## Notes on the Economics of Game Theory - Part I

Written by Sam Vaknin

Continued from page 1

We can use Game Theory methods to analyse both these situations. Wherever we have economic players bargaining for allocation of scarce resources in order to attain their utility functions, to secure outcomes and consequences (the value, preference, that player attaches to his outcomes) which are right for them – we can use Game Theory (GT).

A short recap of basic tenets of theory might be in order.

GT deals with interactions between agents, whether conscious and intelligent – or Dennettic. A Dennettic Agent (DA) is an agent that acts so as to influence future allocation of resources, but does not need to be either conscious or deliberative to do so. A Game is set of acts committed by 1 to n rational DA and one a-rational (not irrational but devoid of rationality) DA (nature, a random mechanism). At least 1 DA in a Game must control result of set of acts and DAs must be (at least potentially) at conflict, whole or partial. This is not to say that all DAs aspire to same things. They have different priorities and preferences. They rank likely outcomes of their acts differently. They engage Strategies to obtain their highest ranked outcome. A Strategy is a vector, which details acts, with which DA will react in response to all (possible) acts by other DAs. An agent is said to be rational if his Strategy does guarantee attainment of his most preferred goal. Nature is involved by assigning probabilities to outcomes. An outcome, therefore, is an allocation of resources resulting from acts of agents. An agent is said to control situation if its acts matter to others to extent that at least one of them is forced to alter at least one vector (Strategy). The Consequence to agent is value of a function that assigns real numbers to each of outcomes. The consequence represents a list of outcomes, prioritized, ranked. It is also known as an ordinal utility function. If function includes relative numerical importance measures (not only real numbers) – we call it a Cardinal Utility Function.

(continued)

Sam Vaknin is the author of Malignant Self Love - Narcissism Revisited and After the Rain - How the West Lost the East. He is a columnist for Central Europe Review, United Press International (UPI) and eBookWeb and the editor of mental health and Central East Europe categories in The Open Directory, Suite101 and searcheurope.com.

Visit Sam's Web site at http://samvak.tripod.com

## Notes on the Economics of Game Theory - Part II

Written by Sam Vaknin

Continued from page 1

A Stable Strategy is similar to a Nash solution – though not identical mathematically. There is currently no comprehensive theory of Information Dynamics. Game Theory is limited to aspects of competition and exchange of information (cooperation). Strategies that lead to better results (independently of other agents) are dominant and where all agents have dominant strategies – a solution is established. Thus, Nash equilibrium is applicable to games that are repeated and wherein each agent reacts to acts of other agents. The agent is influenced by others – but does not influence them (he is negligible). The agent continues to adapt in this way – until no longer able to improve his position. The Nash solution is less available in cases of cooperation and is not unique as a solution. In most cases, players will adopt a minimax strategy (in zero-sum games) or maximin strategies (in nonzero-sum games). These strategies guarantee that loser will not lose more than value of game and that winner will gain at least this value. The solution is "Saddle Point".

The distinction between zero-sum games (ZSG) and nonzero-sum games (NZSG) is not trivial. A player playing a ZSG cannot gain if prohibited to use certain strategies. This is not case in NZSGs. In ZSG, player does not benefit from exposing his strategy to his rival and is never harmed by having foreknowledge of his rival's strategy. Not so in NZSGs: at times, a player stands to gain by revealing his plans to "enemy". A player can actually be harmed by NOT declaring his strategy or by gaining acquaintance with enemy's stratagems. The very ability to communicate, level of communication and order of communication – are important in cooperative cases. A Nash solution:

Is not dependent upon any utility function;

It is impossible for two players to improve Nash solution (=their position) simultaneously (=the Paretto optimality);

Is not influenced by introduction of irrelevant (not very gainful) alternatives;

and

Is symmetric (reversing roles of players does not affect solution).

(continued)

Sam Vaknin is the author of Malignant Self Love - Narcissism Revisited and After the Rain - How the West Lost the East. He is a columnist for Central Europe Review, United Press International (UPI) and eBookWeb and the editor of mental health and Central East Europe categories in The Open Directory, Suite101 and searcheurope.com.

Visit Sam's Web site at http://samvak.tripod.com

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