“Backward” coinduction, Nash equilibrium and the rationality of escalation

Lescanne, Pierre; Perrinel, Matthieu

doi:10.1007/s00236-012-0153-3

Cited by 17 publications

(26 citation statements)

References 26 publications

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“…Zero sum games are the situations where one or more players' gain (loss) equals the loss (gain) of other players. Therefore, a gain (loss) for one must result in a loss (gain) for one or more others, which simply means one player gains the equal amount that its opponent losses [27,28]. On the other hand, when the final result of all players is not zero, the game is anon-zero sum game [24,29].…”

Section: Zero-sum and Non Zero-sum Gamesmentioning

confidence: 99%

Numeric Evaluation of Game-Theoretic Collaboration Modes in Supplier Development

Dastyar

Pannek

2019

Applied Sciences

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To deal with increasingly competitive challenges, today’s companies consider supplier performance as a crucial factor to their competitive advantage. Supplier development is one of the recent approaches to supplier performance enhancement and consistently requires relationship-specific investments. It is important to invest money, experts and/or machines in a supplier to minimize the risk of an inefficient supply chain while maximizing the level of profitability. This paper provides the number of optimization models to confront this issue utilizing Model Predictive Control. We consider a centralized and distributed setting with two manufacturers and one supplier, which enables us to simulate more realistic scenarios. We implement cooperative and non-cooperative scenarios to assess their impact on the manufacturers’ revenue. Results reveal that the cooperative setting between manufacturers pays off better than non-cooperative and collaborative settings in long-term investments. However, for short-term investments, the non-cooperative setting performs better than the others. We can conclude that, in short-term supplier development investments, an added value is generated since both the manufacturers and the supplier gain flexibility, therefore, investing separately can end up with higher profit for both manufacturers.

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Section: Zero-sum and Non Zero-sum Gamesmentioning

confidence: 99%

Numeric Evaluation of Game-Theoretic Collaboration Modes in Supplier Development

Dastyar

Pannek

2019

Applied Sciences

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“…In 2006 Coq was used by [19], which was generalized by [13], to formalize and check a result from game theory: Kuhn's existence of a Nash equilibrium (NE) in finite games in extensive form. Coq was also used to deal with some infinite games in extensive form [15], or with random Boolean games [17]. Isabelle/HOL, another proof software, was used recently [6] to formalize and check a result in game theory for logic and computer science: the positional determinacy of parity games.…”

Section: Introduction and Motivationsmentioning

confidence: 99%

“…• The result features games in normal form, a very general class of games that includes finite and infinite games in extensive form discussed in [19], [13], [15] and [16], and Muller and parity games discussed in [10], [7], [6], and [4].…”

Section: Introduction and Motivationsmentioning

confidence: 99%

An Existence Theorem of Nash Equilibrium in Coq and Isabelle

Roux

Martin-Dorel

Smaus

2017

Electron. Proc. Theor. Comput. Sci.

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Nash equilibrium (NE) is a central concept in game theory. Here we prove formally a published theorem on existence of an NE in two proof assistants, Coq and Isabelle: starting from a game with finitely many outcomes, one may derive a game by rewriting each of these outcomes with either of two basic outcomes, namely that Player 1 wins or that Player 2 wins. If all ways of deriving such a win/lose game lead to a game where one player has a winning strategy, the original game also has a Nash equilibrium. This article makes three other contributions: first, while the original proof invoked linear extension of strict partial orders, here we avoid it by generalizing the relevant definition. Second, we notice that the theorem also implies the existence of a secure equilibrium, a stronger version of NE that was introduced for model checking. Third, we also notice that the constructive proof of the theorem computes secure equilibria for non-zero-sum priority games (generalizing parity games) in quasi-polynomial time.Comment: In Proceedings GandALF 2017, arXiv:1709.0176

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“…Other approaches use dependent types to allow types of choices to dependent on earlier values, but can still only allow more general 'dependent subgames' such as in the market entry game using encoding tricks such as dummy moves, and using large negative utilities to rule out certain plays. (Examples of game theory developed in a dependent type system include [13], [2].) An external choice operator solves the more general problem of dependent subgames in an elegant way.…”

Section: Example: Market Entry Gamementioning

confidence: 99%

Morphisms of Open Games

Hedges

2018

Electronic Notes in Theoretical Computer Science

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We define a notion of morphisms between open games, exploiting a surprising connection between lenses in computer science and compositional game theory. This extends the more intuitively obvious definition of globular morphisms as mappings between strategy profiles that preserve best responses, and hence in particular preserve Nash equilibria. We construct a symmetric monoidal double category in which the horizontal 1-cells are open games, vertical 1-morphisms are lenses, and 2cells are morphisms of open games. States (morphisms out of the monoidal unit) in the vertical category give a flexible solution concept that includes both Nash and subgame perfect equilibria. Products in the vertical category give an external choice operator that is reminiscent of products in game semantics, and is useful in practical examples. We illustrate the above two features with a simple worked example from microeconomics, the market entry game.

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“Backward” coinduction, Nash equilibrium and the rationality of escalation

Cited by 17 publications

References 26 publications

Numeric Evaluation of Game-Theoretic Collaboration Modes in Supplier Development

Numeric Evaluation of Game-Theoretic Collaboration Modes in Supplier Development

An Existence Theorem of Nash Equilibrium in Coq and Isabelle

Morphisms of Open Games

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