2-Nash and Leontief Economy

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# 2-Nash and Leontief Economy - PowerPoint PPT Presentation

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

JugalGarg

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
• Equilibrium prices and allocation?
Pairing Leontief Economy
• n agents and n goods
• W = I (
• utility of agent i
• price of good j
Pairing Leontief Utility
• Market clearing:
• Consider the following LCP:
• How to get prices?
Leontief and Symmetric 2-Nash
• Consider a positive U
• LCP solves the Leontief economy
• Proof on board
• Leontief  symmetric Nash equilibrium
2-Nash and Leontief
• Consider
• All entries in (A,B) are positive.
• 2-Nash  two-group pairing Leontief economy
• Proof on board
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