Delays and equilibria with large and small information in social learning

The general model of social learning with irreversible investment and endogenous timing is analyzed for any distribution of private informations. Strategic complementarities and multiple equilibria appear which are generated solely by information externalities. Different equilibria generate strikingly different amounts of information. The impacts of various assumptions (bounded beliefs, large number of agents, discrete time and short periods) are examined carefully. The properties are robust to the introduction of observation noise with a continuum of agents.     

Concave utility on finite sets

When does a preference relation on a finite set have a concave or a strictly concave utility function? We provide a complete answer. Our proof is an application of the Theorem of the Alternative, and constructs a concave utility if one exists.     

Strategies as states

We define rationality and equilibrium when states specify agents’ actions and agents have arbitrary partitions over these states. Although some suggest that this natural modeling step leads to paradox, we show that Bayesian equilibrium is well defined and puzzles can be circumvented. The main problem arises when player j's partition informs j of i's move and i knows j's strategy. Then i's inference about j's move will vary with i's own move, and i may consequently play a dominated action. Plausible conditions on partitions rule out these scenarios. Equilibria exist under the same conditions, and more generally ε equilibria usually exist.     

Quality dualism

We suggest a theory of quality dualism, defined in terms of the gap between the highest quality good produced in the informal sector and the lowest quality produced in the formal sector. We develop a model of vertically differentiated products, in which firms producing in the formal and informal sectors face different factor prices, and have a relative advantage in the manufacture of different qualities. We then use the model to examine the cyclical behavior of the respective sizes of the two sectors. Finally, we point out that factor price changes, which reduce or increase the size of the informal sector, may have the same or opposite effect on the degree of dualism in the economy.     

Implementation of college admission rules

Summary We consider both Nash and strong Nash implementation of various matching rules for college admissions problems. We show that all such rules are supersolutions of the stable rule. Among these rules the lower bound stable rule is implementable in both senses. The upper bound Pareto and individually rational rule is strong Nash implementable yet it is not Nash implementable. Two corollaries of interest are the stable rule is the minimal (Nash or strong Nash) implementable solution that is Pareto optimal and individually rational, and the stable rule is the minimal (Nash or strong Nash) implementable extension of any of its subsolutions.We wish to thank Professor William Thomson for his efforts in supervision as well as his useful suggestions. We are grateful to the participants in his reading class, workshops at Bilkent University, University of Rochester, and in particular Jeffrey Banks, Stephen Ching, Bhaskar Dutta, Rangarajan Sundaram and an anonymous referee for their helpful comments.     

对科技型中小企业研发的新思考

研发是科技型中小企业技术创新的动力之源，也是企业在激烈的市场竞争中求生存、谋发展的必然选择。文章对影响企业的研发因素进行了分析，在此基础上，指出了企业进行研发的路径选择以及企业在研发中应当注意的一些问题。     

Effective property rights, conflict and growth

This paper shows how the interaction between conflict and growth can give rise to a nonmonotone relationship between property rights and social welfare. This interaction is illustrated in a model of endogenous growth in which equilibrium diversion of resources is the cost of securing effective property rights. A symmetric equilibrium allocation associated with more secure property rights and faster growth can be Pareto dominated by one associated with poorer property rights and slower growth. Faster growth can exacerbate the problem of diversion whenever property rights are sufficiently poor. These results call for caution before a society decides to pursue economic growth independently of the institutional structure of property rights. Furthermore, if this structure is inappropriate piecemeal reform might not be in the interest of society, and a substantial reform might be necessary if it is to be welfare-improving.     

Voting on meritocracy

This paper considers a setting where a resource such as education budget is to be distributed among agents. The latter differ in their ability to make use of the resource, and the issue is that of determining the allocation rule whereby the individual shares of the resource (may) depend on their relative efforts of obtaining it. The paper's focus is on endogenous determination, through voting, of the degree of meritocracy in the resource allocation system, which determines the marginal productivity of one's effort. It is found that a meritocratic system is expected to be supported by highly productive individuals and opposed by those with low productivity. When the decision making becomes less elitist and involves broader participation of population groups the support for meritocracy decreases.     

Contract renegotiation in a continuous state space

Summary. When players are unable to write complete state contingent contracts it is shown, within the context of a non-cooperative contracting-renegotiation game, that the only subgame perfect equilibrium allocations are those that correspond to the set of first-best allocations. Players are able to implement this set of allocations by signing an initial contract that is subsequently renegotiated in all states of the world. The contracting-renegotiation problem is complicated in an interesting way by assuming that the state space is continuous. The issue of the existence of an initial contract, that is subsequently renegotiated to the set of first-best allocations, must be resolved. Unlike Aghion, Dewatripont and Rey [1994], the results here do not require nor depend upon the comonotonicity of the objective functions. Received: January 27, 1995; revised version July 1, 1996     

On the convergence of reinforcement learning

This paper examines the convergence of payoffs and strategies in Erev and Roth's model of reinforcement learning. When all players use this rule it eliminates iteratively dominated strategies and in two-person constant-sum games average payoffs converge to the value of the game. Strategies converge in constant-sum games with unique equilibria if they are pure or if they are mixed and the game is 2×2. The long-run behaviour of the learning rule is governed by equations related to Maynard Smith's version of the replicator dynamic. Properties of the learning rule against general opponents are also studied.