scholarly journals The equal collective gains value in cooperative games

2021 ◽  
Author(s):  
Emilio Calvo Ramón ◽  
Esther Gutiérrez-López
Keyword(s):  
Cooperative Games ◽  
Subgame Perfect Equilibrium ◽  
The Other ◽  
Perfect Equilibrium ◽  
Negotiation Model ◽  
New Class ◽  
Average Productivity

AbstractThe property of equal collective gains means that each player should obtain the same benefit from the cooperation of the other players in the game. We show that this property jointly with efficiency characterize a new solution, called the equal collective gains value (ECG-value). We introduce a new class of games, the average productivity games, for which the ECG-value is an imputation. For a better understanding of the new value, we also provide four alternative characterizations of it, and a negotiation model that supports it in subgame perfect equilibrium.

scholarly journals Subgame Perfect Equilibrium in the Rubinstein Bargaining Game with Loss Aversion

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-23 ◽  
Author(s):  
Zhongwei Feng ◽  
Chunqiao Tan
Keyword(s):  
Loss Aversion ◽  
Reference Point ◽  
Bargaining Power ◽  
Subgame Perfect Equilibrium ◽  
Reference Points ◽  
Bargaining Game ◽  
The Other ◽  
Nash Bargaining ◽  
Perfect Equilibrium ◽  
High Share

Rubinstein bargaining game is extended to incorporate loss aversion, where the initial reference points are not zero. Under the assumption that the highest rejected proposal of the opponent last periods is regarded as the associated reference point, we investigate the effect of loss aversion and initial reference points on subgame perfect equilibrium. Firstly, a subgame perfect equilibrium is constructed. And its uniqueness is shown. Furthermore, we analyze this equilibrium with respect to initial reference points, loss aversion coefficients, and discount factor. It is shown that one benefits from his opponent’s loss aversion coefficient and his own initial reference point and is hurt by loss aversion coefficient of himself and the opponent’s initial reference point. Moreover, it is found that, for a player who has a higher level of loss aversion than the other, although this player has a higher initial reference point than the opponent, this player can(not) obtain a high share of the pie if the level of loss aversion of this player is sufficiently low (high). Finally, a relation with asymmetric Nash bargaining is established, where player’s bargaining power is negatively related to his own loss aversion and the initial reference point of the other and positively related to loss aversion of the opponent and his own initial reference point.

scholarly journals What Do Bargainers' Preferences Look Like? Experiments with a Convex Ultimatum Game

2003 ◽  
Vol 93 (3) ◽  
pp. 672-685 ◽  
Author(s):  
James Andreoni ◽  
Marco Castillo ◽  
Ragan Petrie
Keyword(s):  
Risk Aversion ◽  
Bargaining Power ◽  
Ultimatum Game ◽  
Subgame Perfect Equilibrium ◽  
The Other ◽  
Perfect Equilibrium

The ultimatum game, by its all-or-nothing nature, makes it difficult to discern what kind of preferences may be generating choices. We explore a game that convexifies the decisions, allowing us a better look at the indifference curves of bargainers while maintaining the subgame-perfect equilibrium. We conclude that bargainers' preferences are convex and regular but not always monotonic. Money-maximization is the sole concern for about half of the subjects, while the other half reveal a preference for fairness. We also found, unexpectedly, the importance of risk aversion among money-maximizing proposers, which in turn generates significant bargaining power for fair-minded responders.

scholarly journals Cooperate without looking: Why we care what people think and not just what they do

2015 ◽  
Vol 112 (6) ◽  
pp. 1727-1732 ◽  
Author(s):  
Moshe Hoffman ◽  
Erez Yoeli ◽  
Martin A. Nowak
Keyword(s):  
Game Theory ◽  
Evolutionary Game Theory ◽  
Evolutionary Game ◽  
Subgame Perfect Equilibrium ◽  
Categorical Imperative ◽  
Population Based ◽  
Theory Model ◽  
The Other ◽  
Perfect Equilibrium ◽  
Human Interactions

Evolutionary game theory typically focuses on actions but ignores motives. Here, we introduce a model that takes into account the motive behind the action. A crucial question is why do we trust people more who cooperate without calculating the costs? We propose a game theory model to explain this phenomenon. One player has the option to “look” at the costs of cooperation, and the other player chooses whether to continue the interaction. If it is occasionally very costly for player 1 to cooperate, but defection is harmful for player 2, then cooperation without looking is a subgame perfect equilibrium. This behavior also emerges in population-based processes of learning or evolution. Our theory illuminates a number of key phenomena of human interactions: authentic altruism, why people cooperate intuitively, one-shot cooperation, why friends do not keep track of favors, why we admire principled people, Kant’s second formulation of the Categorical Imperative, taboos, and love.

scholarly journals Weak Berge Equilibrium in Finite Three-person Games: Conception and Computation

2020 ◽  
Vol 11 (1) ◽  
pp. 127-134
Author(s):  
Konstantin Kudryavtsev ◽  
Ustav Malkov
Keyword(s):  
Cooperative Games ◽  
Hippocratic Oath ◽  
The Other ◽  
Mixed Strategies ◽  
Finite Games ◽  
Moral Basis ◽  
Other Hand ◽  
Berge Equilibrium ◽  
Do No Harm ◽  
Non Cooperative Games

AbstractThe paper proposes the concept of a weak Berge equilibrium. Unlike the Berge equilibrium, the moral basis of this equilibrium is the Hippocratic Oath “First do no harm”. On the other hand, any Berge equilibrium is a weak Berge equilibrium. But, there are weak Berge equilibria, which are not the Berge equilibria. The properties of the weak Berge equilibrium have been investigated. The existence of the weak Berge equilibrium in mixed strategies has been established for finite games. The weak Berge equilibria for finite three-person non-cooperative games are computed.

Step-by-Step: The Subgame-Perfect Equilibrium

2020 ◽  
pp. 125-140
Author(s):  
Manfred J. Holler ◽  
Barbara Klose-Ullmann
Keyword(s):  
Subgame Perfect Equilibrium ◽  
Perfect Equilibrium

scholarly journals Holographic RG flows and Janus solutions from matter-coupled $$N=4$$ gauged supergravity

2021 ◽  
Vol 81 (6) ◽  
Author(s):  
Parinya Karndumri
Keyword(s):  
Gauge Group ◽  
The Other ◽  
Three Dimensions ◽  
New Class ◽  
Other Hand ◽  
Genuine Solution ◽  
Coupled Theory

AbstractWe study an $$SO(2)\times SO(2)\times SO(2)\times SO(2)$$ S O ( 2 ) × S O ( 2 ) × S O ( 2 ) × S O ( 2 ) truncation of four-dimensional $$N=4$$ N = 4 gauged supergravity coupled to six vector multiplets with $$SO(4)\times SO(4)$$ S O ( 4 ) × S O ( 4 ) gauge group and find a new class of holographic RG flows and supersymmetric Janus solutions. In this truncation, there is a unique $$N=4$$ N = 4 supersymmetric $$AdS_4$$ A d S 4 vacuum dual to an $$N=4$$ N = 4 SCFT in three dimensions. In the presence of the axion, the RG flows generally preserve $$N=2$$ N = 2 supersymmetry while the supersymmetry is enhanced to $$N=4$$ N = 4 for vanishing axion. We find solutions interpolating between the $$AdS_4$$ A d S 4 vacuum and singular geometries with different residual symmetries. We also show that all the singularities are physically acceptable within the framework of four-dimensional gauged supergravity. Accordingly, the solutions are holographically dual to RG flows from the $$N=4$$ N = 4 SCFT to a number of non-conformal phases in the IR. We also find $$N=4$$ N = 4 and $$N=2$$ N = 2 Janus solutions with $$SO(4)\times SO(4)$$ S O ( 4 ) × S O ( 4 ) and $$SO(2)\times SO(2)\times SO(3)\times SO(2)$$ S O ( 2 ) × S O ( 2 ) × S O ( 3 ) × S O ( 2 ) symmetries, respectively. The former is obtained from a truncation of all scalars from vector multiplets and can be regarded as a solution of pure $$N=4$$ N = 4 gauged supergravity. On the other hand, the latter is a genuine solution of the full matter-coupled theory. These solutions describe conformal interfaces in the $$N=4$$ N = 4 SCFT with $$N=(4,0)$$ N = ( 4 , 0 ) and $$N=(2,0)$$ N = ( 2 , 0 ) supersymmetries.

Quantifying Commitment in Nash Equilibria

2019 ◽  
Vol 21 (02) ◽  
pp. 1940011
Author(s):  
Thomas A. Weber
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
Nash Equilibria ◽  
Dynamic Game ◽  
Subgame Perfect Equilibrium ◽  
Canonical Extension ◽  
Perfect Equilibrium ◽  
Form Game ◽  
Normal Form Game ◽  
The Given

To quantify a player’s commitment in a given Nash equilibrium of a finite dynamic game, we map the corresponding normal-form game to a “canonical extension,” which allows each player to adjust his or her move with a certain probability. The commitment measure relates to the average overall adjustment probabilities for which the given Nash equilibrium can be implemented as a subgame-perfect equilibrium in the canonical extension.

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