Advances in Mathematical Economics Volume 13 (eBook)

Table of Contents 6
Some various convergence results for multivalued martingales 7
1 Introduction 7
2 Preliminaries and background 8
3 Convergence results for cwk(E)-valued martingales and mils 10
4 Convergences and conditional expectationin Pettis integration 19
5 Convergence of cwk(E)-valued Pettis-integrable martingales 32
References 37
A note on Aumann's core equivalence theorem without monotonicity 40
1 Introduction 40
2 The model 42
3 The core and quasi-equilibrium allocations 43
4 Irreducible economies 44
5 Conclusion 50
References 51
On two classical turnpike results for the Robinson–Solow–Srinivasan model 52
1 Introduction 53
2 The model and antecedent results 60
3 The principal results 68
4 The heuristics of the proofs 74
5 Concluding observations 77
6 Six auxiliary propositions 78
7 Four substantive lemmata 83
8 Proofs: proof of Theorem A 94
9 Proofs: proof of Theorem B 97
References 100
A certain limit of iterated conditional tail expectation 103
1 Introduction 103
2 Associated nonlinear PDE 106
3 Proof of main results 109
References 114
Set-valued optimization in welfare economics 116
1 Introduction 117
2 Tools of variational analysis and generalized differentiation 120
3 Solution notions and necessary optimality conditions in constrained multiobjective optimization 124
4 Local versions of the second welfare theorem 133
5 Global versions of the second welfare theorem 148
References 154
Convexity of the lower partition range of a concave vector measure 157
1 Introduction 157
2 Convex combinations of measurable sets 158
3 Convex structure of concave measures 160
4 An application to the fair division problem 161
References 162
Good locally maximal programs for the Robinson–Solow–Srinivasan model 163
1 Introduction 163
2 Main results 168
3 Proof of Theorem 2.1 169
4 Proof of Theorem 2.2 174
5 Proof of Theorem 2.3 177
References 178
Pythagorean mathematical idealism and the framing of economic and political theory 179
1 Introduction 179
2 Pythagoras and his secret societies 180
3 Early use of mathematics for rational administration 181
4 Plato's dedication to rational ideal forms 183
5 The Chaldean tradition of efficient administration 184
6 Bureaucratic individualism and dispute resolution 186
7 Plato's assimilation of Pythagorean thought 187
8 Solving the problem of irrational numbers: the dyad of the greater and the smaller 188
9 Prometheus and fair division 192
10 The process of arriving at settlements: the dyad 194
11 Aristotle's analysis of exchange and the harmonic proportion 195
12 In summary 199
References 200
Subject Index 
202 
Instructions for Authors 
207