Brown–von Neumann–Nash dynamics: The continuous strategy case

Brown and von Neumann introduced a dynamical system that converges to saddle points of zero sum games with finitely many strategies. Nash used the mapping underlying these dynamics to prove existence of equilibria in general games. The resulting Brown–von Neumann–Nash dynamics are a benchmark example for myopic adjustment dynamics that, in contrast to replicator dynamics, allow for innovation, but require less rationality than the best response dynamics. This paper studies the BNN dynamics for games with infinitely many strategies. We establish Nash stationarity for continuous payoff functions. For negative semidefinite games (that include zero sum games), we generalize the results of Brown and von Neumann. In addition, we show that evolutionarily robust Nash equilibria are asymptotically stable. A complete stability analysis for doubly symmetric games is also obtained.     

Management of interacting species: regulation under nonlinearities and hysteresis

We consider the optimal regulation of an open access fishery when biomass dynamics are combined with fishing effort dynamics. The interaction of inelastic demand and backward bending nature of the ecological supply curve introduce nonlinearities that could lead to multiple bionomic equilibria and hysteresis effects. We obtain convergence results for general bionomic models and indicate cases where hysteretic regulation failure could be a problem when economic dynamics are slow enough relative to biological dynamics. We show that when biological dynamics are slow enough relative to the economic dynamics, the social optimum can be achieved by a time dependent landing fee.     

Stylised facts and other empirical evidence on firm dynamics,business cycle and growth

In this paper, we bring together, in a systematised fashion, the scattered empirical evidence relating firm dynamics with both short-run and long-run macroeconomic dynamics. There are numerous studies that focus on firm-level data while controlling for macroeconomic conditions. From these studies a fairly robust set of empirical regularities pertaining to entry, exit, growth and the size distribution of firms has emerged. However, the literature that focuses explicitly on the interplay between firm dynamics and the business cycle is roughly confined to the US experience and to the cyclical properties of firm entry and exit, while the studies about the relationship between firm dynamics and economic growth are limited and unsystematic. We also give a brief account of the most recent theoretical literature on firm dynamics and macroeconomic dynamics, and try to relate it to the empirical findings.     

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1 School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an, China 2 State IJR Center of Aerospace Design and Additive Manufacturing, Northwestern Polytechnical University, Xi’an, China 3 School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, China     

Grazing Games: Sharing Common Property Resources with Complex Dynamics

Grasslands used for domestic livestock are often the common property of several owners and are typically characterized by complex ecosystem dynamics. We account for both these aspects by modeling the problem as a differential game where each farmer maximizes profits, given the dynamics of livestock and grass interaction. We compare the first best outcome obtained when farmers cooperate with that for non-cooperative farmers. By accounting for grassland dynamics, we challenge conventional results from the common pool literature. Although we do identify situations where the standard result holds—a tragedy of the commons unless farmers cooperate—we also find examples where a tragedy is exacerbated due to ecosystem dynamics as well as cases where a non-cooperative regime under-exploits the grassland compared to the first best outcome.     

The econometric challenge to system dynamics and vice versa: Some future perspectives

In the last years, there have been some attempts to compare different approaches for dynamic modeling of socioeconomic systems and to suggest guidelines for choosing among them. This paper continues these efforts with special emphasis on system dynamics and econometrics, which are commonly regarded as the roughest competitors in this field of simulation. It will present a detailed catalogue of model features, relevant for an adequate characterization of system dynamics and econometrics, and will stress the importance to notice the interconnections that exist between different features. The paper then gives a systematic survey of the conceivable relations between system dynamics and econometrics, and closes with a short epistemological outlook.     

城市联盟动力系统研究

城市联盟打破行政区域划分的限制,消除城市市场壁垒;促进城市一体化建设,优化资源配置。研究了城市联盟的动力系统,揭示了城市联盟的根本动力是城市间利益趋同;驱动力是经济一体化进程的加快;连同产业动力、市场动力、技术动力、学习动力、资本动力、结构动力、资源动力、制度动力共同构成城市联盟的动力系统。通过对城市联盟的弓弦箭模型进行分析得出利益趋同性越好,越易达到共振,城市联盟获得的增值价值越大,城市联盟走得越远。     

Dynamics in tree formation games

Network formation games capture two conflicting objectives of selfish nodes in a network: such nodes wish to form a well-connected network and, at the same time, to minimize their cost of participation. We consider three families of such models where nodes avoid forming edges beyond those necessary for connectivity, thus forming tree networks. We focus on two local two-stage best-response dynamics in these models, where nodes can only form links with others in a restricted neighborhood. Despite this locality, both our dynamics converge to efficient outcomes in two of the considered families of models. In the third family of models, both our dynamics guarantee at most constant efficiency loss. This is in contrast with the standard best-response dynamics whose efficiency loss is unbounded in all three families of models. Thus we present a globally constrained network formation game where local dynamics naturally select desirable outcomes.     

Some dynamics of a strategic market game with a large number of agents

This paper is designed to combine the game-theoretic investigation of the static or equilibrium properties of large strategic market games together with the investigation of some very simple dynamics, which nevertheless are sufficient to show differences between two related games, one with only trade and one in which both borrowing from an outside bank and trade take place. The role of banking reserves emerges as relevant and sensitive to the transient state dynamics.Several 100,000 player games are simulated and the behavior is compared with the analytical prediction for the games with a continuum of agents.The dynamics considered here is so simple that it does not show adaptive learning. A natural extension calls for updating via a learning program such as a genetic algorithm.     

Basins of attraction and equilibrium selection under different learning rules

A deterministic learning model applied to a game with multiple equilibria produces distinct basins of attraction for those equilibria. In symmetric two-by-two games, basins of attraction are invariant to a wide range of learning rules including best response dynamics, replicator dynamics, and fictitious play. In this paper, we construct a class of three-by-three symmetric games for which the overlap in the basins of attraction under best response learning and replicator dynamics is arbitrarily small. We then derive necessary and sufficient conditions on payoffs for these two learning rules to create basins of attraction with vanishing overlap. The necessary condition requires that with probability one the initial best response is not an equilibrium to the game. The existence of parasitic or misleading actions allows subtle differences in the learning rules to accumulate.