Synchronization of endogenous business cycles

Comovement of economic activity across sectors and countries is a defining feature of business cycles. However, standard models that attribute comovement to propagation of exogenous shocks struggle to generate a level of comovement that is as high as in the data. In this paper, we consider models that produce business cycles endogenously, through some form of non-linear dynamics---limit cycles or chaos. These models generate stronger comovement, because they combine shock propagation with synchronization of endogenous dynamics. In particular, we study a demand-driven model in which business cycles emerge from strategic complementarities across sectors in different countries, synchronizing their oscillations through input-output linkages. We first use a combination of analytical methods and extensive numerical simulations to establish a number of theoretical results. We show that the importance that sectors or countries have in setting the common frequency of oscillations depends on their eigenvector centrality in the input-output network, and we develop an eigendecomposition that explores the interplay between non-linear dynamics, shock propagation and network structure. We then calibrate our model to data on 27 sectors and 17 countries, showing that synchronization indeed produces stronger comovement, giving more flexibility to match the data

Best reply structure and equilibrium convergence in generic games

Game theory is widely used as a behavioral model for strategic interactions in biology and social science. It is common practice to assume that players quickly converge to an equilibrium, e.g. a Nash equilibrium. This can be studied in terms of best reply dynamics, in which each player myopically uses the best response to her opponent's last move. Existing research shows that convergence can be problematic when there are best reply cycles. Here we calculate how typical this is by studying the space of all possible two-player normal form games and counting the frequency of best reply cycles. The two key parameters are the number of moves, which defines how complicated the game is, and the anti-correlation of the payoffs, which determines how competitive it is. We find that as games get more complicated and more competitive, best reply cycles become dominant. The existence of best reply cycles predicts non-convergence of six different learning algorithms that have support from human experiments. Our results imply that for complicated and competitive games equilibrium is typically an unrealistic assumption. Alternatively, if for some reason "real" games are special and do not possess cycles, we raise the interesting question of why this should be so.Comment: Main paper + Supplemental Informatio

Sensitivity analysis of agent-based models: a new protocol

Agent-based models (ABMs) are increasingly used in the management sciences. Though useful, ABMs are often critiqued: it is hard to discern why they produce the results they do and whether other assumptions would yield similar results. To help researchers address such critiques, we propose a systematic approach to conducting sensitivity analyses of ABMs. Our approach deals with a feature that can complicate sensitivity analyses: most ABMs include important non-parametric elements, while most sensitivity analysis methods are designed for parametric elements only. The approach moves from charting out the elements of an ABM through identifying the goal of the sensitivity analysis to specifying a method for the analysis. We focus on four common goals of sensitivity analysis: determining whether results are robust, which elements have the greatest impact on outcomes, how elements interact to shape outcomes, and which direction outcomes move when elements change. For the first three goals, we suggest a combination of randomized finite change indices calculation through a factorial design. For direction of change, we propose a modification of individual conditional expectation (ICE) plots to account for the stochastic nature of the ABM response. We illustrate our approach using the Garbage Can Model, a classic ABM that examines how organizations make decisions

deep learning based segmentation of breast masses in dedicated breast ct imaging radiomic feature stability between radiologists and artificial intelligence

Abstract A deep learning (DL) network for 2D-based breast mass segmentation in unenhanced dedicated breast CT images was developed and validated, and its robustness in radiomic feature stability and diagnostic performance compared to manual annotations of multiple radiologists was investigated. 93 mass-like lesions were extensively augmented and used to train the network (n = 58 masses), which was then tested (n = 35 masses) against manual ground truth of a qualified breast radiologist with experience in breast CT imaging using the Conformity coefficient (with a value equal to 1 indicating a perfect performance). Stability and diagnostic power of 672 radiomic descriptors were investigated between the computerized segmentation, and 4 radiologists' annotations for the 35 test set cases. Feature stability and diagnostic performance in the discrimination between benign and malignant cases were quantified using intraclass correlation (ICC) and multivariate analysis of variance (MANOVA), performed for each segmentation case (4 radiologists and DL algorithm). DL-based segmentation resulted in a Conformity of 0.85 ± 0.06 against the annotated ground truth. For the stability analysis, although modest agreement was found among the four annotations performed by radiologists (Conformity 0.78 ± 0.03), over 90% of all radiomic features were found to be stable (ICC>0.75) across multiple segmentations. All MANOVA analyses were statistically significant (p ≤ 0.05), with all dimensions equal to 1, and Wilks' lambda ≤0.35. In conclusion, DL-based mass segmentation in dedicated breast CT images can achieve high segmentation performance, and demonstrated to provide stable radiomic descriptors with comparable discriminative power in the classification of benign and malignant tumors to expert radiologist annotation

Sensitivity analysis of agent-based models: a new protocol

Agent-based models (ABMs) are increasingly used in the management sciences. Though useful, ABMs are often critiqued: it is hard to discern why they produce the results they do and whether other assumptions would yield similar results. To help researchers address such critiques, we propose a systematic approach to conducting sensitivity analyses of ABMs. Our approach deals with a feature that can complicate sensitivity analyses: most ABMs include important non-parametric elements, while most sensitivity analysis methods are designed for parametric elements only. The approach moves from charting out the elements of an ABM through identifying the goal of the sensitivity analysis to specifying a method for the analysis. We focus on four common goals of sensitivity analysis: determining whether results are robust, which elements have the greatest impact on outcomes, how elements interact to shape outcomes, and which direction outcomes move when elements change. For the first three goals, we suggest a combination of randomized finite change indices calculation through a factorial design. For direction of change, we propose a modification of individual conditional expectation (ICE) plots to account for the stochastic nature of the ABM response. We illustrate our approach using the Garbage Can Model, a classic ABM that examines how organizations make decisions

Best-Response Dynamics, Playing Sequences, and Convergence to Equilibrium in Random Games

We analyze the performance of the best-response dynamic across all normal-form games using a random games approach. The playing sequence -- the order in which players update their actions -- is essentially irrelevant in determining whether the dynamic converges to a Nash equilibrium in certain classes of games (e.g. in potential games) but, when evaluated across all possible games, convergence to equilibrium depends on the playing sequence in an extreme way. Our main asymptotic result shows that the best-response dynamic converges to a pure Nash equilibrium in a vanishingly small fraction of all (large) games when players take turns according to a fixed cyclic order. By contrast, when the playing sequence is random, the dynamic converges to a pure Nash equilibrium if one exists in almost all (large) games.Comment: JEL codes: C62, C72, C73, D83 Keywords: Best-response dynamics, equilibrium convergence, random games, learning models in game