scholarly journals A Mixed Cooperative Dual to the Nash Equilibrium

Game Theory ◽  
2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
H. W. Corley
Keyword(s):  
Nash Equilibrium ◽  
Mixed Strategy ◽  
The Other ◽  
Mixed Strategies ◽  
Mutual Support ◽  
Equilibrium Models ◽  
Expected Payoff ◽  
Berge Equilibrium

A mixed dual to the Nash equilibrium is defined for n-person games in strategic form. In a Nash equilibrium every player’s mixed strategy maximizes his own expected payoff for the other n-1 players’ strategies. Conversely, in the dual equilibrium every n-1 players have mixed strategies that maximize the remaining player’s expected payoff. Hence this dual equilibrium models mutual support and cooperation to extend the Berge equilibrium from pure to mixed strategies. This dual equilibrium is compared and related to the mixed Nash equilibrium, and both topological and algebraic conditions are given for the existence of the dual. Computational issues are discussed, and it is shown that for each n>2 there exists a game for which no dual equilibrium exists.

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.

On the Foundations of Nash Equilibrium

1996 ◽  
Vol 12 (1) ◽  
pp. 67-88 ◽  
Author(s):  
Hans Jørgen Jacobsen
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Cooperative Game Theory ◽  
Mixed Strategy ◽  
Pure Strategy ◽  
Mixed Strategies ◽  
Positive Theory ◽  
Equilibrium Concept ◽  
Strategy Equilibrium ◽  
Pure Strategies

The most important analytical tool in non-cooperative game theory is the concept of a Nash equilibrium, which is a collection of possibly mixed strategies, one for each player, with the property that each player's strategy is a best reply to the strategies of the other players. If we do not go into normative game theory, which concerns itself with the recommendation of strategies, and focus instead entirely on the positive theory of prediction, two alternative interpretations of the Nash equilibrium concept are predominantly available.In the more traditional one, a Nash equilibrium is a prediction of actual play. A game may not have a Nash equilibrium in pure strategies, and a mixed strategy equilibrium may be difficult to incorporate into this interpretation if it involves the idea of actual randomization over equally good pure strategies. In another interpretation originating from Harsanyi (1973a), see also Rubinstein (1991), and Aumann and Brandenburger (1991), a Nash equilibrium is a ‘consistent’ collection of probabilistic expectations, conjectures, on the players. It is consistent in the sense that for each player each pure strategy, which has positive probability according to the conjecture about that player, is indeed a best reply to the conjectures about others.

scholarly journals A stochastic differential reinsurance game

2010 ◽  
Vol 47 (2) ◽  
pp. 335-349 ◽  
Author(s):  
Xudong Zeng
Keyword(s):  
Nash Equilibrium ◽  
Differential Game ◽  
Payoff Function ◽  
The Other ◽  
Insurance Companies ◽  
Stochastic Differential Game ◽  
Claim Size ◽  
Expected Payoff ◽  
Exit Probability ◽  
Risk Of Exposure

We study a stochastic differential game between two insurance companies who employ reinsurance to reduce the risk of exposure. Under the assumption that the companies have large insurance portfolios compared to any individual claim size, their surplus processes can be approximated by stochastic differential equations. We formulate competition between the two companies as a game with a single payoff function which depends on the surplus processes. One company chooses a dynamic reinsurance strategy in order to maximize this expected payoff, while the other company simultaneously chooses a dynamic reinsurance strategy so as to minimize the same quantity. We describe the Nash equilibrium of this stochastic differential game and solve it explicitly for the case of maximizing/minimizing the exit probability.

scholarly journals A stochastic differential reinsurance game

2010 ◽  
Vol 47 (02) ◽  
pp. 335-349 ◽  
Author(s):  
Xudong Zeng
Keyword(s):  
Nash Equilibrium ◽  
Differential Game ◽  
Payoff Function ◽  
The Other ◽  
Insurance Companies ◽  
Stochastic Differential Game ◽  
Claim Size ◽  
Expected Payoff ◽  
Exit Probability ◽  
Risk Of Exposure

We study a stochastic differential game between two insurance companies who employ reinsurance to reduce the risk of exposure. Under the assumption that the companies have large insurance portfolios compared to any individual claim size, their surplus processes can be approximated by stochastic differential equations. We formulate competition between the two companies as a game with a single payoff function which depends on the surplus processes. One company chooses a dynamic reinsurance strategy in order to maximize this expected payoff, while the other company simultaneously chooses a dynamic reinsurance strategy so as to minimize the same quantity. We describe the Nash equilibrium of this stochastic differential game and solve it explicitly for the case of maximizing/minimizing the exit probability.

A NEW THEOREM TO FIND BERGE EQUILIBRIA

2012 ◽  
Vol 14 (01) ◽  
pp. 1250005 ◽  
Author(s):  
OLIVIER MUSY ◽  
ANTONIN POTTIER ◽  
TARIK TAZDAIT
Keyword(s):  
Nash Equilibrium ◽  
Mutual Support ◽  
Berge Equilibrium

This paper examines the existence of Berge equilibrium. Colman et al. provide a theorem on the existence of this type of equilibrium in the paper [Colman, A. M., Körner, T. W., Musy, O. and Tazdaït, T. [2011] Mutual support in games: Some properties of Berge equilibria, J. Math. Psychol.55, 166–175]. This theorem has been demonstrated on the basis of a correspondence with Nash equilibrium. We propose to restate this theorem without using Nash equilibrium, and deduce a method for the computation of Berge equilibria.

scholarly journals Beating your Neighbor to the Berry Patch

2020 ◽  
Author(s):  
Alan R. Rogers
Keyword(s):  
Nash Equilibrium ◽  
Mixed Strategy ◽  
Human Subjects ◽  
Pure Strategy ◽  
Initial Period ◽  
Mean Value ◽  
Mixed Strategies ◽  
The Mean ◽  
The Cost ◽  
Evolutionarily Stable

AbstractThis paper studies the situation in which multiple foragers compete for a resource that ripens (or otherwise improves) gradually. There is a unique mixed Nash Equilibrium (NE), which is stable against pure-strategy invaders provided that either the cost of visiting the resource or number of competitors is large. This equilibrium is not evolutionarily stable, however, because mixed strategies that are similar to the NE can invade.This mixed-strategy instability was not observed in computer simulations. The process converged to the neighborhood of the NE whenever the parameters implied stablity against pure-strategy invaders. Experiments with human subjects also failed to exhibit this mixed-strategy instability. After an initial period of familiarization, the behavior of human subjects was close to that predicted by the NE.This suggests that the NE may be useful as a prediction of behavior, and when that it true, strange conclusions emerge: the larger the number of foragers, the less likely it is that the resource will be harvested at all, and the greater the mean value of that resource when it is harvested.

MONTE CARLO METHODS IN FUZZY GAME THEORY

2007 ◽  
Vol 03 (02) ◽  
pp. 259-269 ◽  
Author(s):  
AREEG ABDALLA ◽  
JAMES BUCKLEY
Keyword(s):  
Game Theory ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Monte Carlo Methods ◽  
Mixed Strategy ◽  
Minimax Theorem ◽  
Approximate Solutions ◽  
Mixed Strategies ◽  
Fuzzy Game ◽  
Zero Sum

In this paper, we consider a two-person zero-sum game with fuzzy payoffs and fuzzy mixed strategies for both players. We define the fuzzy value of the game for both players [Formula: see text] and also define an optimal fuzzy mixed strategy for both players. We then employ our fuzzy Monte Carlo method to produce approximate solutions, to an example fuzzy game, for the fuzzy values [Formula: see text] for Player I and [Formula: see text] for Player II; and also approximate solutions for the optimal fuzzy mixed strategies for both players. We then look at [Formula: see text] and [Formula: see text] to see if there is a Minimax theorem [Formula: see text] for this fuzzy game.

scholarly journals TOLERANSI ANTAR PENGANUT NAHDHATUL ULAMA, MUHAMMADIYAH, DAN KRISTEN JAWA DI BATANG

2013 ◽  
Vol 5 (1) ◽  
Author(s):  
Adistya Iqbal Irfani, ◽  
Moh. Yasir Alimi ◽  
Rini Iswari
Keyword(s):  
Research Method ◽  
Qualitative Method ◽  
Point Of View ◽  
The Other ◽  
Mixed Marriage ◽  
Mutual Support ◽  
Administrative Leaders ◽  
Religious Aspects ◽  
The Village

Tujuan penelitian ini adalah untuk mengeksplorasi bentuk toleransi dan faktor pendorong dan faktor penghambat toleransi masyarakat Jawa dengan studi kasus di Dukuh Medono Kabupaten Batang. Di dukuh tersebut, penganut organisasi agama seperti NU, Muhammadiyah dan Kristen Jawa di Dukuh Medono saling hidup rukun. Metode penelitian menggunakan metode penelitian kualitatif dengan pendekatan fenomenologi. Hasil penelitian menunjukan bahwa toleransi antar penganut NU, Muhammadiyah, Kristen Jawa tampak berbagai bentuk. Antara NU dan Kristen Jawa dalam bentuk partisipasi dalam ritual tahlilan, sedangkan antar ketiganya tampak dalam bentuk kerja bakti, saling membantu dalam acara hajatan, perkawinan campur dan saling berkunjung bila ada yang sakit. Faktor pendorong toleransi antara lain budaya toleransi yang sudah lama, pernikahan antar penganut yang berbeda, sosialisasi toleransi dalam keluarga, dan kepemimpinan desa yang menekankan pentingnya toleransi. Sedangkan faktor penghambat toleransi yaitu perbedaan pandangan antar penganut NU dan Muhammadiyah dalam pelaksanaan ibadah, pernikahan beda keyakinan, dan sikap menyinggung keyakinan diantara penganut yang ada. The objective of this study is to explore forms of tolerance and the driving factor of religious tolerance in Dukuh Medono, Batang. In that village, the followers of NU, Muhammadiyah, and Kristen Jawa live peacefully and united in tolerance. The research method used here is a qualitative method with phenomenology approach. The result of the research shows that the tolerance between NU followers and Javanese Christians take the form of participation in tahlilan ritual. The tolerance between NU, Muhammadiyah followers, and Kristen Jawa followers are expressed through kerja bakti, mutual support in hajatan rituals, mixed marriage, visits to the sick, and social activities together. The factors which help to create tolerance include the culture of tolerance which exist in the village, marriages between religious followers, the socialization of tolerance within family, the socialization of tolerance within the society and the role of village administrative leaders. On the other hand, the factors which distract tolerance are different point of view between NU dan Muhammadiyah followers in some religious aspects, marriage between different religious followers, and the attitude of insulting others beliefs.

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