Notes on the Economics of Game Theory - Part III

Written by Sam Vaknin


The limitations of this approach are immediately evident. It is definitely not geared to cope well with more complex, multi-player, semi-cooperative (semi-competitive), imperfect information situations.

Von Neumann proved that there is a solution for every ZSG with 2 players, though it might requirerepparttar implementation of mixed strategies (strategies with probabilities attached to every move and outcome). Together withrepparttar 132666 economist Morgenstern, he developed an approach to coalitions (cooperative efforts of one or more players a coalition of one player is possible). Every coalition has a value a minimal amount thatrepparttar 132667 coalition can secure using solely its own efforts and resources. The function describing this value is super-additive (the value of a coalition which is comprised of two sub-coalitions equals, at least,repparttar 132668 sum ofrepparttar 132669 values ofrepparttar 132670 two sub-coalitions). Coalitions can be epiphenomenal: their value can be higher thanrepparttar 132671 combined values of their constituents. The amounts paid torepparttar 132672 players equalrepparttar 132673 value ofrepparttar 132674 coalition and each player stands to get an amount no smaller than any amount that he would have made on his own. A set of payments torepparttar 132675 players, describingrepparttar 132676 division ofrepparttar 132677 coalition's value amongst them, isrepparttar 132678 "imputation", a single outcome of a strategy. A strategy is, therefore, dominant, if: (1) each player is getting more underrepparttar 132679 strategy than under any other strategy and (2)repparttar 132680 players inrepparttar 132681 coalition receive a total payment that does not exceedrepparttar 132682 value ofrepparttar 132683 coalition. Rational players are likely to preferrepparttar 132684 dominant strategy and to enforce it. Thus,repparttar 132685 solution to an n-players game is a set of imputations. No single imputation inrepparttar 132686 solution must be dominant (=better). They should all lead to equally desirable results. Onrepparttar 132687 other hand, allrepparttar 132688 imputations outsiderepparttar 132689 solution should be dominated. Some games are without solution (Lucas, 1967).

Auman and Maschler tried to establish what isrepparttar 132690 right payoff torepparttar 132691 members of a coalition. They went about it by enlarging uponrepparttar 132692 concept of bargaining (threats, bluffs, offers and counter-offers). Every imputation was examined, separately, whether it belongs inrepparttar 132693 solution (=yieldsrepparttar 132694 highest ranked outcome) or not, regardless ofrepparttar 132695 other imputations inrepparttar 132696 solution. But in their theory, every member hadrepparttar 132697 right to "object" torepparttar 132698 inclusion of other members inrepparttar 132699 coalition by suggesting a different, exclusionary, coalition in whichrepparttar 132700 members stand to gain a larger payoff. The player about to be excluded can "counter-argue" by demonstratingrepparttar 132701 existence of yet another coalition in whichrepparttar 132702 members will get at least as much as inrepparttar 132703 first coalition and inrepparttar 132704 coalition proposed by his adversary,repparttar 132705 "objector". Each coalition has, at least, one solution.

The Game in GT is an idealized concept. Some ofrepparttar 132706 assumptions can and should be argued against. The number of agents in any game is assumed to be finite and a finite number of steps is mostly incorporated intorepparttar 132707 assumptions. Omissions are not treated as acts (though negative ones). All agents are negligible in their relationship to others (have no discernible influence on them) yet are influenced by them (their strategies are not butrepparttar 132708 specific moves that they select are). The comparison of utilities is notrepparttar 132709 result of any ranking because no universal ranking is possible. Actually, no ranking common to two or n players is possible (rankings are bound to differ among players). Many ofrepparttar 132710 problems are linked torepparttar 132711 variant of rationality used in GT. It is comprised of a clarity of preferences on behalf ofrepparttar 132712 rational agent and relies onrepparttar 132713 people's tendency to converge and cluster aroundrepparttar 132714 right answer / move. This, however, is only a tendency. Some ofrepparttar 132715 time, players selectrepparttar 132716 wrong moves. It would have been much wiser to assume that there are no pure strategies, that all of them are mixed. Game Theory would have done well to borrow mathematical techniques from quantum mechanics. For instance: strategies could have been described as wave functions with probability distributions. The same treatment could be accorded torepparttar 132717 cardinal utility function. Obviously,repparttar 132718 highest ranking (smallest ordinal) preference should have hadrepparttar 132719 biggest probability attached to it or could be treated asrepparttar 132720 collapse event. But these are more or less known, even trivial, objections. Some of them cannot be overcome. We must idealizerepparttar 132721 world in order to be able to relate to it scientifically at all. The idealization process entailsrepparttar 132722 incorporation of gross inaccuracies intorepparttar 132723 model andrepparttar 132724 ignorance of other elements. The surprise is thatrepparttar 132725 approximation yields results, which tally closely with reality in view of its mutilation, affected byrepparttar 132726 model.

There are more serious problems, philosophical in nature.

It is generally agreed that "changing"repparttar 132727 game can and very often does moverepparttar 132728 players from a non-cooperative mode (leading to Paretto-dominated results, which are never desirable) to a cooperative one. A government can force its citizens to cooperate and to obeyrepparttar 132729 law. It can enforce this cooperation. This is often called a Hobbesian dilemma. It arises even in a population made up entirely of altruists. Different utility functions andrepparttar 132730 process of bargaining are likely to drive these good souls to threaten to become egoists unless other altruists adopt their utility function (their preferences, their bundles). Nash proved that there is an allocation of possible utility functions to these agents so thatrepparttar 132731 equilibrium strategy for each one of them will be this kind of threat. This is a clear social Hobbesian dilemma:repparttar 132732 equilibrium is absolute egoism despiterepparttar 132733 fact that allrepparttar 132734 players are altruists. This implies that we can learn very little aboutrepparttar 132735 outcomes of competitive situations from acquainting ourselves withrepparttar 132736 psychological facts pertaining torepparttar 132737 players. The agents, in this example, are not selfish or irrational and, still, they deteriorate in their behaviour, to utter egotism. A complete set of utility functions including details regarding how much they know about one another's utility functions definesrepparttar 132738 available equilibrium strategies. The altruists in our example are prisoners ofrepparttar 132739 logic ofrepparttar 132740 game. Only an "outside" power can release them from their predicament and permit them to materialize their true nature. Gauthier said that morally-constrained agents are more likely to evade Paretto-dominated outcomes in competitive games than agents who are constrained only rationally. But this is unconvincing withoutrepparttar 132741 existence of an Hobesian enforcement mechanism (a state isrepparttar 132742 most common one). Players would do better to avoid Paretto dominated outcomes by imposingrepparttar 132743 constraints of such a mechanism upon their available strategies. Paretto optimality is defined as efficiency, when there is no state of things (a different distribution of resources) in which at least one player is better off with allrepparttar 132744 other no worse off. "Better off" read: "with his preference satisfied". This definitely could lead to cooperation (to avoid a bad outcome) but it cannot be shown to lead torepparttar 132745 formation of morality, however basic. Criminals can achieve their goals in splendid cooperation and be content, but that does not make it more moral. Game theory is agent neutral, it is utilitarianism at its apex. It does not prescribe torepparttar 132746 agent what is "good" only what is "right". It isrepparttar 132747 ultimate proof that effort at reconciling utilitarianism with more deontological, agent relative, approaches are dubious, inrepparttar 132748 best of cases. Teleology, in other words, in no guarantee of morality.

The Dismal Mind - Economics as a Pretension to Science - Part I

Written by Sam Vaknin


"It is impossible to describe any human action if one does not refer torepparttar meaningrepparttar 132664 actor sees inrepparttar 132665 stimulus as well as inrepparttar 132666 end his response is aiming at." Ludwig von Mises

I. Introduction

Storytelling has been with us sincerepparttar 132667 days of campfire and besieging wild animals. It served a number of important functions: amelioration of fears, communication of vital information (regarding survival tactics andrepparttar 132668 characteristics of animals, for instance),repparttar 132669 satisfaction of a sense of order (predictability and justice),repparttar 132670 development ofrepparttar 132671 ability to hypothesize, predict and introduce theories and so on.

We are all endowed with a sense of wonder. The world around us in inexplicable, baffling in its diversity and myriad forms. We experience an urge to organize it, to "explainrepparttar 132672 wonder away", to order it so that we know what to expect next (predict). These arerepparttar 132673 essentials of survival. But while we have been successful at imposing our mind onrepparttar 132674 outside world we have been much less successful when we tried to explain and comprehend our internal universe and our behaviour.

Economics is not an exact science, nor can it ever be. This is because its "raw material" (humans and their behaviour as individuals and en masse) is not exact. It will never yield natural laws or universal constants (like physics). Rather, it is a branch ofrepparttar 132675 psychology of masses. It deals withrepparttar 132676 decisions humans make. Richard Thaler,repparttar 132677 prominent economist, argues that a model of human cognition should lie atrepparttar 132678 heart of every economic theory. In other words he regards economics to be an extension of psychology.

II. Philosophical Considerations - The Issue of Mind (Psychology)

The relationships betweenrepparttar 132679 structure and functioning of our (ephemeral) mind,repparttar 132680 structure and modes of operation of our (physical) bodies andrepparttar 132681 structure and conduct of social collectives have beenrepparttar 132682 matter of heated debate for millennia.

There are those who, for all practical purposes, identifyrepparttar 132683 mind with its product (mass behaviour). Some of them postulaterepparttar 132684 existence of a lattice of preconceived, born, categorical knowledge aboutrepparttar 132685 universe repparttar 132686 vessels into which we pour our experience and which mould it. Others have regardedrepparttar 132687 mind as a black box. While it is possible in principle to know its input and output, it is impossible, again in principle, to understand its internal functioning and management of information.

The other camp is more "scientific" and "positivist". It speculated thatrepparttar 132688 mind (whether a physical entity, an epiphenomenon, a non-physical principle of organization, orrepparttar 132689 result of introspection) has a structure and a limited set of functions. They argue that a "user's manual" can be composed, replete with engineering and maintenance instructions. The most prominent of these "psychodynamists" was, of course, Freud. Though his disciples (Jung, Adler, Horney,repparttar 132690 object-relations lot) diverged wildly from his initial theories they all shared his belief inrepparttar 132691 need to "scientify" and objectify psychology. Freud a medical doctor by profession (Neurologist) and Bleuler before him came with a theory regardingrepparttar 132692 structure ofrepparttar 132693 mind and its mechanics: (suppressed) energies and (reactive) forces. Flow charts were provided together with a method of analysis, a mathematical physics ofrepparttar 132694 mind.

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