# Microeconomic Absolute Rationality

This paper builds the necessary framework for analyzing some of the most frequent microeconomic problems from a game theoretical point of view.

Revisiting such “classics” as price policy, R&D management, introducing innovation in a standardized world or the repercussions of negative externalities offers a very good starting point for introducing some of the fundamental concepts of game theory, in order just to let the reader realize the full potential of this paradigm in defining absolute rationality behavior patterns for all classes of microeconomic problems.From a scientific point of view, a “game” is a metaphor for a wide range of human interactions where the outcome is the result of concurring if not opposite interests. The theory thereof, the “game theory”, is an interdisciplinary approach employing economics, mathematics and behavioral psychology to predict the outcome of situations where more human players have to choose from a finite set of strategies (decisions), provided that the outcome is influenced only by the full set of the decisions that are being taken.The main aim would therefore be to find criteria by which an individual may fundament her/his decisions, while also taking into account the choices that other players make.

Each outcome is denoted by an n-tuple of real numbers, representing the payoffs or penalties for each and every of the players in the case of that specific outcome. We should now formulate our first example of game theoretical analysis. For simplicity’s sake we shall start with what is probably the most trivial of all possible “games”, the almost “traditional” Prisoner’s Dilemma.Let Tom and Bob be two guys who just robbed a bank. The police caught them but, since they don’t have enough evidence to convict them for armed robbery, they interrogate Tom and Bob separately, hoping for one of them to confess. Both prisoners are told that: “If you confess and your buddy confesses too, then you both get 10 years in jail for armed robbery.

If you confess and he doesn’t you are free to go and he’s in for 20 years. If you deny and he confesses you get 20 years and he walks.If both of you deny then we’ll have to settle for 1 year in jail for both of you, for illegal possession of fire arms”. As already stated one goal of any game theoretical approach is to find perfect rationality criteria given some situation.

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For the prisoner’s dilemma any of the two prisoners should rationally think that “If the other prisoner confesses I am better off if I confess, too, because I will get 10 years instead of 20. If the other prisoner does not confess then, again, I am better off if I confess, since I will get no jail at all”.In this situation both players have a dominant strategy, that is a strategy that gets them better off regardless of the choices other players make. If each of the players in the game have a dominant strategy, then the set of their dominant strategies and their associated payoffs are said to constitute a dominant equilibrium for that game.

Choosing an existing dominant strategy is the first rationality criterion that we have so far discovered giving us the first simple game solution.The following part of this paper analyses some typical microeconomic problems and tries to suggest perfectly rational player behavior by finding at least one rationality criterion for each of the corresponding games. A special emphasis is being put on the day-to-day nature of the chosen examples in order that the validity and usefulness of the game theoretical model may be verified. As above, both supplier and consumer get positive payoffs if the demand and supply meet in the form of GSM or Zapp.The payoffs are obviously greater if the consumer and supplier adopt the advanced technology.

If GSM is demanded and Zapp is supplied or vice-versa the outcome obviously doesn’t yield any satisfaction so both players have a zero-payoff. The first noticeable difference between this game and the Prisoner’s Dilemma is that in this game none of the players has a dominant strategy and that, therefore, an alternative rationality criterion must be designed.Obviously we won’t be able to suggest a winning strategy for any player, since no player can protect herself/himself of the potential negative effects of the other player’s strategy. We will only focus our attention on the possible outcomes and discriminate between them on the basis of desirability and probability.

For instance the outcome (5,5) (Demand GSM, Supply GSM) and (20,20) (Demand Zapp, Supply Zapp) are called Nash-equilibriums and the rationality-driven market should theoretically tend towards one of these situations.A Nash equilibrium is a set of strategies such that any given player cannot get a better payoff by changing her/his strategy if all other players keep their strategic choices constant. Obviously this means that once our hypothetical market reaches a Nash equilibrium, it will be stable, since no individual strategic reconsideration may change anything. This is why, the market is supposed to stick to one of the Nash equilibria in the long run. One criterion to choose the most desirable of multiple Nash equilibria on the basis of perfect rationality is the Pareto optimality concept.

A Pareto optimum is an equilibrium for which no player can get better off without making other players worse off. Obviously, of the two Nash equilibria in this game, the (20,20) (Demand Zapp, Supply Zapp) is the Pareto optimum, which is perfectly compatible with any intuitive analysis. Although this game seems to remain “unsolved” just by identifying Nash equilibria and Pareto-optimums, these concepts will be very useful in section 2.

3. There, we shall define the concept of cooperation, which “solves” this game, too.

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