Price competition and convex costs

In the original model of pure price competition, due to Joseph Bertrand (1883), firms have linear cost functions. For any number of identical such price-setting firms, this results in the perfectly competitive outcome; the equilibrium price equal the firms’ (constant) marginal cost. This paper provides a generalization of Bertrand’s model from linear to convex cost functions. I analyze pure price competition both in a static setting - where the firms interact once and for all - and in dynamic setting - where they interact repeatedly over an indefinite future. Sufficient conditions are given for the existence of Nash equilibrium in the static setting and for subgame perfect equilibrium in the dynamic setting. These equilibrium sets are characterized, and it is shown that there typically exists a whole interval of Nash equilibrium prices in the static setting and subgame perfect equilibria in the dynamic setting. It is shown that firms may earn sizable profits and that their equilibrium profits may increase if their production costs go up.Bertrand competition;

Mean-field approximation of stochastic population processes in games

We here establish an upper bound on the probability for deviations of a Markov population process from its mean-field approximation.

Language, meaning and games A model of communication, coordination and evolution

Language is arguably a powerful coordination device in real-life interactions. We here develop a game-theoretic model of pre-play communication that generalizes the cheap-talk approach by way of introducing a meaning correspondence between messages and actions, and postulating two axioms met by natural languages. Deviations from this correspondence are called dishonest and players have a lexicographic preference for honesty, second to material payoffs. The model is first applied to two-sided preplay communication in finite and symmetric two-player games and we establish that, in generic and symmetric n × n - coordination games, a Nash equilibrium component in such a lexicographic communication game is evolutionarily stable if and only if it results in the unique Pareto efficient outcome of the underlying game. We extend the approach to one-sided communication in finite, not necessarily symmetric, two-player games.

Political Polarization

Failures of government policies often provoke opposite reactions from citizens; some call for a reversal of the policy while others favor its continuation in stronger form. We offer an explanation of such polarization, based on a natural bimodality of preferences in political and economic contexts, and consistent with Bayesian rationality.polarization; voting; information

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.

Outer measure and utility

In most economics textbooks there is a gap between the non-existence of utility functions and the existence of continuous utility functions, although upper semi-continuity is sufficient for many purposes. Starting from a simple constructive approach for countable domains and combining this with basic measure theory, we obtain necessary and sufficient conditions for the existence of upper semi-continuous utility functions on a wide class of domains. Although links between utility theory and measure theory have been pointed out before, to the best of our knowledge this is the first time that the present route has been taken.preferences, utility theory, measure theory, outer measure

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.