Normal Behavior, Altruism and Aggression in Cooperative Game Dynamics

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Normal Behavior, Altruism and Aggression in Cooperative Game Dynamics

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A.F. Kleimenov
A.V. Kryazhimskii

Abstract

The paper introduces a local cooperation pattern for repeated bimatrix games: the players choose a mutually acceptable strategy pair in the next round. A mutually acceptable strategy pair provides each player with a payoff no smaller than that expected, in average, at a historical distribution of players' actions recorded up to the latest round. It may happen that at some points mutually acceptable strategy pairs do not exist. A game round at such "still" points indicates that at least one player revises his/her payoffs and switches from normal behavior to abnormal. We consider payoff switches associated with altruistic and aggressive behaviors, and define measures of all combinations of normal, altruistic and aggressive behaviors on every game trajectory. These behavior measures serve as criteria for the global analysis of game trajectories. Given a class of trajectories, one can identify the measures of desirable and undesirable behaviors on each trajectory and select optimal trajectories, which carry the minimum measure of undesirable behaviors. In the paper, the behavior analysis of particular classes of trajectories in the repeated Prisoner's Dilemma is carried out.

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Paper provided by International Institute for Applied Systems Analysis in its series Working Papers with number ir98076.

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Date of creation: Sep 1998
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Handle: RePEc:wop:iasawp:ir98076

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Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July. [Downloadable!] (restricted)
Other versions:
- Fudenberg, D. & Kreps, D.M., 1992. "Learning Mixed Equilibria," Working papers 92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
Kaniovski Yuri M. & Young H. Peyton, 1995. "Learning Dynamics in Games with Stochastic Perturbations," Games and Economic Behavior, Elsevier, vol. 11(2), pages 330-363, November. [Downloadable!] (restricted)
Y.M. Kaniovski & A.V. Kryazhimskii & H.P. Young, 1997. "Learning Equilibria in Games Played by Heterogeneous Populations," Working Papers ir97017, International Institute for Applied Systems Analysis. [Downloadable!]
Smale, Steve, 1980. "The Prisoner's Dilemma and Dynamical Systems Associated to Non-Cooperative Games," Econometrica, Econometric Society, vol. 48(7), pages 1617-34, November. [Downloadable!] (restricted)
Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November. [Downloadable!] (restricted)

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