Paper 2014/1029

On the Cryptographic Hardness of Finding a Nash Equilibrium

Nir Bitansky, Omer Paneth, and Alon Rosen


We prove that finding a Nash equilibrium of a game is hard, assuming the existence of indistinguishability obfuscation and injective one-way functions with sub-exponential hardness. We do so by showing how these cryptographic primitives give rise to a hard computational problem that lies in the complexity class PPAD, for which finding Nash equilibrium is known to be complete. Previous proposals for basing PPAD-hardness on program obfuscation considered a strong “virtual black-box” notion that is subject to severe limitations and is unlikely to be realizable for the programs in question. In contrast, for indistinguishability obfuscation no such limitations are known, and recently, several candidate constructions of indistinguishability obfuscation were suggested based on different hardness assumptions on multilinear maps. Our result provides further evidence of the intractability of finding a Nash equilibrium, one that is extrinsic to the evidence presented so far.

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Publication info
Published elsewhere. Minor revision. FOCS 2015
obfuscationnash equilibriumPPADcryptographic hardness
Contact author(s)
nirbitan @ csail mit edu
2015-08-14: revised
2015-01-02: received
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      author = {Nir Bitansky and Omer Paneth and Alon Rosen},
      title = {On the Cryptographic Hardness of Finding a Nash Equilibrium},
      howpublished = {Cryptology ePrint Archive, Paper 2014/1029},
      year = {2014},
      note = {\url{}},
      url = {}
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