the invisible hand of the “win-win-win papakonstantinidis equilibrium” 2015: Volunteer: the invisible hand of the “win-win-win papakonstantinidis equilibrium” papakonstantinidis

“when the impossible comes true "Building a new HELLAS a Europe of solidarity and a better world; through beneficence, Volunteering and Solidarity" “when the impossible comes true lp888 papakonstantinidis

win-win-win papakonstantinidis model 2015.. Volunteer: the invisible hand of the “win-win-win papakonstantinidis equilibrium” Prof. papakonstantinidis papakonstantinidis

Incompleteness-Recursion - Impossibility The “win-win-win papakonstantinidis Theory ” Bargaining - Agency -Set- Efficiency Justice-Egalitarian-Socialchoice- Utilitarianism- Sharing Incompleteness-Recursion - Impossibility A proposal on Welfare Economics Papakonstantinidis Professor of political economy ATEI Peloponnesus GR papakonstantinidis

CESD BAKU AJERBAIJAN 2012 CESD SEMINAR ON LOCAL DEVELOPMENT CESD Seminar on Local Development Professor Leonidas  A. Papakonstantinidis,  from School of Management and Economics, Technological Educational Institute of Kalamata, GREECE had his presentation on Local Economic Development: Analysis, Practices and Globalization in the CESD office with participation of representatives from international organizations, embassies, government agencies, universities, think tank,  NGOs and private companies on September [...] papakonstantinidis

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win-win-win l p888 papakonstantinidis

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This study is realized by two (2) main approaches: The one is the theoretical view of the relation between "volunteering" and "the social welfare" and the other is in practical-experimental level: Applying the "win-win-win" in four (4) small Aegean GREEK islands (SKOPELOS (GLOSSA) DONOUSSA,SYMI,KARPATHOS in the form of local people's sensitization For these, the “Central Limit Theorem” (CLT) has been adopted papakonstantinidis

OBJECTIVE papakonstantinidis

MAIN OBJECTIVE To prove that “social welfare” which is based on volunteers exists. The vehicle for this purpose is the process of "sensitization“ To create a highly versatile tool, “win-win-win papakonstantinidis model” able to adapt or be adapted to many different functions or activities, by well-formed formulas (wffs), thus contributing in changing the 2-pole (black –white) perception, in a three pole [0,01,1] welfare cognition, to document the necessity and usefulness of the "win-win-win" based on incompatibilities of five classical theorems and 4 theories, as each of them exclude others To find a base-role for the third win (=the Community) in any bargain between 2 To apply the “win-win-win papakonstantinidis model” based on “volunteering” in relation with the local development approach Papakonstantinidis, 2015 papakonstantinidis

dealing with the incompatibilities of 5 basic theorems and 4 theories that concern the concept of "welfare economics" These theorems/theories are: papakonstantinidis

the theorem of incompleteness (Kurt Gödel (1931) The impossibility theorem (1951 Kenneth Arrow: book: Social Choice and Individual Values, as well as the Amartya Sen “liberal paradox” the theorem of incompleteness (Kurt Gödel (1931) the Rawls Theorem on Justice, 1958)- the veil of ignorance the Nash Equilibrium in Nash “Non cooperative Game Theory 1951(annals of Mathematics,1951 Vol. 54, No. 2 (Sep., 1951), pp. 286-295) The “Pareto optimality in a 3D space according to Caratheodory conjecture (umbilical points in a sphere), then the main issue in this research concerns the possibility that a win-win-win communication should exist in real terms, The agency theory (Stiglitz Joseph 2001) An agency, in general terms, is the relationship between two parties, where one is a principal and the other is an agent who represents the principal in transactions with a third party as each of them to win : ]win-win-win equilibrium the ZBC set theory (a selection of objectives) the cognition by linguistic recursion (EVARETT mind recursion (one-many): Human mind is able to make recursions) papakonstantinidis

win-win-win situation: the “marriage” of volunteering with the individual interest papakonstantinidis

Papakonstantinidis conjectures: “at any bargain, [concerned as a set, including discrete entities] each one from the 2 bargainers (A-B) represents him/her self and(at the same time) the rest of the community So, "what is good for the Community (the third “win”) incorporated in each one from the bargainers’ expectations (in the frame of the “agency theory” or “the principal-agent -problem” AND 3. “a win-win-win situation may be possible if and only if the human mind, as expressed in terms of interaction, is built to accept this situation (the universal cooperation) The answer to this question gives us the linguistic recursion” papakonstantinidis

DEFINITIONS papakonstantinidis

The “core” of the “win-win-win papakonstantinidis model” (2002) Definition: “volunteer” a person who voluntarily offers himself or herself for a service or undertaking 2.a person who performs a service willingly and without pay 3.Military. a person who enters the service voluntarily rather than through conscription or draft, especially for special or temporary service rather than as a member of the regular or permanent army. Law. a person whose actions are not founded on any legal obligation so to act. a person who intrudes into a matter that doesn’t concern him or her, as a person who pays the debt of another where he or  she is neither legally nor morally bound to do so and has no interest to protect in making the payment. The “core” of the “win-win-win papakonstantinidis model” (2002) win-win-win situation: the “marriage” of volunteering with the individual interest papakonstantinidis

What is the role of voluntary in the markets? Markets, Voluntary Exchange, and the Moral Foundation of Markets Market transactions are based on the voluntary buying and selling of goods and services. The basic demonstration of the Pareto optimality of voluntary trade is quite straightforward. With voluntary exchange, each party will not engage in trade unless they regard it as improving their welfare or at least making them no worse off, i.e., causing themselves no harm. Also, because the exchange is voluntary, one party cannot force another to take a bargain that they do not wish. Thus, one cannot cause the other harm. papakonstantinidis

The “WELFARE” DEFINITION – the philosophy side pure theoretical “moral” approach of the "social welfare" Adam Smith  1723 – 11790 Karl Marx, 1818- 1883 Rousseau Jean-Jacque 1712-1778:  Du contrat social ou Principes du droit politique; (Of the Social Contract, or Principles of Political Right) -1762 4. Gödel Kurt 1906 –1978 The Incompleteness Theorem) “1931 5. Russell Bertrand 1872-1970   6. Bernoulli, Daniel,1700-1782 7. Rawls John 1921-2002 Socrates 470/469 – 399 BC, Plato 428/427 or 424/423 – 348/347 BC), Aristotle 384 – 322 BC) Epicurus 341-270 BC Hobbes Thomas1588 –1679 Hume David 1711-1776 Kant Immanuel1724 –1804 Bentham Jeremy 1748-1832 Mill, John Stuart 1806 –1873. Pareto 1848 –1923 papakonstantinidis

KNOWLEDGE CREATION tacit Sympathetic Socialization codified Conceptual Type of Knowledge-1 Type of Knowledge-2 Synthesis Resulted Behavior tacit Sympathetic Socialization codified Conceptual Externalization Procedural Internalization Systemic Networking sympathetic systemic Sensitization Strategic KNOWLEDGE CREATION papakonstantinidis

Five steps towards Local development Arnstein 1967 partnership Involvement Participation sensitization Information papakonstantinidis

FORMS of SENSITIZATION or, “How the International Market is combined with volunteering The International Market Entry Evaluation Process papakonstantinidis

Country Identification, Preliminary Screening, In-Depth Screening, The International Marketing Entry Evaluation Process is a five stage process, and its purpose is to gauge which international market or markets offer the best opportunities for our products or services to succeed. The five steps are : Country Identification,  Preliminary Screening,  In-Depth Screening, Final Selection and  Direct Experience. VOLUNTEERING is classified in the last stage (DIRECT EXPERIENCE) of the international Entry Evaluation Process papakonstantinidis

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The Three-Process View The Three-Process View is a psychological term coined by Janet E. Davidson and Robert Sternberg. According to this concept, there are three kinds of insight: selective-encoding, selective-comparison, and selective-combination. Selective-Encoding Insight - Distinguishing what is important in a problem and what is irrelevant. (i.e. filter) Selective-Comparison Insight - Identifying information by finding a connection between acquired knowledge and experience. Selective-Combination Insight - Identifying a problem through understanding the different components and putting everything together. papakonstantinidis

THE WIN-WIN-WIN PAPAKONSTANTINIDIS EQUILIBRIUM UTILITY FUNCTION: THE WIN-WIN-WIN PAPAKONSTANTINIDIS EQUILIBRIUM papakonstantinidis

Source: Spais, Papakonstantinidis and Papakonstantinidis (2009) UTILITY FUNCTION IN A BARGAIN WIN-WIN Nash equilibrium WIN-WIN-WIN Papakonstantinidis model WIN-LOSE JOHN VON NEUMANN Source: Spais, Papakonstantinidis and Papakonstantinidis (2009) papakonstantinidis

PARETO EFFICIENCY PARETO OPTIMALITY Pareto Efficiency (or unanimity) or Pareto optimality is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off. The concept has applications in academic fields such as economics, engineering and the life sciences   “Given an initial allocation of goods   among a set of individuals, a change to a different allocation that makes at least one individual better off without making any other individual worse off is called a Pareto improvement. An allocation is defined as "Pareto efficient" or "Pareto optimal" when no further Pareto improvements can be made” papakonstantinidis

Pareto optimality: whenever all individuals of a society strictly prefer an outcome x over an outcome y, the choice function doesn't pick y. Formally, a social choice function F is Pareto optimal if whenever p∊Rel(X)N is a configuration of preference relations and there are two outcomes x and y such that x⪲iy for every individual i∊N, then y∉ F(p). Minimal liberalism: More than one individual in the society is decisive on a pair of social outcomes. papakonstantinidis

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Pareto Chart papakonstantinidis

The Arrow (Kenneth) Impossibility Theorem papakonstantinidis

The four conditions set by Arrow are: 1. Freedom of individual preferences (unrestricted domain). Individuals are free to have each any provision of alternative statements. 2. Weak Principle of Pareto. When all the people prefer a alternative state by another, and then collectively this situation should be preferred over the other. 3. Independence of irrelevant Alternative Statements. (Independence of irrelevant alternatives). If two different individual preferences profiles assessments of people on two alternative situations, the XI and chj, do not change, then the social assessment Xi as to chj should not be changed. 4. Non Dictatorship. There should be a person whose preferences to any individual preferences profiles always made the collective preference. (If there is such a person then always what one wants, and therefore is a dictator). papakonstantinidis

VOTING papakonstantinidis

Gödel's incompleteness theorems (2) From the other hand……… Gödel's incompleteness theorems (2) Any effectively generated theory capable of expressing elementary arithmetic cannot be both  consistent  and complete . In particular, for any consistent, effectively generated formal  theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory. For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent. papakonstantinidis

2nd incompleteness theorem This strengthens the first incompleteness theorem, because the statement constructed in the first incompleteness theorem does not directly express the consistency of the theory. The proof of the second incompleteness theorem is obtained by formalizing the proof of the first incompleteness theorem within the theory itself. If T proves P, then T proves ProvA(#(P)). T proves 1.; that is, T proves that if T proves P, then T proves ProvA(#(P)). In other words, T proves that ProvA(#(P)) implies ProvA(#(ProvA(#(P)))). T proves that if T proves that (P → Q) and T proves P then T proves Q. In other words, T proves that ProvA(#(P →Q)) and ProvA(#(P)) imply ProvA(#(Q)). papakonstantinidis

The Principle-Agent Theory papakonstantinidis

AGENCY THEORY [ PRINCIPAL-AGENT THEORY] papakonstantinidis

EGALITARIANISM: Defining the Concept ‘Equality’ is a contested concept: “People who praise it or disparage it disagree about what they are praising or disparaging” Our first task is therefore to provide a clear definition of equality in the face of widespread misconceptions about its meaning as a political idea. ‘Equality’ (or ‘equal’) signifies correspondence between a group of different objects, persons, processes or circumstances that have the same qualities in at least one respect, but not all respects, i.e., regarding one specific feature, with differences in other features. ‘Equality’ needs to thus be distinguished from ‘identity’ — this concept signifying that one and the same object corresponds to itself in all its features: an object that can be referred to through various individual terms, proper names, or descriptions. For the same reason, it needs to be distinguished from ‘similarity’ — the concept of merely approximate correspondence papakonstantinidis

BARGAIN papakonstantinidis

GAME Definitions Strategy: one of the courses of action a player can choose in a game; strategies are mixed or pure, depending on whether they are selected in a randomized fashion or not It describes the complete course of action in a game Rational Choice: a choice that leads to a preferred outcome Total Conflict: a zero-sum or constant-sum game, in which what one player wins the other player loses Partial Conflict: a variable-sum game in which both players can benefit by cooperation but may have strong incentives not to cooperate papakonstantinidis

Partial Conflict Games In the real world, not every player’s loss is another player’s gain. For example, both may benefit or both may lose. Games of partial conflict are variable-sum games, in which the sum of payoffs to the players at the different outcomes varies. papakonstantinidis

“hawk-dove” strategies and payoffs π papakonstantinidis

Prisoner’s dilemma papakonstantinidis

Prisoner’s dilemma papakonstantinidis

BARGAINING PROBLEM papakonstantinidis

win win win papakonstantinidis

CONCLUSIONS papakonstantinidis

FIRST TEAM CONCLUSIONS Capitalism is a strictly coherent system based on rationality, consistency and efficiency (Pareto) at least. People have "consistent priorities" (in a fantastic strictly atomic list of priorities) according to the neoclassical school of thought and make their expectations on these The consequence of preferences (see Nash Equilibrium) and rationality in decision making and the "Common Knowledge Rationality "refer to rigorous rational decisions This assumes "rationality" and "consequence of behavior" (even without morality, justice, equality of opportunity, which further increases the chances of maximizing the profit of certain individuals (or increasing their satisfaction, thus minimizing the satisfaction of other people of the community, (in spite of the Market theory of Adam Smith) For all the "players" "i", for whom, is supposed to be consistent, efficient with "consequence of behavior" as to the decision-making process (an idea on which capitalism is based) the conditions and goals coincide papakonstantinidis

SECOND TEAM CONCLUSIONS Now, according to Kurt Gödel, "If the system is consistent, cannot be complete." This is generally known as the theorem incompleteness. The consistency of the axioms can not be proved within the system Kurt Gödel(1931) On the other hand, the basic Neoclassical School of Thought is based on "win-win" outcome (according to game payoffs, , depending on the strategies used by players This leads us to the conclusion that the "win-win" Equilibria have characteristics (a) rationality (cause and effect at the same time) (b) consistency and (c) efficiency (Pareto)-but not justice/equity (Rawls) Just because they have these characteristics (particularly, the "consistency") means that NE (based on neoclassical thinking belong to a system that is not complete papakonstantinidis

The answer may be YES, by the “win-win-win papakonstantinidis model”  If we could find some system expansion tools, so as to include "social welfare and justice and equity" without reducing (theorem Pareto) its efficiency, would we have a better and hopeful new system? The answer may be YES, by the “win-win-win papakonstantinidis model” The «win-win-win papakonstantinidis model" has been proposed to transfer the system from the Gödel's "incompleteness" in a new situation with less consistency, more justice, more socialization more equity , more effectiveness more cooperation, more self-organization papakonstantinidis

Then, I've focused on main globalization function which is the "bargain" with the coincidence of (a) rationality, (b) consistency, (c) efficiency and I've tried to find the deviation points, from what is called "Social Welfare"  Then, putting the "Bargaining Solution" (one of the Nash Equilibria) on the microscope I've tried to find an alternative social solution, the "third Way" by allowing the Community to participate as the third independent and more integrated "part of the bargain, between two negotiators (if it is accepted by these)  Thus, the problem and its own solution is "transferred" from the two-dimensional space in a three-dimensional space : In this 3D space we are seeking to define the 3-pole bargaining Solution (A, B, and the Community) on the "pin head" as one of the Karatheodory's umbilical points [any isolated point on Sphere, is an umbilical Point]  Any system, which includes the Community as the third and most complete player in the "play", is expected to win the coveted completeness while maintaining a minimum level of consistency, efficiency and logic papakonstantinidis

In the case that “Community” plays role in the “game” (depended on “n”) Win-win-win papakonstantinidis equilibrium including the Community-the “c” factor papakonstantinidis

The BARGAIN The win-win-win papakonstantinidis equilibrium

A bargaining example: STRATEGIES - PAYOFFS A and B (%) UTILITY A,B STRATEGY - PAYOFFS C (%) UTILITY C STRATEG PAYOFF Α PAYOFF B UT Α Β STRATEGY PAYOFF C UT C 90 4 71 1 6 80 13 70 2 140 7 280 22 68 5 340 8 3 1020 60 31 64 10 640 9 2560 50 40 16 960 4800 max 41 52 23 1196 4784 32 1240 3720 24 1920 Papakonstantinidis, 2002 papakonstantinidis

VENN DIAGRAM papakonstantinidis

Win-win-win papakonstantinidis model

win-win-win papakonstantinidis equilibrium

Win-win-win papakonstantinidis model: The Nash Extension The extension of the Nash Bargaining Solution concerns to find that value, among infinite number of the NE equilibria (NE extensions), on the 3-D space, defined by the “Caratheodory Conjecture”: In fact, we must find the value of “x*%” among other “x’ s” (NE extensions) in which the Utility of each one of the independent “players” AND THE COMMUNITY as a total, derive the max UTILITY : papakonstantinidis

Win-win-win papakonstantinidis equilibrium-1 The main difference in win-win-win papakonstantinidis model is that the utility function (UF) has been planned, such as to meet the total needs of the Community and not only the 3rd player in a game GENERALLY BUT papakonstantinidis

Win-win-win papakonstantinidis equilibrium-2

Win-win-win papakonstantinidis equilibrium-3

It’s he/she who will participate with 3 Hand role: He/ She works for the realization of the performance function that gives the player "community" (not represented differently in the specific deal) the performance of this community He / She works in favor of the other two negotiators seeking the broadest possible forms of cooperation and communication between individuals and groups, He/She works in favor of society and even attempts to implement, with peaceful means and instruments in this design, forming a self-managed society in the future. What more beautiful: This is precisely a VOLUNTEER and his /her expected payoff must be = 1/3 win-win-win (of society) papakonstantinidis

win- win- win papakonstantinidis model ΜΑΘΗΜΑΤΙΚΗ ΠΡΟΣΕΓΓΙΣΗ Η λύση-ισορροπία του “win-win-win” αφορά εκείνο το x*% (αν υπάρχει) που μεγιστοποιεί το γινόμενο των ΤΡΙΩΝ (Α Κ Ρ Ι Β Ω Σ) ΑΝΕΞΑΡΤΗΤΩΝ συναρτήσεων ωφέλειας/χρησιμότητας Η διαφορά στο “win-win-win” έγκειται στο ότι η συνάρτηση ωφέλειας έχει σχεδιαστεί έτσι ώστε να αφορά το σύνολο της κοινωνίας και όχι άλλον έναν “N” παίκτη Αυτό σημαίνει, πως στη Συνάρτηση Ωφέλειας/Χρησιμότητας έχει αποτυπωθεί όχι μόνο μιας μορφής «συλλογικής ωφέλειας» των «υπολοίπων» αλλά ακόμα και εκείνης των δύο διαπραγματευτών, x,y papakonstantinidis

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.. Market side papakonstantinidis

Cantor Set 3D papakonstantinidis

Part II: Market approach MARKET STRUCTURE (types of competition): Monopoly Perfect Competition Cournot Theorem (P=MR=MC or ….but Theocharis limit(n=3unstable price: Cournot Duopoly – interactive best responses Cournot Triopoly : papakonstantinidis

MATH APPROACH Starting from Duopoly MATH APPROACH Starting from The inverse demand function: PERFECT COMPETITION In a Cartesian system, the P x Q rectangle area reflects the total revenue of RTDC1 Total Revenue for RTDC 1 Marginal Revenue for RTDC 1 papakonstantinidis

TRIOPOLY : win-win-win situation By the same way, as the DUOPOLY (above) it must be found the triplet (q1, q2, q3) of actions with the property that player 1's action is a best response to player 2's and(at the same time) 3’s action, player 2's a best response to player 1's and(at the same time) 3’s action, and 3’s action is a best response to player 1's and 2’s action   Duopoly < triopoly < perfect competition (max social profit, max Q, at lowest P) Theocharis, 1950 papakonstantinidis

In equilibrium must be: MAX RTDC 1 Best response Equilibrium quantity is papakonstantinidis

duopoly papakonstantinidis

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win-win-win papakonstantinidis model To third "win" "credited" to society as a whole, rather than volunteer-player The "win-win-win" is a way to operate one socially The "win-win-win" itself constitute the methodological crisis solving approach papakonstantinidis

win win win papakonstantinidis

The formal win-win-win papakonstantinidis equilibrium

the basic “win-win- win papakonstantinidis model” (sensitized game) equation is (Papakonstantinidis, IJRCM, 2011)   where 1. N is the set of players. 2. Ω* is the set of the states of the “Intermediate Community”, depended on local people bargaining intra-community behavior 3. Ai is the set of actions for player i. . 4. Ti is the types of player i, decided by the function . So for each state of the nature, the game will have different types of players. The outcome of the players is what determines its type. Players with the same outcome belong to the same type. 5. defines the available actions for player i of some type in Ti. 6. is the payoff function for player i papakonstantinidis

FLAG THEME papakonstantinidis

The practical view: Sensitization Process papakonstantinidis

Steps towards the absolute collaboration partnership Involvement Participation sensitization Information papakonstantinidis

broadest possible forms of cooperation / communication people-DMA Finding, planning and implementation addressing social problems through: broadest possible forms of cooperation / communication people-DMA Design implementation using peaceful means Intensity modulation self-managed society in the future. papakonstantinidis

QUESTIONNAIRE: a/a Questions 1 YES N0 NOT AT ALL 1 How many deals you remember that you do in one day? (one, more than one, not at all) 2 Are you a volunteer? 3 You want always winning? you want to even if you are wrong in your position with another individual? 4 Usually lost or won in your transactions (not just economic, but also social, political etc.) with other people? 5 Have you regretted for a daily choice of yours (whatever is)? 6 Do you gain experience (or try to correct your mistakes) or not, in a subsequent transaction with individuals or with the State? 7 Affected, usually from external sources in your choices or not? Esis affects other people around you, trying to force your will? 8 Do you believe that other people they interact with follow Personal winning strategies in order to get as much as possible from any agreement? 9 Are you a businesslike? prepare strategies of dealing you do with another person? papakonstantinidis

win-win-win expectations Conflict resolution Conflict bargaining solution Crisis management decision making Local decision making Accepted relations Alternative behaviors Creating team psychology Volunteering Trans bargain in l-d proc Flag theme as a motivation to joint around it in the S-limit Application Fields: l-d, management, marketing history, psychology, decision sciences, biology engineering , any reaction Methodological tool for: The “new” form: papakonstantinidis

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“when the impossible comes true lp888 win-win-win “when the impossible comes true lp888 papakonstantinidis

End papakonstantinidis

APPENDIX GREEK papakonstantinidis

Α) ΕΠΙΘΕΤΙΚΗ συμπεριφορά Β) ΣΥΝΤΟΝΙΣΜΟΣ ( αν θέλουν τη συμφωνία) ΚΕΝΤΡΙΚΗ ΙΔΕΑ : Α) ΕΠΙΘΕΤΙΚΗ συμπεριφορά Β) ΣΥΝΤΟΝΙΣΜΟΣ ( αν θέλουν τη συμφωνία) Γ) Κ Α Τ Α Ν Ο Μ Ε Σ ΣΥΜΦΩΝΙΑΣ Οι Διαπραγματευτές ΕΧΟΥΝ το ΚΙΝΗΤΡΟ του ΣΥΝΤΟΝΙΣΜΟΥ αλλιώς δεν θα έχουν νόημα οι κατανομές μεταξύ των 2 (βασικά) παικτών (αφού η Συμφωνία θα έχει καταρρεύσει) σε μια Διαπραγμάτευση που ΔΕΝ οδηγεί έτσι σε «Ισορροπία Nash» Παράλληλα έχουν κίνητρο το κίνητρο της ΕΠΙΘΕΤΙΚΗΣ ΣΥΜΠΕΡΙΦΟΡΑΣ , μέσα σε αυτό το ΣΥΝΤΟΝΙΣΜΟ προκειμένου να μεγιστοποιήσουν όσο πιο πολύ γίνεται το «κομμάτι» της κατανομής (που κερδίζει ο καθένας από τη συμφωνία) ΚΑΤΑΝΟΜΕΣ αυτού του συντονισμού μεταξύ τους (να πάρει κανείς όσο πιο πολλά μπορεί από τον άλλο : Για να πάρει το «κομμάτι της Κατανομής» χρειάζεται συντονισμός papakonstantinidis

Έτσι, η ΣΥΜΦΩΝΙΑ (παρά την επώδυνη για τον «αδύναμο» διαπραγματευτή λύση) μεροληπτεί υπέρ αυτού, ακριβώς επειδή έχουμε τη συμφωνία και όχι τη κατάρρευση αυτής, από την οποία κανείς δεν θα πάρει τίποτα, αλλά ο αδύναμος είναι εκείνος που θέλει να πάρει από τη συμφωνία: Όταν ο καταστηματάρχης που έχει ακόμα ρούχα της προηγούμενης σεζόν θέλει επειγόντως να τα πουλήσει για να μην του μείνουν στο χέρι .. είναι τα λεγόμενα «ρετάλια» (εκείνα που μένουν απούλητα) Ο έμπορος πιέζεται και εκείνος που πουλά με πίστωση .. και άρα επείγεται να «κλείσει» τη συμφωνία με τον πιθανό καταναλωτή… )αρκεί να «κλείσει» όπως-όπως που λέει ο λαός μας) papakonstantinidis

ΠΑΛΙΟΤΕΡΕΣ ΠΡΟΣΠΑΘΕΙΕΣ Αν ΔΕΝ κατέληγαν σε Συμφωνία, κανείς τους δεν θα κέρδιζε τίποτα (δες τε διαφορά από το ZERO SUM (o θάνατό σου η ζωή μου)… ενώ εδώ ΔΙΝΕΤΑΙ-ΠΑΡΕΧΕΤΑΙ Η ΕΥΚΑΙΡΙΑ να κερδίσουν και οι ΔΥΟ (2) – Σημασία έτσι δίνεται στη κατανομή των payoffs που σε καμιά περίπτωση δεν σχετίζεται με το μέγεθος, την ένταση και της ποιότητα της ΩΦΕΛΕΙΑΣ, που για τον κάθε Διαπραγματευτή είναι μια εντελώς προσωπική- ατομική περίπτωση : Ενδέχεται να είναι πιο ευχαριστημένος (ωφέλεια) από ένα μικρότερο κομμάτι κατανομής, ΑΡΚΕΙ η «Δ» να καταλήξει σε ΣΥΜΦΩΝΙΑ ΠΑΛΙΟΤΕΡΕΣ ΠΡΟΣΠΑΘΕΙΕΣ Το ZERΟ-SUM ήταν καλό για το πόλεμο και τη ψυχροπολεμική λογική Η “Δ” (NASH) όχι απλά έλυνε τα έλυνε τα ZERO-SUM αλλά και όλα τα υπόλοιπα της σύγκρουσης (ιδανικά για περίοδο ειρήνης, στην οποία έμπαινε ο κόσμος από το 50+ ΔΗΛΑΔΗ Από τις διάφορες εναλλακτικές «συμφωνίες» επιλέγεται με βάση το Nash ΜΙΑ ΚΑΙ ΜΟΝΑΔΙΚΗ εκείνη που μεγιστοποιεί προσδοκίες-πιθανότητες των 2 (για την ευκολία του θέματος διαπραγματευτών (που αντανακλάται με το γινόμενο της φαντασιακής μονάδας Ωφέλειας Χ την αντίστοιχη ΠΙΘΑΝΟΤΗΤΑ (πραγματικός αριθμός) papakonstantinidis

Η Συμφωνία αντανακλά μια από τις άπειρες Ισορροπίες NASH papakonstantinidis

Μια άριστη Συμφωνία βασισμένη στη βέλτιστη απόκριση των Διαπραγματευτών αποτυπώνεται με το 100% της απόδοσης (αντίστοιχα, τα payoffs της Θ. Παιγνίων) Αν οι Διαπραγματευτές δεν κατέληγαν σε συμφωνία (Δ>100) τότε η Δ δεν θα είχε ενδιαφέρον Αν, αντίθετα καταλήξουν σε συμφωνία, τότε και μόνο τότε, εξετάζεται πώς μπόρεσαν οι διαπραγματευτές να μεγιστοποιήσουν την κάλυψη των αναγκών τους ταυτόχρονα, χωρίς να χρειαστεί το ZERO-SUM .. είναι δηλαδή μια win-win κατάσταση Σε αυτή τη περίπτωση, (μας λέει ο Nash), σημασία έχει το να ελέγξουμε σε ποιο επίπεδο της Δ θα καταλήξουμε: Τίθεται, λοιπόν, μια διαδικασία «δοκιμών» (κατανομών) προσδοκιών (υποκειμενικής ωφέλειας + τη πιθανότητα υλοποίησής της) που αντανακλάται σε «κατανομές βέλτιστων αποκρίσεων» papakonstantinidis

Αν οι Α, Β βρίσκονται σε μια διαπραγμάτευση που τείνει στη συμφωνία (αλλιώς, , δεν υπάρχει «Δ») τότε, αν η Α εκτιμά/πιθανολογεί ότι ο Β θα επιλέξει “x” τότε εκείνη, θα επιλέξει (100-x) [βέλτιστη απόκριση] προκειμένου η Διαπραγμάτευση να έχει αίσιο τέλος= ΣΥΜΦΩΝΙΑ Οι μονάδες ωφέλειας είναι αυθαίρετες και εντελώς υποκειμενικές- δίπλα σε αυτές υπάρχει το αντίστοιχο μέγεθος κατανομής : Αυτό μας λέει «σε ποιο επίπεδο “προσδοκίας” (πχ %) θα ήταν ικανοποιημένος ο κάθε διαπραγματευτής από τη Διαπραγμάτευση Ο Nash θεώρησε τη συμφωνία μεταξύ 2 ορθολογιστών ως δεδομένη και εξέτασε το πώς επιτεύχθηκε αυτή Δεν έδωσε «ΠΡΟΣΤΑΚΤΙΚΟΥΣ τυποποιημένους κανόνες δράσης» (κάνε αυτό !!) papakonstantinidis

ΟΙ ΤΡΕΙΣ ΣΗΜΑΝΤΙΚΕΣ ΠΑΡΑΤΗΡΗΣΕΙΣ Οι μονάδες ωφέλειας της Α δεν είναι συγκρίσιμες με εκείνες του Β (Καθένας/μια από αυτούς έχει προσωπική ατομική κλίμακα κατάταξης (ταξινομική, όχι μετρήσιμη) Ο σχετικός ρυθμός αύξησης των μονάδων ωφέλειας/χρησιμότητας του ατόμου αντανακλά το φόβο του από τη προοπτική της κατάρρευσης της Συμφωνίας Όλες οι κατανομές αποτελούν ισορροπία Nash: Η Ισορροπία Nash είναι ένα σύνολο στρατηγικών (μία για κάθε παίκτη) έτσι ώστε η στρατηγική του ενός να είναι η βέλτιστη απόκριση στη στρατηγική των άλλων Έτσι εξηγείται η σχετικότητα κατανομών-στρατηγικών ΒΑΣΙΚΟ ΕΡΩΤΗΜΑ NASH: δεν ξέρουμε ποια θα είναι η συμφωνία στην οποία θα κατασταλάξουν οι εργαλειακά ορθολογικοί διαπραγματευτές, θα κοιτάξουμε μια-μια όλες τις πιθανές κατανομές (όλες τις Ισορροπίες Nash)- papakonstantinidis

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N.E % Α ΚΑΤΑΝΟΜΕΣ σε Συνθήκες ΙΣΟΡΡΟΠΙΑΣ % Β ΩΦΕΛΕΙΑ Α Υποκειμενική κατάταξη Β ΓΙΝΟΜΕΝΟ ΩΦΕΛΕΙΩΝ 1 100 71 2 90 10 70 3 80 20 68 5 340 4 30 64 960 60 40 16 6 50 52 23 1196 7 31 1240 μέγιστο 8 24 9 12 244 61 11 papakonstantinidis

ΜΑΘΗΜΑΤΙΚΗ ΠΡΟΣΕΓΓΙΣΗ ΤΗΣ ΛΥΣΗΣ ΤΟΥ ΔΙΑΠΡΑΓΜΑΤΕΥΤΙΚΟΥ ΠΡΟΒΛΗΜΑΤΟΣ ΜΑΘΗΜΑΤΙΚΗ ΠΡΟΣΕΓΓΙΣΗ ΤΗΣ ΛΥΣΗΣ ΤΟΥ ΔΙΑΠΡΑΓΜΑΤΕΥΤΙΚΟΥ ΠΡΟΒΛΗΜΑΤΟΣ Έστω πως η Α και ο Β επιτυγχάνουν [μετά από συνεννόηση, μέσα στη Διαπραγμάτευση], ΣΥΜΦΩΝΙΑ ΑΡΙΣΤΗ = 100% τέτοια, δηλαδή που να οδηγεί σε NASH EQUILIBRIUM (όπου τίποτα δεν περισσεύει, αλλά και τέτοια που να μην επιδέχεται αλλαγών, χωρίς να χειροτερεύσει η θέση του ενός από τους 2, ή και των 2 (εργαλειακός ορθολογισμός) Έτσι, πχ, αν η Α υπολογίζει ότι ο Β θα ζητήσει “x” %, προκειμένου να αποδεχθεί τη ΣΥΜΦΩΝΙΑ, τότε η Α που θέλει τη Συμφωνία περισσότερο από αυτόν τον Β θα προτείνει (στην ουσία θα αποδεχθεί) (100-x) % Άλλωστε μη ξεχνάμε ότι, αντίθετα από το ΠΑΙΓΝΙΟ, η ΔΙΑΠΡΑΓΜΑΤΕΥΣΗ είναι μια διαδικασία ΣΥΝΤΟΝΙΣΜΟΥ και επιθετικότητας των Α και Β, λόγω κινήτρου συμφωνίας όπου η προσοχή εστιάζεται στη κατανομή, αντί στα ψυχροπολεμικά παίγνια εξόντωσης του αντιπάλου Από κει και πέρα εξετάζουμε τη μαθηματική έκφραση του «συντονισμού και κατανομών» Έστω, όπου x το επί τις % μερίδιο (κατανομή) που παίρνει (μετά τη συμφωνία-συντονισμό) με τον Β) η Α papakonstantinidis

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  Όταν οι Α,Β έχουν τις ίδιες ακριβώς γραμμικές συναρτήσεις ωφέλειας/χρησιμότητας ΠΙΘΑΝΌΤΗΤΑ 50-50 ο ρυθμός αύξησης ωφέλειας/χρησιμότητας του Β είναι μικρότερος εκείνου της Α (που –στο παράδειγμα αυτό- είναι πάντα ίσος με 1) Όσο πιο μεγάλο είναι το “k” τόσο πιο φοβισμένος είναι ο Β σε σχέση με την Α και τόσο πιο μεγάλο είναι το % της κατανομής, της Α [ ο Β είναι ευχαριστημένος και με μικρότερο ποσοστό, αρκεί να “κλείσει η συμφωνία” (πχ αν k=2, τότε x*=33.33%) και ο Β θα «χάσει» ακόμα περισσότερο(+17% περίπου) στη κατανομή , αν επιδιώκει (λόγω φόβου) τη κατάληξη της «Δ» σε Συμφωνία papakonstantinidis

Η κοινωνικοποίηση της Διαπραγμάτευσης Προτεινόμενη «Μοιρασιά» μεταξύ “A , “B” και “C” Μερίδ Χρησ Χρη Α Β AXB C AXBXC  (%) (%)   90 4 71 1 6 80 13 70 2 140 7 280 22 68 5 340 8 3 1020 60 31 64 10 640 9 2560 50 40 16 960 4800 max 41 52 23 1196 4784 32 1240 3720 24 1920 14 12 600 papakonstantinidis

win- win- win papakonstantinidis model ΜΑΘΗΜΑΤΙΚΗ ΠΡΟΣΕΓΓΙΣΗ Η λύση-ισορροπία του “win-win-win” αφορά εκείνο το x*% (αν υπάρχει) που μεγιστοποιεί το γινόμενο των ΤΡΙΩΝ (Α Κ Ρ Ι Β Ω Σ) ΑΝΕΞΑΡΤΗΤΩΝ συναρτήσεων ωφέλειας/χρησιμότητας Η διαφορά στο “win-win-win” έγκειται στο ότι η συνάρτηση ωφέλειας έχει σχεδιαστεί έτσι ώστε να αφορά το σύνολο της κοινωνίας και όχι άλλον έναν “N” παίκτη Αυτό σημαίνει, πως στη Συνάρτηση Ωφέλειας/Χρησιμότητας έχει αποτυπωθεί όχι μόνο μιας μορφής «συλλογικής ωφέλειας» των «υπολοίπων» αλλά ακόμα και εκείνης των δύο διαπραγματευτών, x,y papakonstantinidis

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.. Market side papakonstantinidis

Cournot duopoly Cournot triopoly < < Perfect competition Comparing the 3 situations (2-poly, 3-poly, and PC) : < < But, according to Theocharis Theorem (1959) papakonstantinidis

= the best “social” form of market Monopoly < duopoly < triopoly < perfect competition < < unstable = the best “social” form of market papakonstantinidis

THEOCHARIS : ENDLESS OSCILLATION (1959) Analysis of Triopoly Game with Isoelastic Demand Function and Heterogeneous Players THEOCHARIS : ENDLESS OSCILLATION (1959) papakonstantinidis

MARKET STRUCTURE papakonstantinidis

Perfect competition Duopoly Triopoly papakonstantinidis

Monopoly: higher price –less quantity Less social profit Perfect Competition: max quantity in the less price Max social profit papakonstantinidis

Cournot Duopoly : best response q1 q2 quantities, given price , 0<bi<1 slope of Ri, qi → ai strategy of i player papakonstantinidis

Market Structure papakonstantinidis

Triopoly ’ s ideal best responses Cournot Triopoly : Best responses His/her strategy depends on choices of the other two simultaneously , by zero response time papakonstantinidis

END of APPENDIX GREEK papakonstantinidis

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