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 forrepparttar allocation of scarce resources in order to attain their utility functions, to securerepparttar 132675 outcomes and consequences (the value,repparttar 132676 preference, thatrepparttar 132677 player attaches to his outcomes) which are right for them we can use Game Theory (GT).

A short recap ofrepparttar 132678 basic tenets ofrepparttar 132679 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 influencerepparttar 132680 future allocation of resources, but does not need to be either conscious or deliberative to do so. A Game isrepparttar 132681 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 controlrepparttar 132682 result ofrepparttar 132683 set of acts andrepparttar 132684 DAs must be (at least potentially) at conflict, whole or partial. This is not to say that allrepparttar 132685 DAs aspire torepparttar 132686 same things. They have different priorities and preferences. They rankrepparttar 132687 likely outcomes of their acts differently. They engage Strategies to obtain their highest ranked outcome. A Strategy is a vector, which detailsrepparttar 132688 acts, with whichrepparttar 132689 DA will react in response to allrepparttar 132690 (possible) acts byrepparttar 132691 other DAs. An agent is said to be rational if his Strategy does guaranteerepparttar 132692 attainment of his most preferred goal. Nature is involved by assigning probabilities torepparttar 132693 outcomes. An outcome, therefore, is an allocation of resources resulting fromrepparttar 132694 acts ofrepparttar 132695 agents. An agent is said to controlrepparttar 132696 situation if its acts matter to others torepparttar 132697 extent that at least one of them is forced to alter at least one vector (Strategy). The Consequence torepparttar 132698 agent isrepparttar 132699 value of a function that assigns real numbers to each ofrepparttar 132700 outcomes. The consequence represents a list of outcomes, prioritized, ranked. It is also known as an ordinal utility function. Ifrepparttar 132701 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 torepparttar aspects of competition and exchange of information (cooperation). Strategies that lead to better results (independently of other agents) are dominant and where allrepparttar 132673 agents have dominant strategies a solution is established. Thus,repparttar 132674 Nash equilibrium is applicable to games that are repeated and wherein each agent reacts torepparttar 132675 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,repparttar 132676 players will adopt a minimax strategy (in zero-sum games) or maximin strategies (in nonzero-sum games). These strategies guarantee thatrepparttar 132677 loser will not lose more thanrepparttar 132678 value ofrepparttar 132679 game and thatrepparttar 132680 winner will gain at least this value. The solution isrepparttar 132681 "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 notrepparttar 132682 case in NZSGs. In ZSG,repparttar 132683 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 torepparttar 132684 "enemy". A player can actually be harmed by NOT declaring his strategy or by gaining acquaintance withrepparttar 132685 enemy's stratagems. The very ability to communicate,repparttar 132686 level of communication andrepparttar 132687 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 improverepparttar 132688 Nash solution (=their position) simultaneously (=the Paretto optimality);

Is not influenced byrepparttar 132689 introduction of irrelevant (not very gainful) alternatives;

and

Is symmetric (reversingrepparttar 132690 roles ofrepparttar 132691 players does not affectrepparttar 132692 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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