The evolution of exchange

Stochastic stability is applied to the problem of exchange. We analyze the stochastic stability of two dynamic trading processes in a simple housing market. In both models, traders meet in pairs at random and exchange their houses when trade is mutually beneficial, but occasionally they make mistakes. The models differ in the probability of mistakes. When all mistakes are equally likely, the set of stochastically stable allocations contains the set of efficient allocations. When more serious mistakes are less likely, the stochastically stable states are those allocations, always efficient, with the lowest envy level.     

The evolution of conventions in minimum effort games

The literature on minimum effort game has been concerned with a symmetric game with linear payoff functions. The main aim of the present paper is to study the coordination problem arising in a not necessarily symmetric minimum effort game with two players. The sources of asymmetry can be twofold: the productivity of effort and the distribution of the join output. To select among the Pareto ranked equilibria we use the stochastic stability criterion. We show that, for any configuration parameters, the set of stochastically stable equilibria coincides with the set of potential maximizers. We also show that when the disutility of effort is linear, the Pareto dominant equilibrium is stochastically stable provided that the distributive parameter belongs to a well defined range. When the disutility of effort is nonlinear no distributive arguments can be used to successfully affect the selection process. Lastly we prove that the connection between stochastic stability and maximum potential can fail when more than two agents are considered.     

Performance, Promotion, and the Peter Principle

This paper considers why organizations use promotions, rather than just monetary bonuses, to motivate employees even though this may conflict with efficient assignment of employees to jobs. When performance is unverifiable, use of promotion reduces the incentive for managers to be affected by influence activities that would blunt the effectiveness of monetary bonuses. When employees are risk neutral, use of promotion for incentives need not distort assignments. When they are risk averse, it may—sufficient conditions for this are given. The distortion may be either to promote more employees than is efficient (the Peter Principle effect) or fewer.
" Promotions serve two roles in an organization. First, they help assign people to the roles where they can best contribute to the organization's performance. Second, promotions serve as incentives and rewards. " (Milgrom and Roberts (1992, p. 364))
" Promotions are used as the primary incentive device in most organizations, including corporations, partnerships, and universities . . . This . . . is puzzling to us because promotion-based incentive schemes have many disadvantages and few advantages relative to bonus-based incentive schemes. " (Baker, Jensen and Murphy (1988, p. 600))     

Voting under ignorance of job skills of unemployed: the overtaxation bias

Usual models on voting over basic income–flat tax schedules rest on the assumption that voters know the whole distribution of skills even if at equilibrium some individuals do not work. If individuals’ productivity remains unknown until they work, it may be more convincing to assume that voters have only beliefs about the distribution of skills and that a learning process takes place. In this paper, at each period, individuals vote according to their beliefs which are updated when getting new information from the job market. The voting process converges towards some steady-state equilibrium that depends on both the true distribution of skills and the initial beliefs. The equilibrium tax rate is higher than (or equal to) the tax rate achieved in the perfect information framework. An illustration is provided on French data: if voters are over-pessimistic as to the potential productivity of unemployed people, majority voting may lock the economy in an “informational trap” with a high tax rate and a high level of inactivity.     

On the formation of interaction networks in social coordination games

There are many situations where two interacting individuals can benefit from coordinating their actions. We examine the endogenous choice of partners in such social coordination games and the implications for resulting play. We model the interaction pattern as a network where individuals periodically have the discretion to add or sever links to other players. With such endogenous interaction patterns we see multiple stochastically stable states of play, including some that involve play of equilibria in the coordination game that are neither efficient nor risk-dominant. Thus the endogenous network structure not only has implications for the interaction pattern that emerges, but it also has a significant impact on the play in the coordination game relative to what would arise if the same interaction network were exogenous.     

Fast convergence in evolutionary equilibrium selection

Stochastic best response models provide sharp predictions about equilibrium selection when the noise level is arbitrarily small. The difficulty is that, when the noise is extremely small, it can take an extremely long time for a large population to reach the stochastically stable equilibrium. An important exception arises when players interact locally in small close-knit groups; in this case convergence can be rapid for small noise and an arbitrarily large population. We show that a similar result holds when the population is fully mixed and there is no local interaction. Moreover, the expected waiting times are comparable to those in local interaction models.     

The tragedy of the commons revisited: The importance of group decision-making

We use a laboratory experiment to compare the way groups and individuals behave in an inter-temporal common pool dilemma. The experimental design distinguishes between a non-strategic problem where players (individuals or groups of three) make decisions without interaction and a strategic part where players harvest from a common pool. This allows us to correct for differences between individuals and groups in the quality of decisions when testing for differences in competitiveness. Group decisions are either made by majority rule or unanimity. The results show that groups are less myopic than individuals (i.e., they make qualitatively better decisions) but that they are more competitive than individuals when placed in a strategic setting. The net result for groups deciding by majority rule is that they make less efficient decisions in the strategic game than individuals do. We are able to show that this is caused by the median voter departing from her original preference in early periods with a shrinking pool. When groups have to make unanimous decisions they start playing the strategic game more efficiently then individuals do, but they rapidly become more competitive with repetition of the game.     

Strongly stable networks

We analyze the formation of networks among individuals. In particular, we examine the existence of networks that are stable against changes in links by any coalition of individuals. We show that to investigate the existence of such strongly stable networks one can restrict focus on a component-wise egalitarian allocation of value. We show that when such strongly stable networks exist they coincide with the set of efficient networks (those maximizing the total productive value). We show that the existence of strongly stable networks is equivalent to core existence in a derived cooperative game and use that result to characterize the class of value functions for which there exist strongly stable networks via a “top convexity” condition on the value function on networks. We also consider a variation on strong stability where players can make side payments, and examine situations where value functions may be non-anonymous—depending on player labels.     

Stability and Segregation in Group Formation

This paper presents a model of group formation based on the assumption that individuals prefer to associate with people similar to them. It is shown that, in general, if the number of groups that can be formed is bounded, then a stable partition of the society into groups may not exist. (A partition is defined as stable if none of the individuals would prefer be in a different group than the one he is in.) However, if individuals' characteristics are one-dimensional, then a stable partition always exists. We give sufficient conditions for stable partitions to be segregating (in the sense that, for example, low-characteristic individuals are in one group and high-characteristic ones are in another) and Pareto efficient. In addition, we propose a dynamic model of individual myopic behavior describing the evolution of group formation to an eventual stable, segregating, and Pareto efficient partition. Journal of Economic Literature Classification Numbers: C72, H41.     

Optimality and renegotiation in dynamic contracting

We characterize the optimal renegotiation-proof contract in a dynamic principal–agent model in which the type of the agent may change stochastically over time. We show that, under general conditions, the optimal contract with commitment is renegotiation proof even when type realizations are serially correlated. When the renegotiation-proofness constraint is binding, it is always optimal to partially screen the types by offering a menu of choices to the agent; and the distortion induced by the renegotiation-proofness constraint is non-decreasing in the persistence of types.     

Elderly labor supply and fertility decisions in aging-population economies

With a longer life expectancy, individuals who plan to work when they are old may increase the number of their children. Therefore, when individuals choose the time of retirement, the fertility rate may not necessarily decline but even rise.     

The merger of populations, the incidence of marriages, and aggregate unhappiness

Let a society??s unhappiness be measured by the aggregate of the levels of relative deprivation of its members. When two societies of equal size, F and M, merge, unhappiness in the merged society is shown to be higher than the sum of the levels of unhappiness in the constituent societies when apart; merger alone increases unhappiness. But when societies F and M merge and marriages are formed such that the number of households in the merged society is equal to the number of individuals in one of the constituent societies, unhappiness in the merged society is shown to be lower than the aggregate unhappiness in the two constituent societies when apart. This result obtains regardless of which individuals from one society form households with which individuals from the other, and even when the marriages have not (or not yet) led to income gains to the married couples from increased efficiency, scale economies, and the like. While there are various psychological reasons for people to become happier when they get married as opposed to staying single, the very formation of households reduces social distress even before any other happiness-generating factors kick in.     

Networks of Free Trade Agreements among Heterogeneous Countries

The paper examines the formation of free trade agreements as a network formation game. We consider an n‐country model in which international trade occurs between economies with imperfectly competitive product markets. In each country, the labor market is either unionized or non‐unionized. We show that, if all countries are non‐unionized, the global free trade network is both the unique pairwise stable network and the unique efficient network. If all countries are unionized, the global free trade network is pairwise stable and the unique efficient network among the class of symmetric networks. If some countries are unionized while others are non‐unionized, other networks apart from the global free trade network may be pairwise stable. However, the efficient network is still the global free trade network. Thus, a conflict between stability and efficiency may occur. Moreover, starting from the network in which no country has signed a free trade agreement, all sequences of networks due to continuously profitable deviations do not lead (in most cases) to the global free trade network, even when global free trade is stable.     

For how long to tie your hands? Stable relationships in an unstable environment

The Kreps–Wilson–Milgrom–Roberts framework is one of the most renowned ways of modeling reputation-building. Once the number of repetitions of the game is considered as a choice variable, such a framework can fruitfully be employed to study the optimal length of the commitment to a relationship. We analyze a model where a principal plays with an agent a finitely repeated trust game, characterize the optimal length of the relationship between principal and agent when the principal’s preferences on the agent’s type stochastically change over time and show that a commitment to a stable relationship may be optimal (even) in very unstable environments.      

Economies with observable types

We study economies of asymmetric information with observable types. Trade takes place in lotteries. Individuals face a standard budget constraint, while the incentive compatibility constraints are imposed on the production set of the intermediaries. This formalization encompasses moral hazard, as in [Jerez, 2003] and [Jerez, 2005], and private information economies. Equilibrium allocations are constrained efficient, but, contrary to what stated for example in Jerez (2005), the set of equilibrium allocations may be empty and the Second Welfare Theorem may fail. This happens for two reasons. First, constrained efficient allocations may violate the necessary and sufficient conditions of price supportability for the individuals. Second, even when constrained efficient allocation are price supportable, they may fail to be a profit maximizing choice of the firm at the individual supporting prices. To restore existence of an equilibrium the firm has to be restricted to supply allocations with support in the set of incentive compatible contracts.     

Private copying,reproduction costs,and the supply of intellectual property

Recent technological advances that have substantially reduced the cost of private copying of intellectual property, and led to widespread copying, have produced claims of severe harm to producers. This paper develops a model to analyze the effect of private copying on the profits of producers and the welfare of consumers. When originals and copies are perfect substitutes and all originals are copied the same number of times, a necessary and sufficient condition for both profits and consumer welfare to decrease is that copying is less efficient than producing originals. However, when some originals are copied and others are not, producer profits may decline even when copying is efficient, and some consumers may benefit from inefficient copying. The analysis suggests that published estimates of the harm to producers resulting from private copying may be seriously in error.     

On the median regression for SURE models with applications to 3-generation immigrants data in Sweden

In this paper we generalize the median regression method to be applicable to system of regression equations, in particular SURE models. Giving the existence of proper system wise medians of the residuals from different equations, we apply the weighted median regression with the weights obtained from the covariance matrix of the equations obtained from ordinary SURE method. The benefit of this model in our case is that the SURE estimators utilise the information present in the cross regression (or equations) error correlation and hence more efficient than other estimation methods like the OLS method. The Seemingly Unrelated Median Regression Equations (SUMRE) models produce results that are more robust than the usual SURE or single equations OLS estimation when the distributions of the dependent variables are not normally distributed or the data are associated with outliers. Moreover, the results are also more efficient than is the cases of single equations median regressions when the residuals from the different equations are correlated. A theorem is derived and indicates that even if there is no statistically significant correlation between the equations, using SUMRE model instead of SURE models will not damage the estimation of parameters.     

A bargaining model in general equilibrium

The goal of the paper is to present a simple model of rational endogenous household formation in a general equilibrium framework in which Pareto optimality at the economy level is not necessarily obtained. The simplest example of household formation is the case in which pairs of individuals engage themselves in a bargaining process on the division of some wealth: if an agreement on the distribution is (not) reached, we can say that the household is (not) formed. The vast majority of existing bargaining models predicts agreements on an efficient outcome. A seminal paper by Crawford (Econometrica 50:607–637, 1982) describes a very simple game with incomplete information in which, even with rational agents, disagreement causes welfare losses. We embed that model in a general equilibrium framework and present some results on equilibria both in the bargaining game and the associated exchange economy. Crawford’s results support Schelling’s intuition on the reasons of disagreement: it may arise if players’ commitments are reversible. Crawford shows that high probabilities of reversibility tend to favor the bargaining impasse, in fact with low probability. We prove that even if those probabilities are arbitrarily close to zero, disagreement is an equilibrium outcome, with high probability. That conclusion seems to be an even stronger support to Schelling’s original viewpoint. In the exchange economy model with that noncooperative bargaining game as a first stage, we present significant examples of economies for which equilibria exist. Because of disagreement, Pareto suboptimal exchange economy equilibria exist for all elements in the utility function and endowment spaces and they may coexist with Pareto optimal equilibria even at the same competitive prices.     

Criminal mobility,fugitives, and extradition rules

Two countries set their enforcement noncooperatively to deter native and foreign individuals from committing a crime in their territory. Crime is mobile, ex ante (migration) and ex post (fleeing), and criminals hiding abroad after committing a crime in a country must be extradited. When extradition is not too costly, countries overinvest in enforcement: insourcing foreign criminals is more costly than paying the extradition cost. When extradition is sufficiently costly, instead, significant enforcement may induce criminals to flee the country whose law they infringed on. The fear of paying the extradition cost enables the countries to coordinate on the efficient outcome.