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Journal of Quantitative Economics
Erschienen in: Journal of Quantitative Economics 4/2019

16.04.2019 | Original Article

Unilateral Support Equilibrium, Berge Equilibrium, and Team Problems Solutions

verfasst von: Bertrand Crettez

Erschienen in: Journal of Quantitative Economics | Ausgabe 4/2019

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Abstract

We compare two notions of equilibrium for other-regarding agents, namely Berge and unilateral support equilibria. A Berge equilibrium is a strategy profile such that the teammates of each agent choose their strategies in order to maximize his utility. A unilateral support equilibrium is a strategy profile such that the teammates of each agent non-cooperatively choose their strategies to maximize his utility. By definition the level of cooperation in a unilateral support equilibrium is no higher than in a Berge equilibrium. Yet, relying on ideas from Team theory, we provide conditions under which a unilateral support equilibrium is also a Berge equilibrium. We also provide conditions under which a unilateral support equilibrium is a Berge–Vaisman equilibrium, i.e., a strategy profile which is a Berge equilibrium and such that the payoff of each player is no lower than his maximin value.
Vorheriger Artikel Production Sectors and Regions in Macroeconometric Models of India
Nächster Artikel Political Risk and Real Exchange Rate: What Can We Learn from Recent Developments in Panel Data Econometrics for Emerging and Developing Countries?

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Fußnoten
1
In French, “point d’équilibre pour P relativement à un ensemble K de joueurs.”
 
2
Courtois et al. (2018) call this equilibrium a coalitional Berge equilibrium.
 
3
A presentation and a history of Berge equilibrium can be found in Collman et al. (2011) as well as in Courtois et al. (2015). A recent survey of this notion is proposed by Larmani and Zhukovskii (2017).
 
4
We shall always assume that the maximum and the minimum are realized.
 
5
Studies of Berge–Vaisman equilibrium can be found in Collman et al. (2011), Larbani and Nessah (2008), Musy et al. (2012), Crettez (2017a) and Courtois et al. (2018).
 
6
Existence results for the notions of Berge equilibrium, Berge–Vaisman equilibrium, Berge–Nash equilibrium and coalitional Berge equilibrium can be found in Courtois et al. (2018).
 
7
Of course, the donnees usually do not give to the donators. To account for this fact we may assume that the payoff functions of the donators do not depend on the decisions of the donnees.
 
8
Saflaty and Abdou (2018) use tensors to study the relationship between unilateral support equilibria, Nash and Berge equilibria.
 
9
In this paper we disregard the possibility that agents base their actions on different information sets. Heterogeneity in information is a key assumption in Team theory (see Radner 1991, for a quick presentation of Team theory).
 
10
See also Başar (2017).
 
11
A function \(f : D \subseteq \mathbb {R}^n \rightarrow \mathbb {R}\) is pseudoconcave if for all \(\mathbf {x}_{0}\) and \(\mathbf {x}\) in D, \(\nabla f(\mathbf {x}_{0})(\mathbf {x}-\mathbf {x}_{0}) \le 0 \Rightarrow f(\mathbf {x}) \le f(\mathbf {x}_{0})\).
 
12
The parameter \(\rho \) represents a tipping point of the game.
 
13
In this inequation \(U_k(\mathbf {s}^*_{G}, \mathbf {s}_{N \setminus G})\) is the utility of player k when all the group members follow the practice while the non-members play the strategy profile \(\mathbf {s}_{N \setminus G}\).
 
14
The notion of strict unilateral support equilibrium parallels that of a strict Nash equilibrium (see, e.g., Peters 2008, p. 118).
 
15
We indeed have for all \(G \not = N\), for all i in G, and for all \(j \not \in G\), \( \min _{ \mathbf {s}_{N \setminus G} \in \Pi _{j \in N \setminus G} S_j, } U_i(\mathbf {s}^u_{G}, \mathbf {s}_{N \setminus G}) \le U_{i}(s^u_{i}, s_{j},\mathbf {s^u}_{- \lbrace i, j \rbrace }) < U_{i}(\mathbf {s}^u)\) for \(s_j \not = s_j^u\).
 
16
In what follows we adapt to unilateral support equilibrium what was done for Berge equilibrium in Crettez (2017b).
 
Literatur
Abalo, Kokou Y., and Michael M. Kostreva. 2004. Some existence theorems of Nash and Berge equilibria. Applied Mathematics Letters 17: 569–573.CrossRef
Başar, Tamer. 2017. Introduction to the theory of games. In Handbook of dynamic game theory, ed. T. Başar, and G. Zaccour. New York: Springer.
Berge, Claude. 1957. Théorie générale des jeux à n personnes [General theory of n-person games], Paris, Gauthier-Villars. This document is available at Théorie des jeux à \(n\) personnes.
Brooks, Richard. 2018. Loyalty and agency in economic theory, Working paper.
Colman, Andrew M., Briony D. Pulford, and Jo Rose. 2008. Collective rationality in interactive decisions: Evidence for team reasoning. Acta Psychologica 128: 387–397.CrossRef
Collman, Andrew M., Tom W. Koerner, Musy Olivier, and Tarik Tazdait. 2011. Mutual support in games: Some properties of Berge equilibria. Journal of Mathematical Psychology 55 (2): 166–175.CrossRef
Courtois, Pierre, Nessah Rabia, and Tarik Tazdait. 2015. How to play games? Nash versus Berge behavior rules. Economics and Philosophy 31 (1): 123–139.CrossRef
Courtois, Pierre, Nessah Rabia, and Tarik Tazdait. 2018. Existence and computation of Berge equilibrium and of two refinements. Journal of Mathematical Economics 72: 7–15.CrossRef
Crettez, Bertrand. 2017. A new sufficient condition for a Berge equilibrium to be a Berge–Vaisman equilibrium. Journal of Quantitative Economics 15 (3): 451–459.CrossRef
Crettez, Bertrand. 2017. On Sugden’s “mutually beneficial practice” and Berge equilibrium. International Review of Economics 64 (4): 357–366.CrossRef
Guala, Francesco, Mittone Luigi, and Matteo Ploner. 2013. Group membership, team preferences and expectations. Journal of Economic Behavior and Organization 86: 183–190.CrossRef
Larbani, Moussa, and Vladislav Iiosifovich Zhukovskii. 2017. Berge equilibrium in normal form static games: A literature review. Izv. IMI UdGU 49: 80110.
Larbani, Moussa, and Rabia Nessah. 2008. A note on the existence of Berge and Berge–Nash equilibria. Mathematical Social Sciences 55: 258–271. (Recent).CrossRef
Marschak, Jabob. 1955. Elements for a theory of teams. Management Science 1 (2): 127–137.CrossRef
Musy, Olivier, Pottier Antonin, and Tarik Tazdait. 2012. A new theorem to find Berge equilibria. International Game Theory Review 14 (1): 1250005-1–1250005-10.CrossRef
Ok, Efe A. 2007. Real analysis with economic applications. Princeton: Princeton University Press.CrossRef
Saflaty, E., and J. E. Abdou. 2018. A new tensor approach of computing pure and mixed unilateral support Equilibria. Working paper, Faculty of Economics and Business Administration, Lebanese University, Beirut, Lebanon.
Schouten, Jop, Born, Peter, and Ruud Hendrickx. 2018. Unilateral support equilibria. Working paper, Tilburg University.
Sugden, Robert. 2015. Team reasoning and intentional cooperation for mutual benefit. Journal of Social Ontology 1 (1): 143166.CrossRef
Sugden, Robert. 2018. The community of advantage. Oxford: Oxford University Press.CrossRef
Radner, Roy. 1962. Team decision problems. The Annals of Mathematical Statistics 33 (3): 875–881.CrossRef
Radner, Roy. 1991. Teams. In The New Palgrave, vol. 4, ed. John Eatwell, Murray Migate, and Peter Newman, 613–616. London: The Macmillan Press Limited.
Zhukovskii, Vladislav I. 1985. Some Problems of Non-Antagonistic Differential Games, Mathematical Methods in Operations Research (in Russian), Bulgarian Academy of Science, Sofia, 103-195.
Zhukovskii, Vladislav I., and A. A. Chikrii. 1994. Linear-quadratic differential games, Kiev, Naukova Dumka (in Russian).
Metadaten
Titel
Unilateral Support Equilibrium, Berge Equilibrium, and Team Problems Solutions
verfasst von
Bertrand Crettez
Publikationsdatum
16.04.2019
Verlag
Springer India
Erschienen in
Journal of Quantitative Economics / Ausgabe 4/2019
Print ISSN: 0971-1554
Elektronische ISSN: 2364-1045
DOI
https://doi.org/10.1007/s40953-019-00168-w

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