A Class of Games with Unique Solutions

Abstract

In a game with payoff M(x,y) = 0(xy) + rho(x) + tau(y) played over the unit square (such that rho, tau are continuous and 0 is analytic and with sufficiently many non-vanishing coefficients in its power series expansion about zero) if either player has a non-step function 1 optimal strategy, the opposing player has a unique optimal strategy. Examples are included which illustrate the fact that games with well-behaved payoffs can have unique solutions which are more or less pathological.

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Document Details

Document Type
Technical Report
Publication Date
Feb 12, 1951
Accession Number
ADA801499

Entities

People

  • I. Glicksberg
  • O. Gross

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Analytic Functions
  • Coefficients
  • Corporations
  • Identities
  • Information Operations
  • Instructions
  • Intervals
  • Mathematical Analysis
  • Mathematics
  • Power Series
  • Spectra
  • Step Functions

Fields of Study

  • Economics

Readers

  • Analytical Mechanics
  • Game Theory.
  • Systems Analysis and Design