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Nash-2 equilibrium: selective farsightedness under uncertain response

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  • Sandomirskaia, Marina

Abstract

This paper provides an extended analysis of an equilibrium concept for non-cooperative games with boundedly rational players: a Nash-2 equilibrium. Players think one step ahead and account all profitable responses of player-specific subsets of opponents because of both the cognitive limitations to predict everyone's reaction and the inability to make more deep and certain prediction even about a narrow sample of agents. They cautiously reject improvements that might lead to poorest profit after some possible reasonable response. For $n$-person games we introduce a notion of reflection network consisting of direct competitors to express the idea of selective farsightedness. For almost every 2-person game with a complete reflection network, we prove the existence of Nash-2 equilibrium. Nash-2 equilibrium sets in the models of price and quantity competition, and in Tullock's rent-seeking model with 2 players are obtained. It is shown that such a farsighted behavior may provide a strategic support for tacit collusion.

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  • Sandomirskaia, Marina, 2017. "Nash-2 equilibrium: selective farsightedness under uncertain response," MPRA Paper 83152, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:83152
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    Keywords

    Iterated thinking; Improving deviation; Direct competitor; Heterogeneous farsightedness; Tacit collusion;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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