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1 author: Leonidas A. Papakonstantinidis Technological Educational Institute of Peloponnese 146 PUBLICATIONS 73 CITATIONS SEE PROFILE

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CSR- or Stakeholder Theory Integrative Business Ethics by the "win-win-win papakonstantinidis model PAPAKONSTANTINIDIS LA

1. Integrative Business Ethics 2. Stakeholder Theory Stakeholder Theory is a view of capitalism that stresses the interconnected relationships between a business, its customers, suppliers, employees, investors, communities and others who have a stake in the organization. This website brings together thought leadership from around the world and serves as a resource for scholars, students and practitioners. and 3. the win-win-win papakonstantinidis model Now, our efforts are focused on finding a “new” “social welfare form…”.. treating the community as a whole as an aggregate entity that participates in a social welfare game(Creg Tovey, RG,2016)1

Preface If we merge the Stakeholders-players, a triangle relation could be resulted: 1.

Business with its employees, investors, suppliers

2.

Its customers,

3.

Community –the “C” factor

Each of these players makes efforts to dominate over the other two A 3-ple space concept, based on the utility function of A-B-C including the community(C) is given below:

1

Creg Tovey and alle (1992) "How Hard Is It to Control an Election?" Mathematical and Computer Modeling Volume 16, Issues 8–9, August–September 1992, Pages 27-40

the win-win-win papakonstantinidis model

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Theoretical base: CONTRADICTIONS

Pareto Efficiency

Pareto efficiency or Pareto optimality is a state of allocation of resources from which it is impossible to reallocate so as to make any one individual or preference criterion better off without making at least one individual or preference criterion worse off.

max U ( x1 , x2 ,...x n ) Subject to: n

 p i xi  M i 1

under the constraint


xi  0

 i  {1,2,..., n)

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Cooperative bargaining game theory has often been concerned with whether expected bargaining outcomes could be altered by certain contractions of the feasible set. There is strong theoretical support2 on both sides - while there are allocation rules that require that certain contractions of the feasible set are immaterial in terms of the predicted final outcome (Nash, 1950), there are also others that suggest that those very contractions should significantly alter the predicted outcome (Kalai-Smorodinsky, 1950). Nydegger and Owen (1974) provided empirical support for the former set of allocation rules by experimentally demonstrating that certain contractions of the feasible set leave the expected bargaining outcome unchanged. Since then the ineffectiveness of such contractions has never been questioned. We revisit this question in our experiment and _nd that certain contractions of feasible sets do significantly alter bargaining outcomes when the negotiating agents are asymmetric (in terms of bargaining power) - and the higher the asymmetry between the agents, the greater is the e_ect of such contractions. As an immediate consequence, we see that contractionsof feasible sets do not alter bargaining outcomes when the agents are perfectly

2

Subrato Banerjeey (February 2018) “Effect of Reduced Opportunities on Bargaining Outcomes: An Experiment With Status Asymmetries”


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symmetric, thereby subsuming the findings of Nydegger and Owen (1974) in our more generalizing. Interestingly, each allocation rule known in the literature either always predictsa change in bargaining outcomes, or never predicts so. We provide important insights on when to, and when not to, expect changes in bargaining outcomes due to contraction.

Differentiation Rate (R*) from the conflict point: “COMMUNITY definition in its limit A

win – win - win

R* Conflict

B

888 As a basis for social interaction and decision making, utility maximizing agents frequently act according to the potential consequences on other agents’ utilities. Social decision making interests academics across diverse disciplines from psychology to evolutionary biology, and includes the seminal works of John Nash and Kenneth Arrow who studied situations where two or more agents must jointly decide on a social outcome deemed acceptable to each agent. The celebrated approaches to understanding social decision making, include among others, the problem of an aggregation of individual preferences (Arrow), and a bargaining problem (Nash). What is common about these approaches is a set of prerequisites (axioms) that require some notion of fairness, efficiency, and the independence of irrelevant alternatives (IIA, hereafter) among still others Fairness, for example, is implicit in Arrow’s axiom of non-dictatorship, and Nash’s axiom of symmetry. We formally test the validity of the IIA the win-win-win papakonstantinidis model

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axiom in the setting of Nash, which is contextually different from that in Arrow’s setting. We now turn to an explanation of the IIA axiom keeping in mind that the use of many axioms in theory often stems from an intuitive understanding of our immediate experiences (presented in the motivating examples of the introductory paragraph). The IIA axiom in Nash’s (1950) framework can be explained as follows: the equilibrium outcome of the bargaining problem for a given feasible set (of outcomes) will also be the equilibrium outcome of the bargaining problem for any subset of that original feasible set, provided that such a subset has the initial outcome as one of its elements. In this paper we revisit the validity of Nash’s (1950) IIA axiom in a general setting involving dialogue - a key element in an real life negotiation. Formally, all allocation rules proposed in cooperative bargaining game theory, either always validate or always violate the IIA axiom (Roth, 1985). Our purpose is to provide useful insights on where to expect validity and where to expect a violation. To the best of my knowledge, this is a _first attempt at such an endeavor. The Nash solution has been criticized because of this axiom (Raifa, 1953; Yu, 1973, Kalai and Smorodinsky, 1975; and Perles and Maschler, 1981)The criticism, as Thomson (1994) puts it, was that, \the crucial axiom on which Nash had based his characterization requires that the solution outcome be unaffected by certain contractions of the feasible set, corresponding to the elimination of some of the options initially available ... but this independenceis often not fully justified"3 .This axiom, however, witnessed its first experimentalvalidity when Nydegger and Owen (1974), found evidence against the Kalai-Smorodinsky(KS) solution (where contraction matters) in favor of the Nash solution in their controlled experimental set up. Since then, the 3

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The word ’symmetry’ here (see Roth, 1985) does not refer to the axiom of symmetry in the context of cooperative bargaining. Here, by ’symmetry’ we only mean that the individuals involved in bargaining are fidentical in every respect (in particular, their bargaining powers). For more examples, see the discussions in Bardsley et al, 2009; Chaudhuri, 2009; Smith, 2008; Henrich and Henrich, 2007; and Camerer, 2003 (and the papers cited therein). Cardenas and Carpenter (2008), for example, also point out that the perception of how deserving recipients are, could be a strong predictor of altruism. Ball et al, (2001) interprets this (significant) effect of test performance as a ’status e_ect’. These interpretations are consistent with Aristotle’s idea of fairness which should be proportional to some measure of agents’ need, ability, e_ort and status. This means that one of the individuals has a ’status’ advantage. .For more literature on bargaining with fairness considerations, see Binmore (2014), Birkeland and Tungodden (2014), Bruyn and Bolton (2008), Burrows and Loomes (1994), and Buchan et al, (2004). The 50%-50% outcome (which is almost always deemed fair) may also be seen as a focal point (see Crawford et al, 2008).


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validity of the IIA axiom in situations involving bargaining,has never been questioned. However, there still remains one concern related tothe random selection of the individual in the advantageous position (due to the contraction) against his counterpart. For more detailed discussions on axiomatic approaches to bargaining theory, see Moulin (1988, 2003)and Roth (1979, 1985).the random selection of the individual in the advantageous position (due to the contraction)against his counterpart. As Hoffman et al. (1994) point out, "randomization maynot be neutral, since it can be interpreted by subjects as an attempt by the experimenterto treat them fairly ... thus experimenters may unwittingly induce ’fairness’. A subjectmay feel that, since the experimenter is being fair to them, they should be fair to eachother." They could explain why _first movers in ultimatum games offered significantly moreto their counterparts than non-cooperative game theory would suggest. Hence, because ofrandomization, the axiom was validated only under symmetric bargaining in the Nydegger and Owen (1974) framework. In this paper we check if these results would survive in a more general asymmetric setting, so we borrow ideas from ultimatum games.

In the experiment of Hoffman et al. (1994), the roles of sender and receiver were assigned randomly in the control group, and in the treatment group, the right to be the first mover was earned (as reinforced by the instructions) by scoring high on a general knowledge quiz. To that effect, the role of the trivia test was to eradicate potential interpretation of fairness by the subjects that arises from randomization. The modal offer observed in the treatment group was significantly less than that made in the control group.4 We borrow this idea to address the concern above by replacing randomization by a test to generate self-regarding behavior and extend the research of Nydegger and Owen (1974) to test for contraction effects under asymmetric bargaining5 - an open question so far. The central motivation of this experiment is thus, to test contraction effects under asymmetry, when the experiment itself does not explicitly oblige the subjects to be fair. In other words, we do not want the subjects’ own intrinsic notions of fairness (that we are able to capture and observe) to befiinuenced by the experiment. This means that the subjects are free to carry their own notions of fairness to the bargaining table, uncontaminated by any experimental e_ect.6 While we are testing a very important axiom in a very general setting, it must be noted the win-win-win papakonstantinidis model

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thateach example of a contraction in its specificity, is important in its own right, andtherefore, our research immediately connects with a wider range of disciplines. For example, MRPs are an issue of significant interest in the field of competition law (see the detailed discussion in van den Bergh and Camesasca, 2001). The effects of contraction in the form of minimum wage laws also interests psychologists. For example, Smith (2015) emphasizes positive effects of minimum wages on low-income agents who are otherwise more prone to emotional, developmental, and behavioral disorders and worse educational attainment, which further translate to lower success in future. It is also argued that the biases and stereotypes often associated with the poor, eventually make way for social exclusion with direct implications on job prospects. This ultimately translates to frustration and aggression, that reduce the ability of the poor and the marginalized to make sound decisions.

Wenow observe that several cities (such as Seattle and San Francisco) are experimenting with increased minimum wages.

To cite more examples of contraction, in May 2015, the Los Angeles city council voted for raising the city’s minimum wage to $15 (from $9) per hour. This move was pushed hard by trade unions and the wage oor is expected to be fully implemented by 2020. In July 2015, the minimum wage was raised from Rupees (Rs.) 137 to Rs. 160 per day by the Ministry of Labor and Employment in India.7 Clearly, contractions of feasible sets are very frequently prevalent everywhere and effectively amount to reduced sets of available alternatives (very often for instances of bargaining or negotiation) and therefore, the IIA axiom easily relates to real market situations that frequently interest various other fields of research. We study the effects of such contractions of given feasible sets in a laboratory setting to understand the empirically observed departures (if any) from the equilibrium predictions known to us from existing theory.


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It is also worth noting that the two parties involved in each of the examples above (e.g. consumers against sellers; or firms against trade unions) need not be symmetric in terms of bargaining power. One such source of asymmetry in bargaining power is the existence of ’status gaps’ between agents who are from different backgrounds - which is why people often sacrifice material resources to attain higher status (Huberman et al, 2004). We study the IIA axiom with the introduction of asymmetries (see Roth, 1985) in the context of bargaining problems subject to contractions of the feasible set. We find that the IIA axiom is validated when there is symmetry in agent bargaining power, and it is violated when there is asymmetry in agent bargaining power.

In a nutshell, we weigh and compare the predictive capacity of models of cooperativebargaining against our experimental findings in a realistic scenario that actually involves bargaining

The theoretical formulation In the following discussion on the (theoretical) effects of contraction, the Kalai-Smorodinsky (KS hereafter) solution4 concept is used only as a representative example of allocation rules that violate the IIA axiom, many of which have been mentioned in the previous (introductory) section. While the KS solution itself is not central to the main theme (that is, effects of contraction) of this paper, it will be useful for the understanding of how set contractions may alter bargaining outcomes (contrary to the Nash solution).8 Throughout the discussion, we assume that the agents involved in bargaining gain nothing when there is a disagreement (that is, the disagreement payoffs_ is zero for each agent). In general, disagreement payoffs may play an important role in the determination of bargaining outcomes (see Anbarci and Feltovich, 2013). 4

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Kalai, Ehud &Smorodinsky, Meir (1975). "Other solutions to Nash's bargaining problem". Econometrica. 43 (3): 513–

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Herve Moulin (2004). Fair Division and Collective Welfare. Cambridge, Massachusetts: MIT Press


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Kalai–Smorodinsky bargaining solution

The Kalai–Smorodinsky (KS) bargaining solution is a solution to the Bargaining problem. It was suggested by Ehud Kalai and Meir Smorodinsky, as an alternative to Nash's bargaining solution suggested 25 years earlier. The main difference between the two solutions is that the Nash solution satisfies independence of irrelevant alternatives while the KS solution satisfies monotonicity.

Settings

A two-person bargain problem consists of a pair {\displaystyle (F,d)} {\displaystyle (F,d)}:

A feasible agreements set {\displaystyle F} F. This is a closed convex subset of {\displaystyle \mathbb {R} ^{2}} \mathbb {R} ^{2}. Each element of {\displaystyle F} F represents a possible agreement between the players. The coordinates of an agreement are the utilities of the players if this agreement is implemented. The assumption that {\displaystyle F} F is convex makes sense, for example, when it is possible to combine agreements by randomization. A disagreement point {\displaystyle d=(d_{1},d_{2})} d=(d_1, d_2), where {\displaystyle d_{1}} d_{1} and {\displaystyle d_{2}} d_{2} are the respective payoffs to player 1 and player 2 when the bargaining terminates without an agreement. It is assumed that the problem is nontrivial, i.e, the agreements in {\displaystyle F} F are better for both parties than the disagreement.

A bargaining solution is a function {\displaystyle f} f that takes a bargaining problem {\displaystyle (F,d)} {\displaystyle (F,d)} and returns a point in its feasible agreements set, {\displaystyle f(F,d)\in F} {\displaystyle f(F,d)\in F}.

Requirements from bargaining solutions The Nash and KS solutions both agree on the following three requirements:


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Pareto optimality is a necessary condition. For every bargaining problem, the returned agreement {\displaystylef(F,d)} {\displaystyle f(F,d)} must be Pareto-efficient.

Symmetry is also necessary. The names of the players should not matter: if player 1 and player 2 switch their utilities, then the agreement should be switched accordingly.

Invariant to affine transformations also seems like a necessary condition: if the utility function of one or more players is transformed by a linear function, then the agreement should also be transformed by the same linear function. This makes sense if we assume that the utility functions are only representations of a preference relation, and do not have a real numeric meaning.

In addition to these requirements, Nash requires Independence of irrelevant alternatives (IIR). This means that, if the set of possible agreements grows (more agreements become possible), but the bargaining solution picks an agreement that was contained in the smaller set, then this agreement must be the same as the agreement reached when only the smaller set was available, since the new agreements are irrelevant. For example, suppose that in Sunday we can agree on option A or option B, and we pick option A. Then, in Monday we can agree on option A or B or C, but we do not pick option C. Then, Nash says that we must pick option A. The new option C is irrelevant since we do not select it anyway.

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The KS solution The KS solution can be calculated geometrically in the following way.

Let { b(F)} /b(F)} be the point of best utilities { (Best 1F),Best2F { (Best_{1}(F), Best1F),Best2F Draw a line {\displaystyle L} L from {\displaystyle d} d (the point of disagreement) to {\displaystyle b} b (the point of best utilities).

By the non-triviality assumption, the line {\displaystyle L} L has a positive slope. By the convexity of {\displaystyle F} F, the intersection of {\displaystyle L} L with the set {\displaystyle F} F is an interval. The KS solution is the top-right point of this interval. the win-win-win papakonstantinidis model

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Mathematically, the KS solution is the maximal point which maintains the ratios of gains. I.e, it is a point {\displaystyle \mu } \mu on the Pareto frontier of {\displaystyle F} F, such that:

{\displaystyle {\mu _{1}-d_{1} \over \mu _{2}-d_{2}}={Best_{1}(F)-d_{1} \over Best_{2}(F)-d_{2}}} {\displaystyle {\mu _{1}-d_{1} \over \mu _{2}-d_{2}}={Best_{1}(F)d_{1} \over Best_{2}(F)-d_{2}}}

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it is suggested: 1. Nash Bargaining Problem 2. Desirable Properties for bargaining Solutions 2a. (INV) Invariance to coordinate-wise affine transformation 2b. (SYM) Symmetry preservation 2c. (EFF) Efficiency 2d. (IND) Independence of irrelevant alternatives 2e. (MON) Monotonicity

analysis

Nash Bargaining Problem


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Kalai - Smorodinsky solution to bargaining problems5 2009 NASH BARGENING PROBLEM

(U,u) e 2Rn x Rn is a Nash bargaining problem if U is nonempty, compact and convex, and there exists u e U such that u