Nash-2 equilibrium: selective farsightedness under uncertain response

Sandomirskaia, Marina (2017): Nash-2 equilibrium: selective farsightedness under uncertain response.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Iterated thinking; Improving deviation; Direct competitor; Heterogeneous farsightedness; Tacit collusion
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; D - Microeconomics > D0 - General > D03 - Behavioral Microeconomics: Underlying Principles; D - Microeconomics > D4 - Market Structure, Pricing, and Design > D43 - Oligopoly and Other Forms of Market Imperfection; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D70 - General; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets

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