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When cooperation is beneficial to all agents

Alessandro Doldi, Marco Frittelli, Marco Maggis

Abstract

Within a general semimartingale framework, we study the relationship between collective market efficiency and individual rationality. We derive a necessary and sufficient condition for the existence of (possibly zero-sum) exchanges among agents that strictly increase their indirect utilities and characterize this condition in terms of the compatibility between agents' preferences and collective pricing measures. The framework applies to both continuous- and discrete-time models and clarifies when cooperation leads to a strict improvement in each participating agent's indirect utility.

When cooperation is beneficial to all agents

Abstract

Within a general semimartingale framework, we study the relationship between collective market efficiency and individual rationality. We derive a necessary and sufficient condition for the existence of (possibly zero-sum) exchanges among agents that strictly increase their indirect utilities and characterize this condition in terms of the compatibility between agents' preferences and collective pricing measures. The framework applies to both continuous- and discrete-time models and clarifies when cooperation leads to a strict improvement in each participating agent's indirect utility.

Paper Structure

This paper contains 17 sections, 24 theorems, 162 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Structure of the paper
  3. Assumptions and statement of the main result
  4. Proof of the main result
  5. Proof of Theorem \ref{['corben']}
  6. The utility maximization with random endowment of a single agent
  7. Benefits from Collective Free Lunches or Arbitrages
  8. The discrete time framework
  9. An informative proof of existence of beneficial exchanges if a CA exists
  10. The continuous time framework
  11. An informative proof of existence of beneficial exchanges if a $\mathbf{CFL}(\mathcal{Y})$ exists
  12. Example: discrete time
  13. Example: continuous time
  14. Appendix: miscellaneous results
  15. Mackey topology and utility maximization
  16. ...and 2 more sections

Key Result

Theorem 1.3

Suppose that Assumption assOK holds and that ${\mathbb R}^N_0 \subseteq \mathcal{Y}$. Then there exists a unique optimizer $Q_{X^i}^i$ of the dual representation of $U^i(X^i,0)$ in dual11, and the following are equivalent $\blacktriangleleft$$\blacktriangleleft$

Figures (1)

  • Figure 1: Tree for the stocks $(X^1,X^2)$ at times $t=0,1,2$.

Theorems & Definitions (61)

  • Definition 1.1
  • Remark 1.2
  • Theorem 1.3
  • Remark 1.4
  • Corollary 1.5
  • Remark 1.7
  • Remark 1.8
  • Lemma 2.2
  • proof
  • Remark 2.3
  • ...and 51 more