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<p>This paper extends Scarf’s (J Econ Theory 3:169–187, 1971) <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation>-core result to HK-<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\delta\)</EquationSource> </InlineEquation> and PZ-<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\delta\)</EquationSource> </InlineEquation>-cores in an <i>n</i>-player dynamic Cournot game. It shows that HK-<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\delta\)</EquationSource> </InlineEquation> and PZ-<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\delta\)</EquationSource> </InlineEquation>-cores are identical to <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\gamma\)</EquationSource> </InlineEquation>-core and both non-empty in the 2-player case (<InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(n=2\)</EquationSource> </InlineEquation>); the two cores are both proper subsets of <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\gamma\)</EquationSource> </InlineEquation>-core and PZ-<InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(\delta\)</EquationSource> </InlineEquation>-core is non-empty while HK-<InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(\delta\)</EquationSource> </InlineEquation>-core may be empty in the multi-player case (<InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(n\ge 3\)</EquationSource> </InlineEquation>).</p>

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Two interesting \(\delta\)-cores in a dynamic Cournot game

  • 期刊论文

  • 发表日期：

    2025年10月27日

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  • Lei Wang,
  • Hongwei Gao

摘要

This paper extends Scarf’s (J Econ Theory 3:169–187, 1971) \(\alpha\) -core result to HK- \(\delta\) and PZ- \(\delta\) -cores in an n-player dynamic Cournot game. It shows that HK- \(\delta\) and PZ- \(\delta\) -cores are identical to \(\gamma\) -core and both non-empty in the 2-player case ( \(n=2\) ); the two cores are both proper subsets of \(\gamma\) -core and PZ- \(\delta\) -core is non-empty while HK- \(\delta\) -core may be empty in the multi-player case ( \(n\ge 3\) ).