Abstract
Game-theoretical models of of team building, team adaptation and team learning are considered for multi-agent organizational systems. It’s shown that models of team building and functioning described in terms of reflexive games reproduce the autonomy and coordination of team activity. Team adaptation is considered as the beliefs’ updating under the absence of common knowledge among the agents. In the framework of the joint learning model the optimal learning problem is stated and solved as the allocation of the volumes of works performed by agents in certain time intervals.
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Notes
- 1.
By assumption, the costs of an agent represent a decreasing function of its type.
- 2.
- 3.
Note that increasing the step size improves the rate of convergence; on the other hand, the procedure may become instable for sufficiently large step sizes.
- 4.
Traditionally, control theory studies models of adaptation mostly with the probabilistic uncertainties of an external environment. Applying the corresponding (and well-developed) mathematical tools to the problems of team adaptation seems to have good prospects.
- 5.
Possible extensions of the model are different cases of incomplete observations; e.g., an agent does not observe the action vectors of other agents, their payoffs, etc. (see the previous section).
- 6.
More complicated cases are also possible, where agents have nontrivial mutual awareness. Then the parametric Nash equilibrium (1.20) is replaced by the informational equilibrium in the game of agents.
- 7.
In the discrete model studied, the “static” mode corresponds to one-time choice of actions by agents, whereas the “dynamic” mode answers to a sequence of such choices.
- 8.
In the case of two agents, each of them can evaluate the action of another based on the known total action and its own action. For three and more agents, such information becomes insufficient for retrieving unambiguously the actions of the opponents.
но.
- 9.
Of course, generally adaptation of a system presumes not only changing the awareness and behavior of its elements (the first and the second levels of adaptation), but also changing system parameters (the third level of adaptation), e.g., the types of agents, in response to varying external conditions. Moreover, active adaptation can be considered when the system directly influences on an external environment (the fourth level of adaptation).
- 10.
Learning and adaptation are close phenomena. However, learning may take place in invariable external conditions, whereas adaptation happens only when these conditions vary.
- 11.
Throughout this section, the superscript denotes the number of a time period, whereas the subscript designates the number of an agent. In the single-agent model, the subscript is omitted.
- 12.
In more general case, one would desire to extremize some functional (e.g., learning expenses, learning quality, etc.) taking into account some additional constraints, varying several variables simultaneously, etc. All these problems form the prospective subject of future research.
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Novikov, D.A. (2016). Teams: Building, Adaptation and Learning. In: Różewski, P., Novikov, D., Bakhtadze, N., Zaikin, O. (eds) New Frontiers in Information and Production Systems Modelling and Analysis. Intelligent Systems Reference Library, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-319-23338-3_1
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