Conservative belief and rationality

Playersʼ beliefs may be incompatible, in the sense that player i can assign probability 1 to an event E to which player j assigns probability 0. One way to block incompatibility is to assume a common prior. We consider here a different approach: we require playersʼ beliefs to be conservative, in the sense that all players must ascribe the actual world positive probability. We show that common conservative belief of rationality (CCBR) characterizes strategies in the support of a subjective correlated equilibrium where all playersʼ beliefs have common support. We also define a notion of strong rationalizability, and show that it is characterized by CCBR.     

Cheap talk with multiple audiences: An experimental analysis

We examine strategic information transmission in a controlled laboratory experiment of a cheap talk game with one sender and multiple receivers. We study the change in equilibrium behavior from the addition of another audience as well as from varying the degree of conflict between the senderʼs and receiversʼ preferences. We find that, as in cheap talk games with just one receiver, information transmission is higher in games with a separating equilibrium, than in games with only a babbling equilibrium. More interestingly, we find clear evidence that the addition of another audience alters the communication between the sender and the receiver in a way consistent with the theoretical predictions. There is evidence of the presence of agents that are systematically truthful as senders and trusting as receivers: deviations from the theoretical predictions, however, tend to disappear with experience, and learning is faster precisely in the games where deviations are more pronounced.     

Decreasing absolute prudence: Characterization and applications to second-best risk sharing

In this paper, we provide two basic properties of utility functions u which exhibit decreasing absolute prudence i.e. (− u/u″)′ ≤ 0. These properties are used to examine the allocation of risks in an economy when some agents bear non-transferable risks. We show that it is fair Pareto-efficient to let those with a non-transferable risk bear relatively less of the transferable risk in the economy if and only if absolute prudence is decreasing. In another model, there is a complete set of contingent markets, but some agents have no direct access to them. We examine the fair efficient allocation of risk in a pool gathering a trader and a non-trader. Decreasing absolute prudence provides an upper bound to the share of the pool's risk that should be borne by the trader.     

Taste-homogeneity of optimal jurisdictions in a Tiebout economy with crowding types and endogenous educational investment choices

We examine a local public goods economy with differentiated crowding. The main innovation is that we assume that the crowding effects of agents are a result of choices that agents make. For example, agents may be crowded (positively or negatively) by the skills that other members of their jurisdiction possess and these skills may be acquired through utility maximizing educational investment choices made in response to equilibrium wages and educational costs. In such an environment, we show that taste-homogeneous jurisdictions are optimal. This contrasts with results for both the standard differentiated crowding model and the crowding types model. We also show that the core and equilibrium are equivalent, and that decentralization is possible through anonymous prices having a structure similar to cost–share equilibrium prices.     

Optimal collusion under imperfect monitoring in multimarket contact

We investigate optimal collusion in repeated multimarket contact under imperfect public monitoring, where two firms operate in m markets and in each market, each firmʼs decision and public signals are binary. We show that in an optimal pure strategy strongly symmetric perfect public equilibrium, the size of efficiency loss is equal to that in the market with the most tempting deviation under single-market contact. Furthermore, we show a sufficient condition under which the symmetric equilibrium is optimal for joint payoff maximization among any perfect public equilibrium.     

Instrumental cardinal concerns for social status in two-sided matching with non-transferable utility

In this paper we apply the instrumental approach to social preferences in order to distinguish among various shapes of preferences for social status. In particular, we consider the shape of reduced preferences that emerge in the equilibrium of a two-sided matching model with non-transferable utility. Cole et al., 1992, Cole et al., 1995 show that, under full observability of potential mates׳ attributes, instrumental concerns for social status are ordinal, i.e., only one׳s own rank in the distribution of attributes matters. We show that when we depart from full observability, instrumental concerns for social status become cardinal, i.e., also other features of the distribution of attributes matter. We also show that the actual shape of cardinal concerns depends on how individuals can deal with the informational asymmetry, alternatively leading to upward concerns, i.e., making comparisons with higher rank people; downward concerns, i.e., making comparisons with lower rank people; or bidirectional concerns, i.e, being both upward and downward.     

Representing equilibrium aggregates in aggregate games with applications to common agency

An aggregate game is a normal-form game with the property that each playerʼs payoff is a function of only his own strategy and an aggregate of the strategy profile of all players. Such games possess properties that can often yield simple characterizations of equilibrium aggregates without requiring that one solves for the equilibrium strategy profile. When payoffs have a quasi-linear structure and a degree of symmetry, we construct a self-generating maximization program over the space of aggregates with the property that the solution set corresponds to the set of equilibrium aggregates of the original n-player game. We illustrate the value of this approach in common-agency games where the playersʼ strategy space is an infinite-dimensional space of nonlinear contracts. We derive equilibrium existence and characterization theorems for both the adverse selection and moral hazard versions of these games.     

Strategic nonlinear income tax competition with perfect labor mobility

Tax competition between two governments who choose nonlinear income tax schedules to maximize the average utility of their residents when skills are unobservable and labor is perfectly mobile is examined. We show that there are no equilibria in which there is a skill type that pays positive taxes to one country and whose utility is larger than the average utility in the other country or in which the lowest skilled are subsidized. We also show that it is possible for the most highly skilled to receive a net transfer funded by taxes on lower skilled individuals in equilibrium. These findings confirm the race-to-the-bottom thesis in this setting.     

TAXATION IN MATCHING MARKETS

We analyze the effects of taxation in two-sided matching markets where agents have heterogeneous preferences over potential partners. Our model provides a continuous link between models of matching with and without transfers. Taxes generate inefficiency on the allocative margin, by changing who matches with whom. This allocative inefficiency can be nonmonotonic, but is weakly increasing in the tax rate under linear taxation if each worker has negative nonpecuniary utility of working. We adapt existing econometric methods for markets without taxes to our setting, and estimate preferences in the college-coach football market. We show through simulations that standard methods inaccurately measure deadweight loss.     

A spillover‐based theory of credentialism

I propose a model in which credentials, such as diplomas, are instrumentally valuable to workers. The model avoids an important criticism of standard job market signalling models by tying a worker's wage to their output. A worker's productivity is influenced by the skills of their co‐workers, where such skills arise from an ability‐augmenting investment that is made prior to matching with co‐workers. Credentials allow workers to demonstrate their investment to the labour market, thereby allowing them to match with high‐skill co‐workers in equilibrium. Despite the positive externality associated with a worker's investment, I show how overinvestment is pervasive in equilibrium.     

Search theory,competitive equilibrium,and the Nash bargaining solution

We investigate a canonical search-theoretic model without entry. Two agents are randomly matched with a long side being rationed. The matched agents face a pair of randomly drawn non-transferable payoffs, and then choose whether or not to form a partnership subject to a small probability of exogenous break down. As this probability and friction vanish, the Nash bargaining solution emerges as the unique undominated strategy equilibrium outcome if the mass of each party is the same. If the size of one party is larger than the other, the short side extracts the entire surplus, a sharp contrast to Rubinstein and Wolinsky (1985) [16].     

Cooperative games in permutational structure

Summary. By a cooperative game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a set of payoffs for each coalition being a nonempty subset of the grand coalition of all players. It is well-known that balancedness is a sufficient condition for the nonemptiness of the core of such a cooperative non-transferable utility game. In this paper we consider non-transferable utility games in which for any coalition the set of payoffs depends on a permutation or ordering upon any partition of the coalition into subcoalitions. We call such a game a cooperative game in permutational structure or shortly permutational game. Doing so we extend the scope of the standard cooperative game theory in dealing with economic or political problems. Next we define the concept of core for such games. By introducing balancedness for ordered partitions of coalitions, we prove the nonemptiness of the core of a balanced non-transferable utility permutational game. Moreover we show that the core of a permutational game coincides with the core of an induced game in coalitional structure, but that balancedness of the permutational game need not imply balancedness of the corresponding coalitional game. This leads to a weakening of the conditions for the existence of a nonempty core of a game in coalitional structure, induced by a game in permutational structure. Furthermore, we refine the concept of core for the class of permutational games. We call this refinement the balanced-core of the game and show that the balanced-core of a balanced permutational game is a nonempty subset of the core. The proof of the nonemptiness of the core of a permutational game is based on a new intersection theorem on the unit simplex, which generalizes the well-known intersection theorem of Shapley. Received: October 31, 1995; revised version: February 5, 1997     

Fair Income Tax

In a model where agents have unequal skills and heterogeneous preferences over consumption and leisure, we look for the optimal tax on the basis of efficiency and fairness principles and under incentive-compatibility constraints. The fairness principles considered here are: (1) a weak version of the Pigou–Dalton transfer principle; (2) a condition precluding redistribution when all agents have the same skills. With such principles we construct and justify specific social preferences and derive a simple criterion for the evaluation of income tax schedules. Namely, the lower the greatest average tax rate over the range of low incomes, the better. We show that, as a consequence, the optimal tax should give the greatest subsidies to the working poor (the agents having the lowest skill and choosing the largest labour time).     

Income Taxes,Subsidies to Education,and Investments in Human Capital

We study a two‐sector economy with investments in human and physical capital and imperfect labor markets. Investments are irreversible and noncontractible, due to random matching between firms and workers. Income is allocated according to the Nash bargaining mechanism. At equilibrium, given the distribution of the agents across sectors, there is underinvestment in both human and physical capital, due to the holdup problem generated by bargaining and noncontractibility. Self‐selection of the agents into the two sectors typically induces too many workers to invest in high skills. Compared to the constrained efficient allocation, at each equilibrium, there are too many people investing too little effort in the high‐skill sector. We also study the effects of several tax policies on total expected surplus.     

Information sharing between vertical hierarchies

When do principals independently choose to share the information obtained from their privately informed agents? Information sharing affects contracting within competing organizations and induces agentsʼ strategies to be correlated through the distortions imposed by principals to obtain information. We show that the incentives to share information depend on the nature of upstream externalities between principals and the correlation of agentsʼ information. With small externalities, principals share information when externalities and correlation have opposite signs, and do not share information when externalities and correlation have the same sign. In this second case, principals face a prisonersʼ dilemma since they obtain higher profits by sharing information.     

On the impact of leverage constraints on asset prices and trading volume

Abstract. Researchers have used stylized facts on asset prices and trading volume in stock markets (in particular, the mean reversion of asset returns and the correlations between trading volume, price changes and price levels) to support theories where agents are not rational expected utility maximizers. This paper shows that this empirical evidence is in fact consistent with a standard infinite horizon – perfect information – expected utility economy where some agents face leverage constraints similar to those found in todays financial markets. In addition, and in sharp contrast to the theories above, we explain some qualitative differences that are observed in the price-volume relation on stock and on futures markets. We consider a continuous-time economy where agents maximize the integral of their discounted utility from consumption under both budget and leverage constraints. Building on the work by Vila and Zariphopoulou (1997), we find a closed form solution, up to a negative constant, for the equilibrium prices and demands in the region of the state space where the constraint is non-binding. We show that, at the equilibrium, stock holdings volatility as well as its ratio to stock price volatility are increasing functions of the stock price and interpret this finding in terms of the price-volume relation. We would like to thank the editor and two anonimous referees for valuable substantive comments. Our gratitude also to Franklin Allen, Kerry Back, Domenico Cuoco, Xavier Freixas, Sanford Grossman, Michel Habib, Lutz Hendricks, Richard Kihlstrom, Fernando Restoy, Mary Thomson, Jean-Luc Vila, participants to seminars at Birkbeck College, Carnegie-Mellon, Columbia, ESSEC, HEC, IAE, INSEAD, London Business School, London School of Economics, McGill, Michigan, National University of Singapore, Pompeu Fabra, North Carolina, Washington-St-Louis, Wharton, the Jornadas de Economía Financiera BBV, and the Meetings of the Society for Economic Dynamics and Control and the American Finance Association. Special thanks are due to Süleyman Basak for his enthusiastic support and many helpful suggestions. The usual disclaimer applies. We gratefully acknowledge the support of the BBV and Caja de Madrid Foundations and CREF (both authors) and of the Spanish Ministry of Education under DGICYT grant no. PB93-0388 (first author).     

A Directed Search Model of Inequality with Heterogeneous Skills and Skill–Biased Technology

In this paper I analyse the directed search/matching problem in an economy with heterogeneous skills and skill–biased technology. A unique symmetric equilibrium exists and is socially efficient. Matching is partially mixed in the equilibrium. A high–tech firm receives both skilled and unskilled applicants with positive probability, and favours skilled workers, while a low–tech firm receives only unskilled applicants. The model generates wage inequality among identical unskilled workers, as well as between–skill inequality, despite the fact that all unskilled workers perform the same task and have the same productivity in the two types of firms. Inequality has interesting responses to skill–biased technological progress, a general productivity slowdown, and an exogenous increase in the skill supply elasticity.     

Cooperation,imitation and partial rematching

We study a setting in which imitative players are matched into pairs to play a Prisonerʼs Dilemma game. A well-known result in such setting is that under random matching cooperation vanishes for any interior initial condition. The novelty of this paper is that we consider partial rematching: players that belong to a pair in which both parties cooperate repeat partner next period, while all other players are randomly matched into pairs. Under certain conditions, this rematching mechanism makes cooperation the unique outcome in the long run. Furthermore, we show that if imitation happens infrequently enough then cooperative behavior is always present in the population.     

Existence of equilibria in countable games: An algebraic approach

Although mixed extensions of finite games always admit equilibria, this is not the case for countable games, the best-known example being Waldʼs pick-the-larger-integer game. Several authors have provided conditions for the existence of equilibria in infinite games. These conditions are typically of topological nature and are rarely applicable to countable games. Here we establish an existence result for the equilibrium of countable games when the strategy sets are a countable group, the payoffs are functions of the group operation, and mixed strategies are not requested to be σ-additive. As a byproduct we show that if finitely additive mixed strategies are allowed, then Waldʼs game admits an equilibrium. Finally we extend the main results to uncountable games.     

Contests where there is variation in the marginal productivity of effort

Summary. We provide a characterization of participants' behavior in a contest or tournament where the marginal productivity of effort varies across contestants and individual productivity is private information. We then consider the optimal design of such a contest. We first analyze contestant behavior for the usual type of contest, where the highest output wins. Abilities need not be independently distributed. We demonstrate that there is a unique symmetric equilibrium output function, that output is increasing in ability, and that marginal effort is increasing in ability, while effort decreases when the cost of effort increases. Next we consider the case where the highest output need not win, with independently distributed abilities. We analyze the contest designer's decisions in choosing contest rules optimal from her perspective. We show that the output produced, probability of winning, and contest designer's expected revenue are generally increasing in contestants' ability. We examine the relationship between the marginal cost of producing output and marginal utility per dollar of the net award for winning. Received: July 30, 1998; revised version: August 7, 2000