Cooperative equilibria in differential games

Tolwinski, Boleslaw; Haurie, Alain; Leitmann, G.

doi:10.1016/0022-247x(86)90152-6

Cited by 90 publications

(32 citation statements)

References 11 publications

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“…(Friedman, 1971;Malafeyev, 2000;Olsder, 2001;Ramasubraanian, 2007;Tolwinski, Haurie & Leitmann, 1986) for informative discussions, including links with viscosity solutions of the systems of HJB equations. It is not our objective here to contribute to this development.…”

Section: Several Players With Coupled Mean-field Interactionmentioning

confidence: 99%

Nonlinear Markov Games on a Finite State Space (Mean-field and Binary Interactions)

Kolokoltsov¹

2012

IJSP

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Managing large complex stochastic systems, including competitive interests, when one or several players can control the behavior of a large number of particles (agents, mechanisms, vehicles, subsidiaries, species, police units, etc), say N k for a player k, the complexity of the game-theoretical (or Markov decision) analysis can become immense as N k → ∞. However, under rather general assumptions, the limiting problem as all N k → ∞ can be described by a well manageable deterministic evolution. In this paper we analyze some simple situations of this kind proving the convergence of Nashequilibria for finite games to equilibria of a limiting deterministic differential game.

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Section: Several Players With Coupled Mean-field Interactionmentioning

confidence: 99%

Nonlinear Markov Games on a Finite State Space (Mean-field and Binary Interactions)

Kolokoltsov¹

2012

IJSP

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“…This last inequality means that the incentive strategy works also as a trigger strategy (see, for example, [14][15][16]), against possible deviation of Player 2 in the set U 2 . In Figure 5, we can observe, with more detail, the mechanism through which the incentive defined by (7) is able to annihilate the possible advantage of a deviating player.…”

Section: Credibilitymentioning

confidence: 99%

“…The first is to use trigger strategies (see, for example, [14][15][16]). In the 80s [14,15], among others, showed how the use of control-dependent memory strategies permits the inclusion of a threat in a cooperative strategy, which leads to a class of acceptable equilibria in dynamic games.…”

Section: Introductionmentioning

confidence: 99%

“…In the 80s [14,15], among others, showed how the use of control-dependent memory strategies permits the inclusion of a threat in a cooperative strategy, which leads to a class of acceptable equilibria in dynamic games. These strategies are based on past actions and they include a threat to punish, credibly and effectively, any player who cheats on the agreement.…”

Section: Introductionmentioning

confidence: 99%

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Does Flexibility Facilitate Sustainability of Cooperation Over Time? A Case Study from Environmental Economics

Frutos

Martín‐Herrán

2014

J Optim Theory Appl

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In this paper we present nonlinear incentive strategies that can be applied to a class of differential games that are frequently used in the literature, in particular, in environmental economics literature. We consider a class of nonlinear incentive functions that depend on the control variables of both players and on the current value of the state variable. The strategies are constructed to allow some flexibility in the sense that, unlike the common literature on the subject, the optimal state path evolves close to the cooperative trajectory. As a consequence of this flexibility, the incentive equilibrium is credible in a larger region than the one associated with the usual linear incentive strategies.

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“…Using this approach some process of preplay communication is needed to realise such a strategy. Aumann's approach has been extended in various manners (eg see [13,17,19,20,38]). The process of adapting correlated equilibria to stopping games starts from the idea of correlated stopping times.…”

Section: Introductionmentioning

confidence: 99%

Correlated equilibria in competitive staff selection problem

Ramsey

Szajowski

2006

Game Theory and Mathematical Economics

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Abstract. This paper deals with an extension of the concept of correlated strategies to Markov stopping games. The Nash equilibrium approach to solving nonzero-sum stopping games may give multiple solutions. An arbitrator can suggest to each player the decision to be applied at each stage based on a joint distribution over the players' decisions. This is a form of equilibrium selection. Examples of correlated equilibria in nonzero-sum games related to the staff selection competition in the case of two departments are given. Utilitarian, egalitarian, republican and libertarian concepts of correlated equilibria selection are used.

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Cooperative equilibria in differential games

Cited by 90 publications

References 11 publications

Nonlinear Markov Games on a Finite State Space (Mean-field and Binary Interactions)

Nonlinear Markov Games on a Finite State Space (Mean-field and Binary Interactions)

Does Flexibility Facilitate Sustainability of Cooperation Over Time? A Case Study from Environmental Economics

Correlated equilibria in competitive staff selection problem

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