Adverse Selection, Heterogeneous Beliefs, and Evolutionary Learning

We relax the common assumption of homogeneous beliefs in principal-agent relationships with adverse selection. Principals are competitors in the product market and write contracts also on the base of an expected aggregate. The model is a version of a cobweb model. In an evolutionary learning set-up, which is imitative, principals can have different beliefs about the distribution of agents’ types in the population. The resulting nonlinear dynamic system is studied. Convergence to a uniform belief depends on the relative size of the bias in beliefs.

Learning in a double-phase cobweb model

In this paper, we study a class of markets, among which we can mention agricultural and energy markets, characterized by seasonality, i.e., in which demand and/or supply conditions cyclically alternate with a precise and known periodicity. We propose a new theoretical framework based on a cobweb model with adaptive expectations, accordingly modified to be consistent with market’s seasonality. The model, consisting in a second-order non-autonomous difference equation, is investigated with the aim of understanding how the periodical nature of the market together with the agents’ expectation formation mechanism affects the resulting dynamics. We analytically prove the emergence of dynamical scenarios that are missing in the classic cobweb model for non-seasonal markets, such as quasi-periodic dynamics and an ambiguous role on stability of the expectation weight. Finally, we discuss their economic rationale with the help of numerical simulations. In such a peculiar economic framework, agents’ learning plays a key role to explain the dynamical properties of economic observables.

GFPMX: A Cobweb Model of the Global Forest Sector, with an Application to the Impact of the COVID-19 Pandemic

The GFPMX projects forest area and stock, consumption, production, imports, exports, and prices of industrial roundwood, fuelwood, sawnwood, wood-based panels, wood pulp, and paper and paperboard in 180 countries, and currently from 2018 to 2070. The core principle of the model is the cobweb theorem, according to which markets are not necessarily in equilibrium, but take some time to adjust to shocks—such as demand shifts—leading to oscillatory dynamics of prices and quantities. This paper presents the model’s structure and the estimation of its parameters from international statistics on production, trade, forest area, and forest stock. This is followed by an application of the GFPMX to the impact on the global forest sector of the economic recession caused by the COVID-19 pandemic.

Development Assessment of Higher Education System Based on TOPSIS-Entropy, Hopfield Neural Network, and Cobweb Model

This paper first extracted 11 indicators from four aspects of infrastructure, educational equity, teaching quality, and scientific research level and established a multidimensional higher education evaluation system. After that, according to TOPSIS and the entropy method, a comprehensive score of the development of higher education was obtained, and a comprehensive index of higher education was proposed. According to the level of the score, we divide the development status into 5 categories, and use discrete Hopfield neural network for verification. In addition, we applied the model to many countries and chose Vietnam to conduct an in-depth analysis of the model, including reforming policies and evaluating policy effects based on cobweb model. Finally, we found that the application of the model is very universal, but in reality the reform is very difficult.

Further Investigations on the Dynamics and Multistability Coexisted in a Memory-Based Cobweb Model

Based on a nonlinear demand function and a market-clearing price, a cobweb model is introduced in this paper. A gradient mechanism that depends on the marginal profit is adopted to form the 1D discrete dynamic cobweb map. Analytical studies show that the map possesses four fixed points and only one attains the profit maximization. The stability/instability conditions for this fixed point are calculated and numerically studied. The numerical studies provide some insights about the cobweb map and confirm that this fixed point can be destabilized due to period-doubling bifurcation. The second part of the paper discusses the memory factor on the stabilization of the map’s equilibrium point. A gradient mechanism that depends on the marginal profit in the past two time steps is adopted to incorporate memory in the model. Hence, a 2D discrete dynamic map is constructed. Through theoretical and numerical investigations, we show that the equilibrium point of the 2D map becomes unstable due to two types of bifurcations that are Neimark–Sacker and flip bifurcations. Furthermore, the influence of the speed of adjustment parameter on the map’s equilibrium is analyzed via numerical experiments.