Abstract
A non-antagonistic positional (feedback) differential two-person game is considered in which each of the two players, in addition to the usual normal (nor) type of behavior oriented toward maximizing own functional, can use other types of behavior. In particular, it is altruistic (alt), aggressive (agg) and paradoxical (par) types. It is assumed that in the course of the game players can switch their behavior from one type to another. In this game, each player simultaneously with the choice of positional strategy selects the indicator function defined over the whole time interval of the game and taking values in the set {nor, alt, agg, par}. Player’s indicator function shows the dynamics for changing the type of behavior that this player adheres to. The concept of BT-solution for such game is introduced. The use by players of types of behaviors other than normal can lead to outcomes more preferable for them than in a game with only normal behavior. An example of a game with the dynamics of simple motion on a plane and phase constraints illustrates the procedure for constructing BT-solutions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Basar, T., Olsder, G.J.: Dynamic Noncooperative Game Theory, 2nd edn. SIAM, New York (1999)
Friedman, J.: A noncooperative equilibrium for supergames. Rev. Econ. Stud. 38, 1–12 (1971)
Haurie, A., Krawczyk, J.B., Zaccour, G.: Games and Dynamic Games. World Scientific-Now Publishers Series in Business, vol. 1. World Scientific, Singapore (2012)
Kleimenov, A.F.: Nonantagonistic Positional Differential Games. Nauka, Yekaterinburg (1993)
Kleimenov, A.F.: On solutions in a nonantagonistic positional differential game. J. Appl. Math. Mech. 61(5), 717–723 (1997). https://doi.org/10.1016/S0021-8928(97)00094-4
Kleimenov, A.F.: An approach to building dynamics for repeated bimatrix 2 × 2 games involving various behavior types. In: Leitman, G. (ed.) Dynamics and Control. Gordon and Breach, London (1999)
Kleimenov, A.F.: Altruistic behavior in a non-antagonistic positional differential game. Math. Theory Games Appl. 7(4), 40–55 (2015)
Kleimenov, A.F.: Application of altruistic and aggressive behavior types in a non-antagonistic positional differential two-person game. Proc. Inst. Math. Mech. Ural Branch RAS 23(4), 181–191 (2017)
Kleimenov, A.F., Kryazhimskii A.V.: Normal behavior, altruism and aggression in cooperative game dynamics. Interim Report IR-98-076. IIASA, Laxenburg (1998)
Krasovskii, N.N.: Control of a Dynamic System. Nauka, Moscow (1985)
Krasovskii, N.N., Subbotin, A.I.: Game-Theoretical Control Problems. Springer, New York (1988)
Petrosyan, L.A., Zenkevich, N.A., Shevkoplyas E.V.: Game Theory. BHV-Petersburg, St. Petersburg (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Kleimenov, A. (2018). Altruistic, Aggressive and Paradoxical Types of Behavior in a Differential Two-Person Game. In: Petrosyan, L., Mazalov, V., Zenkevich, N. (eds) Frontiers of Dynamic Games. Static & Dynamic Game Theory: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-92988-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-92988-0_3
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-92987-3
Online ISBN: 978-3-319-92988-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)