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2-Nash and Leontief Economy

2-Nash and Leontief Economy. Jugal Garg. 2-Nash. Recall the LCP formulation (A, B): payoff matrices Every non-zero solution of above LCP is in one-to-one correspondence with Nash equilibrium of (A,B). Leontief Economy. m agents, n goods Agent i has endowment

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2-Nash and Leontief Economy

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  1. 2-Nash and Leontief Economy JugalGarg

  2. 2-Nash • Recall the LCP formulation • (A, B): payoff matrices Every non-zero solution of above LCP is in one-to-one correspondence with Nash equilibrium of (A,B)

  3. Leontief Economy • m agents, n goods • Agent i has endowment • Equilibrium prices and allocation?

  4. Pairing Leontief Economy • n agents and n goods • W = I ( • utility of agent i • price of good j

  5. Pairing Leontief Utility • Market clearing: • Consider the following LCP: • How to get prices?

  6. Leontief and Symmetric 2-Nash • Consider a positive U • LCP solves the Leontief economy • Proof on board • Leontief  symmetric Nash equilibrium

  7. 2-Nash and Leontief • Consider • All entries in (A,B) are positive. • 2-Nash  two-group pairing Leontief economy • Proof on board

  8. Conclusion • 2-Nash is no harder than Leontief economy • NP-hard: • more than one equilibrium • Equilibrium with positive price of a given set of goods

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