We analyze an anonymous randomized majority rule that has a unique equilibrium. This equilibrium is strict, votes are informative, and the equilibrium implements the optimal decision with probability one in the limit as the committee size goes to infinity. We show that this also holds for the usual majority rule under certain perturbations of the behavioral assumptions: (i) a slight preference for voting according to one's conviction, and (ii) transparency and a slight preference for esteem. We also show that a slight probability for voting mistakes strengthens the incentive for informative voting.: time-consistency, hyperbolic discounting, stochastic dynamic programming, multiplicity, uniqueness.

Deterministic Approximation of Stochastic Evolution in Games

This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The deterministic approximation is defined in continuous time as a system of ordinary differential equations of the type studied in evolutionary game theory. We establish precise connections between the long-run behavior of the stochastic process, for large populations, and its deterministic approximation. In particular, we show that if the deterministic solution through the initial state of the stochastic process at some point in time enters a basin of attraction, then the stochastic process will enter any given neighborhood of that attractor within a finite and deterministic time with a probability that exponentially approaches one as the population size goes to infinity. The process will remain in this neighborhood for a random time that almost surely exceeds an exponential function of the population size. During this time interval, the process spends almost all time at a certain subset of the attractor, its so-called Birkhoff center. We sharpen this result in the special case of ergodic processes.  Game Theory; Evolution; Approximation

Uniqueness in Infinitely Repeated Decision Problems

Dynamic decision-making without commitment is usually modelled as a game between the current and future selves of the decision maker. It has been observed that if the time-horizon is infinite, then such games may have multiple subgame-perfect equilibrium solutions. We provide a sufficient condition for uniqueness in a class of such games, namely infinitely repeated decision problems with discounting. The condition is two-fold: the range of possible utility levels in the decision problem should be bounded from below, and the discount factor between successive periods should be non-decreasing over time, a condition met by exponential, quasi-exponential and hyperbolic discounting.  Game Theory; Time Preference; Hyperbolic Discounting; Repeated Decision Problems