Sandomirskaia, Marina (2017): Nash2 equilibrium: selective farsightedness under uncertain response.

PDF
MPRA_paper_83152.pdf Download (2MB)  Preview 
Abstract
This paper provides an extended analysis of an equilibrium concept for noncooperative games with boundedly rational players: a Nash2 equilibrium. Players think one step ahead and account all profitable responses of playerspecific 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 2person game with a complete reflection network, we prove the existence of Nash2 equilibrium. Nash2 equilibrium sets in the models of price and quantity competition, and in Tullock's rentseeking 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 

Original Title:  Nash2 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 DecisionMaking > 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 52:137 d'Aspremont C, Dos Santos Ferreira R, GerardVaret LA (2007) Competition for Market Share or for Market Size: Oligopolistic Equilibria with Varying Competitive Toughness. Int Econ Rev 48(3):761784 Aumann RJ, Maschler M (1964) The bargaining set for cooperative games. Advanced in game theory 52:443476 Baye M, Kovenock D, De Vries C (1994) The solution to the Tullock rentseeking game when $R>2$: Mixedstrategy equilibria and mean dissipation rates. Public Choice 81:363380 Binmore K (1988) Modeling rational players: Part II. Economics and Philosophy 4(1):955 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):337356 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):934945 Cabral L (1995) Conjectural variations as a reduced form. Econ Lett 49(4):397402 Camerer CF, Ho TH, Chong JK (2004) A cognitive hierarchy model of games. Q J Econ 119(3):861898 Crawford V, CostaGomes M, Iriberri N (2013) Structural Models of Nonequilibrium Strategic Thinking: Theory, Evidence, and Applications. J Econ Lit 51(1):562 Dockner E (1992) A dynamic theory of conjectural variations. J Ind Econ 40(4):377395 Fang L, Hipel K, Kilgour D (1989) Conflict models in graph form: Solution concepts and their interrelationships. EJOR 41:86100 Fraser N, Hipel K (1984) Conflict Analysis: Models and Resolutions. NorthHolland, 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. NorthHolland, New York Gabszewicz JJ, Thisse JF (1986) Spatial competition and the location of firms. In: Location Theory (Fundamentals of Pure and Applied Economics) 5:171 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 117:115118 Iskakov M, Iskakov A (2014) Equilibium contained by counterthreats and complex equilibrium in secure strategies. Large scale systems control 51: 130157 (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 RentSeeking 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. levelk analysis: An experimental study of cheaptalk games with private information. GEB 66(1):238255 Kilgour DM, Fang L, Hipel KW (1990) A decision support system for the graph model of conflicts. Theory Decis 28(3):289311 Maskin E, Tirole J (1988) A theory of dynamic oligopoly, I: Overview and quantity competition with large fixed costs. Econometrica 56(3):549569 Tullock G (1980) Efficient rent seeking. In: JM Buchanan, RD Tollison, G Tullock (Eds.) Toward a theory of the rentseeking society. Texas A and M University Press, College Station 97112 Rezaei G, Kirley M, Pfau J (2009) Evolving cooperation in the nplayer prisoner's dilemma: A social network model. Artificial Life: Borrowing from Biology. Springer Berlin Heidelberg 4352 Sandomirskaia M (2016) A model of tacit collusion: Nash2 equilibrium concept. Recent Advances in Game Theory and Applications, in Static \& Dynamic Game Theory: Foundations \& Applications. Springer International Publishing Switzerland 243260 Stahl D (1993) Evolution of smart$ _n$ players. GEB 5:604617 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/83152 