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Summary
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Optimizing resource allocation with peer effects is computationally difficult. However, efficient solutions exist when individuals are grouped, achieving near-optimal social welfare.

Keywords:
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Area of Science:

  • Computational Social Science
  • Algorithmic Game Theory
  • Operations Research

Background:

  • Resource allocation problems are common in various domains, including education, urban planning, and social platforms.
  • Peer effects, where individuals' preferences are influenced by their neighbors, complicate traditional allocation models.
  • Optimizing social welfare in these scenarios is challenging due to complex interdependencies.

Purpose of the Study:

  • To develop a mathematical framework for position allocation problems with peer effects.
  • To analyze the computational complexity of welfare maximization under peer effects.
  • To propose efficient allocation strategies for scenarios with a fixed number of demographic groups.

Main Methods:

  • Formulated a unified mathematical framework for the position allocation problem with peer effects.
  • Investigated the computational intractability of welfare maximization for general peer effects.
  • Developed efficient algorithms for specific cases with demographic groups and network constraints.

Main Results:

  • Welfare maximization with peer effects is computationally intractable even with simplified preferences.
  • Efficiently computable allocations are possible when individuals are classified into a fixed number of groups.
  • The proposed methods achieve optimal or near-optimal social welfare for natural preference structures.

Conclusions:

  • Position allocation with peer effects presents significant computational challenges.
  • Grouping individuals based on demographics offers a practical approach to achieving efficient and near-optimal resource allocation.
  • The developed framework provides a foundation for designing allocation strategies in complex social systems.