Myopic-farsighted absorbing networks
(2023) Theory and Decision : an international journal for multidisciplinary advances in decision sciences — Vol. 94, p. 405-422 (2023)
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- We propose the notion of myopic-farsighted absorbing set to determine the networks that emerge in the long run when some players are myopic while others are farsighted. A set of networks is a myopic-farsighted absorbing set if (No External Deviation) there is no myopic-farsighted improving path from networks within the set to some networks outside the set, (External Stability) there is a myopic-farsighted improving path from any network outside the set to some network within the set, and (Minimality) there is no proper subset satisfying No External Deviation and External Stability. Contrary to the notion of myopic-farsighted stable set, we show that a myopic-farsighted absorbing set always exists. We partially characterize the myopic-farsighted absorbing sets and we provide sufficient conditions for the equivalence between a myopic-farsighted absorbing set and a myopic-farsighted stable set. We also introduce and fully characterize the notion of proper myopic-farsighted absorbing set that refines the concept of myopic-farsighted absorbing set by selecting the more absorbing networks. Finally, we consider a threshold game that illustrates the role of the relative number of farsighted and myopic players for reaching efficiency.
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de Callataÿ, P., Mauleon, A., & Vannetelbosch, V. (2023). Myopic-farsighted absorbing networks. Theory and Decision : an international journal for multidisciplinary advances in decision sciences, 94, 405-422. https://doi.org/10.1007/s11238-022-09895-8 (Original work published 2023)