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We study a condition of favoring cooperation in a Prisoner's Dilemma game on complex networks. There are two kinds of players: cooperators and defectors. Cooperators pay a benefit b to their neighbors at a cost c, whereas defectors only receive the benefit b. The game is a death-birth process with weak selection. Although it has been widely thought that b/c > k is a condition of favoring cooperation [1], we find that b/c > k nn is the condition. We also show that among three representative networks, namely, regular, random, and scale-free, a regular network favors cooperation the most, whereas a scale-free network favors cooperation the least. In an ideal scale-free network where network size is infinite, cooperation is never realized. Whether or not the scale-free network and network heterogeneity favor cooperation depends on the details of a game, although it is occasionally believed that scale-free networks favor cooperation irrespective of game structures. If the number of players are small, then the cooperation is favored in scale-free networks.

This paper proposes a logit response game with a spatial social structure and solves it exactly. We derive closed-form solutions for the strategy choice probabilities, the spatial correlation function of strategies of distant players, and the expected utility. We study how the probability of adopting a cooperative strategy in a prisoner's dilemma game and the probability of adopting Pareto efficient strategies in a cooperation game are affected by changes in the parameter that expresses payoff-responsiveness.

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Analysis from 800,000 Firms Terms of use: Documents in EconStor may Tomohiko Konno Graduate School of Economics, University of Tokyo Research Fellow of the Japan Society for the Promotion of Science AbstractWe analyze fundamental characteristics of the inter-firm transaction network through the data of 800,000 Japanese firms. We find that there exists a hierarchical structure and a negative degree correlation in this transaction network. We also find that this undirected network is a scale-free network. We bring to light these characteristics of the network and discuss why there is an important need to conduct research work on the actual network structure. Special issue Reconstructing Macroeconomics JEL: L16

We found an easy and quick post-learning method named "Icing on the Cake" to enhance a classification performance in deep learning. The method is that we train only the final classifier again after an ordinary training is done. Classifier Extract Feature maps Re-trained Classifier ClassifierRe-train only the classifier Put backFigure 1: The sketch of the proposed method.("Icing on the Cake"). Left: Train a deep neural network as usual. Center: Extract features of input data as estimation from the layer before the final classifier, and then train the final classifier again by the extracted features. Right: Put the re-trained classifier back to the network.

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We show that coordination always occurs in scale-free networks by social local interactions regardless of the values of parameters, while it occurs in regular networks if and only if the number of links times a payoff parameter exceeds the threshold. Scale-free networks are ubiquitous in the reality. We study a two-strategy pure coordination game on networks that indicate who plays with whom. A player chooses a strategy by Logit choice and the strategies are dynamically updated. Stable steady states are investigated.

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