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Player Aggregation in Noncooperative Games.

A J Goldman1, D R Shier1

  • 1National Bureau of Standards, Washington, D.C. 20234.

Journal of Research of the National Bureau of Standards (1977)
|September 27, 2021
PubMed
Summary
This summary is machine-generated.

Players in noncooperative games can be combined into aggregate players without altering equilibrium solutions. This holds true when individual player payoffs are independent of their aggregate group

Keywords:
Aggregationequilibriumgame theorymathematical economicsnoncooperative games

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Area of Science:

  • Game theory
  • Mathematical economics

Background:

  • Noncooperative game theory analyzes strategic interactions among independent agents.
  • Equilibrium concepts, such as Nash equilibrium, are central to predicting outcomes in these games.
  • The complexity of large games often necessitates simplification through aggregation.

Purpose of the Study:

  • To identify conditions under which players in a noncooperative game can be aggregated.
  • To ensure that such aggregation does not alter the set of equilibrium-point solutions.
  • To explore approximate aggregation methods for broader applicability.

Main Methods:

  • Formal definition of an "aggregate player" concept.
  • Derivation of the specific condition for preserving equilibrium solutions during aggregation.
  • Development and proof of "approximate" aggregation theorems.

Main Results:

  • A precise condition is established for the valid aggregation of player subsets.
  • The core condition requires individual player payoffs to be independent of strategies within their aggregate group.
  • Approximate aggregation results are demonstrated, extending the primary finding.

Conclusions:

  • The study provides a rigorous framework for simplifying complex noncooperative games through player aggregation.
  • The independence of payoffs within an aggregate group is the key determinant for maintaining solution sets.
  • The findings offer practical implications for computational game theory and economic modeling.