Analytical methods in economics by Akira Takayama PDF

By Akira Takayama

ISBN-10: 0472081357

ISBN-13: 9780472081356

ISBN-10: 0745010369

ISBN-13: 9780745010366

An obtainable advent to the analytical origin of economics

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In} C N (g) such that {ili2, i2 i3," " in-lin} C g. The graph g' egis a component of g, if for all i E N (g') and j E N (g'), i 'f j, there exists a path in g' connecting i and j, and for any i E N (g') and j E N(g), ij E 9 implies ij E g'. I The graphs analyzed here are nondirected. That is, it is not possible for one individual to link to another, without having the second individual also linked to the first. ) Furthermore, links are either present or not, as opposed to having connections with variable intensities (a valued graph).

Since {12, 13} cannot be defeated by {12}, it must be that YI ({12 , 13} , v) ;:::: 1/2. It follows from component balance that I/ 2+f;:::: Y2 ({I2, 13},v)+Y3 ({I2, 13} , v). Since {I2, 13} cannot be defeated by {I2, 13, 23}, it must be that 18 One can try to account for the incentives of pairs by considering an extensive form game which sequentially considers the addition of each link and uses a solution such as subgame perfection (as in Aumann and Myerson [I]). See Dutta, van den Nouweland, and Tijs [3] for a discussion of this approach and an alternative approach based on coalition-proof Nash equilibrium.

The concept of Nash equilibrium does not admit such considerations. Incorporating deviations by pairs (or larger groups) of agents might most naturally involve a refinement of Nash equilibrium which explicitly allows for such deviations, such as strong equilibrium, coalition-proof Nash equilibrium,18 or some other notion which allows only for certain coalitions to form. This constitutes a large project which we do not pursue here. Appendix Theorem 1'. If N ;:::: 3, then there is no Y which is component balanced and such that for each v no strongly efficient graph is defeated (allowing for side payments) by an inefficient one.

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Analytical methods in economics by Akira Takayama

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