Models of repeated games have used the concept of strategic equilibrium to help analyze global economic and political problems. My research focuses on the stability of behavioral strategies in this context. The main goal of the work is the analysis of iterated social dilemmas that will help reveal features of stability of interactions, allowing individuals to cope with behavioral uncertainty, understand the interests of other individuals, and to adapt to changing social environments.
In analysis of the Nash equilibrium in the class of behavior strategies, the mathematical expectations of the players’ current benefits (averaged over all game rounds) will play the key role. To define those expectations, we construct corresponding probability spaces and show that the game trajectories form an irreducible and aperiodic finite-order Markov chain with finite state spaces. The corresponding stationary distribution is then used to define the mathematical expectations of the players’ average benefits. To prove that a perturbed behavior strategy is an equilibrium we analyze the derivative of the expected average benefit with respect to a parameter responsible for perturbation. In more complex cases, the existence of Nash equilibria needs to be proved in a multi-step behavioral “meta-game” using the Kakutani fixed-point theorem. In this context, we expect the players’ sets of admissible behavior strategies to sometimes require further transformations—convexification or compactification. Such transformations may require extensions of the behavioral strategies originally divided into classes of countably additive or finitely additive probability measures. To carry out and evaluate numerical experiments we use statistical analysis.
Recently research reveals the effects of structural stability of Nash equilibria with respect to uncertainty in complexity of behavioral strategies of opponents. This uncertainty is restricted to some range of underlying beliefs reflecting the ability of opponents to perform (observe) some specific actions or states in infinitely repeated bimatrix games. Moreover, general characterization of Nash equilibrium pairs was obtained in the class of reactive stochastic strategies. The proposed approach will allow the results to be generalized further. The outcome provides tools for policymakers that allow them to make the correct choice of Nash equilibria with respect to possible change and uncertainty in the structure of behavioral strategies of players.
Artem Baklanov is a Russian citizen, and a IIASA-funded Postdoctoral Scholar (Aug 2014 – Aug 2016).
Last edited: 02 March 2016
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