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

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## 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 |
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Original Title: | Nash-2 equilibrium: selective farsightedness under uncertain response |

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 |

Item ID: | 83152 |

Depositing User: | Dr. Marina Sandomirskaia |

Date Deposited: | 10 Dec 2017 09:06 |

Last Modified: | 03 Oct 2019 02:00 |

References: | Alaoui L, Penta A (2015) Endogenous depth of reasoning. Rev Econ Stud 52:1--37 d'Aspremont C, Dos Santos Ferreira R, Gerard-Varet L-A (2007) Competition for Market Share or for Market Size: Oligopolistic Equilibria with Varying Competitive Toughness. Int Econ Rev 48(3):761--784 Aumann RJ, Maschler M (1964) The bargaining set for cooperative games. Advanced in game theory 52:443--476 Baye M, Kovenock D, De Vries C (1994) The solution to the Tullock rent-seeking game when $R>2$: Mixed-strategy equilibria and mean dissipation rates. Public Choice 81:363--380 Binmore K (1988) Modeling rational players: Part II. Economics and Philosophy 4(1):9--55 Bowley A (1924) The mathematical groundwork of economics: an introductory treatise. Oxford University Press Boyd R, Richerson P (1988) The evolution of reciprocity in sizable groups. J Theor Biol 132(3):337--356 Brams S, Kilgour M (1988) Game Theory and National Security. Basil Blackwell, New York Bresnaham T (1981) Duopoly models with consistent conjectures. Am Econ Rev 71(5):934--945 Cabral L (1995) Conjectural variations as a reduced form. Econ Lett 49(4):397--402 Camerer CF, Ho TH, Chong JK (2004) A cognitive hierarchy model of games. Q J Econ 119(3):861--898 Crawford V, Costa-Gomes M, Iriberri N (2013) Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications. J Econ Lit 51(1):5--62 Dockner E (1992) A dynamic theory of conjectural variations. J Ind Econ 40(4):377--395 Fang L, Hipel K, Kilgour D (1989) Conflict models in graph form: Solution concepts and their interrelationships. EJOR 41:86--100 Fraser N, Hipel K (1984) Conflict Analysis: Models and Resolutions. North-Holland, New York Frey S, Goldstone R (2015) Flocking in the depths of strategic iterated reasoning. arXiv preprint arXiv:1506.05410 Friedman J (1977) Oligopoly and the Theory of Games. North-Holland, New York Gabszewicz JJ, Thisse J-F (1986) Spatial competition and the location of firms. In: Location Theory (Fundamentals of Pure and Applied Economics) 5:1--71 Iskakov M, Iskakov A (2012) Equilibrium in secure strategies. CORE Discussion Paper 2012/61 Iskakov M, Iskakov A (2012) Equilibrium in secure strategies -- intuitive formulation. Working paper WP7/2012/06. Math methods for decision making in economics, business and politics Iskakov M, Iskakov A (2012) Solution of the Hotelling's game in secure strategies. Econ Lett 117:115--118 Iskakov M, Iskakov A (2014) Equilibium contained by counter-threats and complex equilibrium in secure strategies. Large scale systems control 51: 130--157 (in Russian) Iskakov M, Iskakov A (2015) Asymmetric equilibria in secure strategies. Working paper WP7/2015/03. Math methods for decision making in economics, business and politics Iskakov M, Iskakov A, Zakharov A (2013) Tullock Rent-Seeking Contest and its Solution in Secure Strategies. Working paper WP7/2013/01. Math methods for decision making in economics, business and politics Kawagoe T, Takizawa H (2009) Equilibrium refinement vs. level-k analysis: An experimental study of cheap-talk games with private information. GEB 66(1):238--255 Kilgour DM, Fang L, Hipel KW (1990) A decision support system for the graph model of conflicts. Theory Decis 28(3):289--311 Maskin E, Tirole J (1988) A theory of dynamic oligopoly, I: Overview and quantity competition with large fixed costs. Econometrica 56(3):549--569 Tullock G (1980) Efficient rent seeking. In: JM Buchanan, RD Tollison, G Tullock (Eds.) Toward a theory of the rent-seeking society. Texas A and M University Press, College Station 97--112 Rezaei G, Kirley M, Pfau J (2009) Evolving cooperation in the n-player prisoner's dilemma: A social network model. Artificial Life: Borrowing from Biology. Springer Berlin Heidelberg 43--52 Sandomirskaia M (2016) A model of tacit collusion: Nash-2 equilibrium concept. Recent Advances in Game Theory and Applications, in Static \& Dynamic Game Theory: Foundations \& Applications. Springer International Publishing Switzerland 243--260 Stahl D (1993) Evolution of smart$ _n$ players. GEB 5:604--617 |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/83152 |