质量随机的研发竞赛模型与最优奖励

假设研发质量具有随机性,建立了研发竞赛的非合作博弈模型,分别探讨了完全信息和不完全信息条件下竞赛参与人与竞赛发起者的最优策略。研究发现：竞赛参与人的研发投入水平在完全信息和不完全信息条件下都随自身研发效率的降低而降低;研发参与人的类型信息不完全程度越高,参与人的均衡研发投入越低;在每一种信息类型组合下都存在着最优奖励使得竞赛发起者的期望收益最大。     

Tullock and Hirshleifer: a meeting of the minds

We introduce the serial contest by building on the desirable properties of two prominent contest games. This family of contest games relies both on relative efforts (as Tullock’s proposal) and on absolute effort differences (as difference-form contests). An additional desirable feature is that the serial contest is homogeneous of degree zero in contestants’ efforts. The family is characterized by a parameter representing how sensitive the outcome is to contestants’ efforts. It encompasses as polar cases the (fair) lottery and the (deterministic) all-pay auction. Equilibria have a close relationship to those of the (deterministic) all-pay auction and important properties of the latter hold for the serial contest, too.      

Markov Perfect equilibria in repeated asynchronous choice games

This paper examines the issue of multiplicity of Markov Perfect equilibria in alternating move repeated games. Such games are canonical models of environments with repeated, asynchronous choices due to inertia or replacement. Our main result is that the number of Markov Perfect equilibria is generically finite with respect to stage game payoffs. This holds despite the fact that the stochastic game representation of the alternating move repeated game is “non-generic” in the larger space of state dependent payoffs. We further obtain that the set of completely mixed Markov Perfect equilibria is generically empty with respect to stage game payoffs.     

Evolving densities in continuous strategy games through particle simulations

Many cases of strategic interaction between agents involve a continuous set of choices. It is natural to model these problems as continuous space games. Consequently, the population of agents playing the game will be represented with a density function defined over the continuous set of strategy choices. Simulating evolutionary dynamics on continuous strategy spaces is a challenging problem. The classic approach of discretizing the strategy space is ineffective for multidimensional strategy spaces. We present a principled approach to simulation of adaptive dynamics in continuous space games using sequential Monte Carlo methods. Sequential Monte Carlo methods use a set of weighted random samples, also named particles to represent density functions over multidimensional spaces. Sequential Monte Carlo methods provide computationally efficient ways of computing the evolution of probability density functions. We employ resampling and smoothing steps to prevent particle degeneration problem associated with particle estimates. The resulting algorithm can be interpreted as an agent based simulation with elements of natural selection, regression to mean and mutation. We illustrate the performance of the proposed simulation technique using two examples: continuous version of the repeated prisoner dilemma game and evolution of bidding functions in first-price closed-bid auctions.     

Stationary Markovian equilibrium in altruistic stochastic OLG models with limited commitment

We introduce a new class of infinite horizon altruistic stochastic OLG models with capital and labor, but without commitment between the generations. Under mild regularity conditions, for economies with either bounded or unbounded state spaces, continuous monotone Markov perfect Nash equilibrium (henceforth MPNE) are shown to exist, and form an antichain. Further, for each such MPNE, we can also construct a corresponding stationary Markovian equilibrium invariant distribution. We then show for many versions of our economies found in applied work in macroeconomics, unique MPNE exist relative to the space of bounded measurable functions. We also relate all of our results to those obtained by promised utility/continuation methods based upon the work of Abreu et al. (1990). As our results are constructive, we can provide characterizations of numerical methods for approximating MPNE, and we construct error bounds. Finally, we provide a series of examples to show the potential applications and limitations of our results.     

Changes in risk and strategic interaction

In this paper we study the comparative statics of Nth degree stochastic dominance shifts in a large class of non-cooperative games. We consider symmetric equilibria as well as asymmetric equilibria in which the risk changes are idiosyncratic and not necessarily of the same stochastic order. Furthermore, we establish conditions for risk changes to produce multiplier effects on equilibrium strategies. Finally, we evaluate the comparative statics of stochastic dominance shifts in supermodular games, which may feature multiple equilibria and non-convex strategy sets.     

Escape dynamics and equilibria selection by iterative cycle decomposition

This paper explores the medium-run behaviour of bounded rational players in repeatedly played games when they occasionally experiment or make mistakes. The formal analysis introduces a hierarchical structure of limit sets to characterize the most possible medium-run behaviour over gradually increased time intervals. The paper refines the notion of stochastic stability and offers a precise measure of the speed at which stochastically stable equilibria occur. Finally, the paper applies the results to a 3×3 symmetric game of Young (1993).     

Equivalence of optimal noisy-ranking contests and Tullock contests

We analyze a noisy-ranking contest in which participants compete in several dimensions. The organizer randomly samples a number of dimensions and awards a prize to the most productive agent. When the contest is optimally designed, we establish a structural equivalence between this family of noisy-ranking contests and contests built upon Tullock contest success functions. Our result also shows that in this class of noisy-contests, the profit-maximization problem of the planner can be turned into a stochastic choice problem for a planner who has some deterministic preferences over the contestants’ win probabilities.     

“Reverse” nested lottery contests

This paper proposes a multi-prize “reverse” nested lottery contest model, which can be viewed as the “mirror image” of the conventional nested lottery contest of  Clark and Riis (1996a). The reverse-lottery contest model determines winners by selecting losers based on contestants’ one-shot effort through a hypothetical sequence of lotteries. We provide a microfoundation for the reverse-lottery contest from a perspective of (simultaneous) noisy performance ranking and establish that the model is underpinned by a unique performance evaluation rule. We further demonstrate that the noisy-ranking model can be interpreted intuitively as a “worst-shot” contest, in which contestants’ performances are evaluated based on their most severe mistakes. The reverse-lottery contest model thus depicts a great variety of widely observed competitive activities of this nature. A handy closed-form solution for a symmetric equilibrium of the reverse-lottery contest is obtained. We show that the winner-take-all principle continues to hold in reverse-lottery contests. Moreover, we find that a reverse-lottery contest elicits more effort than a conventional lottery contest whenever the prizes available to contestants are relatively scarce.     

Deterministic multi-player Dynkin games

A multi-player Dynkin game is a sequential game in which at every stage one of the players is chosen, and that player can decide whether to continue the game or to stop it, in which case all players receive some terminal payoff.We study a variant of this model, where the order by which players are chosen is deterministic, and the probability that the game terminates once the chosen player decides to stop may be strictly less than 1.We prove that a subgame-perfect ε-equilibrium in Markovian strategies exists. If the game is not degenerate this ε-equilibrium is actually in pure strategies.     

Technical Inefficiency Effects Among Paddy Farmers in the Villages of the ‘Office du Niger’, Mali,West Africa

A stochastic frontier production function incorporating a model for technical inefficiency effects (Battese and Coelli, 1995) is applied to field data on paddy farmers from 29 villages in the Office du Niger in Mali. Four conventional factors (land, labor, fertilizer and machinery) are considered as inputs of production. The technical inefficiency effects in the stochastic frontier were related to firm-specific variables, institutional factors, social organisation, ecological considerations and health factors. Data were obtained from an economic survey conducted during two consecutive agricultural seasons (1989 and 1990) on 844 farms of the Office du Niger. The null hypothesis of the absence of technical inefficiency effects was rejected. A supportive institutional environment and a coherent organisation of land use were the best correlates of technically efficiency. The social environment was also found to contribute to technical efficiency of the paddy farmers: within the village, the greater the degree of ethnic cohesion, the greater the efficiency of the farmers. Health status of households had an effect in that healthy families tended to be more technically efficient than unhealthy ones. Farmers with more extensive sorghum cultivation were less efficient as paddy farmers. These results may help agricultural policy makers formulate strategies. Technical efficiency may be improved by intensifying agricultural training regarding one specific crop and, through the control of parasitic diseases which place a burden on family households.     

On measures of technical inefficiency and production uncertainty in stochastic frontier production model with correlated error components

Analysis of the behavior of technical inefficiency with respect to parameters and variables of a stochastic frontier model is a neglected area of research in frontier literature. An attempt in this direction, however, has recently been made. It has been shown that in a “standard” stochastic frontier model that both the firm level technical inefficiency and the production uncertainty are monotonically decreasing with observational error. In this paper we show, considering a stochastic frontier model whose error components are jointly distributed as truncated bivariate normal, that this property holds if and only if the distribution of observational error is negatively skewed. We also derive a necessary and sufficient condition under which both firm level technical inefficiency and production uncertainty are monotonically increasing with noise-inefficiency correlation. We next propose a new measure of the industry level production uncertainty and establish the necessary and sufficient condition for firm level technical inefficiency and production uncertainty to be monotonically increasing with industry level production uncertainty. We also study the limiting probabilistic behavior of these conditions under different parametric configuration of our model. Finally we carry out Monte Carlo simulations to study the sample behavior of the population monotonic property of the firm level technical inefficiency and production uncertainty in our model.