Revealing perceived individuals' self-interest

In non-cooperative game-theory models, the Nash equilibrium concept is used to assess the outcome of rational decision-makers' strategic involvement. This method allows researchers to look into certain outcomes while keeping in mind people's self-interest restrictions. Participants, on the other hand, are not bound to provide accurate information when acting in their own self-interest. In this work, we investigate noncooperative behavior in a repeating game and suggest a new method in game theory for designing an observer. An average repeated non-cooperative Markov game with imperfect information is used to determine the categories of participants in this situation. A sequential technique, in which information is revealed a finite number of times, can approximate all of Nash's equilibria. By computing the derivative of the player's equilibrium with regard to his or her present type, we explain how to instrument the observer's design. The dynamic observer creates the imperfect information game. We study a Markov model extension that incorporates a new variable that reflects the product of the observer design and the distribution vector to solve the problem. The strategies and the observation kernel make up the observer design. In this approach, the approaches are first seen as mappings from private and reported states to lotteries over alternatives. We build equations to retrieve the variables of interest using the available type: observer, strategies, observation kernels, and distribution vectors. We provide a numerical example of an industrial organization in which enterprises compete on the market and decide on the amount of production they will produce simultaneously and independently of one another.