Fall Back Equilibrium

Fall back equilibrium is a refinement of the Nash equilibrium concept. In the underly- ing thought experiment each player faces the possibility that, after all players decided on their action, his chosen action turns out to be blocked. Therefore, each player has to decide beforehand on a back-up action, which he plays in case he is unable to play his primary action. In this paper we introduce the concept of fall back equilibrium and show that the set of fall back equilibria is a non-empty and closed subset of the set of Nash equilibria. We discuss the relations with other equilibrium concepts, and among other results it is shown that each robust equilibrium is fall back and for bimatrix games also each proper equilibrium is a fall back equilibrium. Furthermore, we show that for bimatrix games the set of fall back equilibria is the union of finitely many polytopes, and that the notions of fall back equilibrium and strictly fall back equilibrium coincide. Finally, we allow multiple actions to be blocked, resulting in the notion of complete fall back equilibrium. We show that the set of complete fall back equilibria is a non-empty and closed subset of the set of proper equilibria.strategic game;equilibrium refinement;blocked action;fall back equilibrium

Modelling interactive behaviour, and solution concepts

The final chapter of this thesis extensively studies fall back equilibrium. This equilibrium concept is a refinement of Nash equilibrium, which is the most fundamental solution concept in non-cooperative game theory.

Modelling interactive behaviour, and solution concepts.

The final chapter of this thesis extensively studies fall back equilibrium. This equilibrium concept is a refinement of Nash equilibrium, which is the most fundamental solution concept in non-cooperative game theory.

Fall back proper equilibrium

Proper equilibrium plays a prominent role in the literature on non-cooperative games. The underlying thought experiment in which the players play a passive role is, however, unsatisfying, as it gives no justification for its fundamental idea that severe mistakes are made with a significantly smaller probability than innocuous ones. In this paper, we introduce a more active role for the players, leading to the refinement of fall back proper equilibrium

Discovery of a natural CO2 seep in the German North Sea: implications for shallow dissolved gas and seep detection

A natural carbon dioxide (CO2) seep was discovered during an expedition to the southern German North Sea (October 2008). Elevated CO2 levels of ∼10–20 times above background were detected in seawater above a natural salt dome ∼30 km north of the East-Frisian Island Juist. A single elevated value 53 times higher than background was measured, indicating a possible CO2 point source from the seafloor. Measured pH values of around 6.8 support modeled pH values for the observed high CO2 concentration. These results are presented in the context of CO2 seepage detection, in light of proposed subsurface CO2 sequestering and growing concern of ocean acidification. We explore the boundary conditions of CO2 bubble and plume seepage and potential flux paths to the atmosphere. Shallow bubble release experiments conducted in a lake combined with discrete-bubble modeling suggest that shallow CO2 outgassing will be difficult to detect as bubbles dissolve very rapidly (within meters). Bubble-plume modeling further shows that a CO2 plume will lose buoyancy quickly because of rapid bubble dissolution while the newly CO2-enriched water tends to sink toward the seabed. Results suggest that released CO2 will tend to stay near the bottom in shallow systems (<200 m) and will vent to the atmosphere only during deep water convection (water column turnover). While isotope signatures point to a biogenic source, the exact origin is inconclusive because of dilution. This site could serve as a natural laboratory to further study the effects of carbon sequestration below the seafloor

Solutions in multi-actor projects with collaboration and strategic incentives

This dissertation focuses on the mathematical analysis of projects involving decisions by multiple players. These players all have their own capabilities, requirements, and incentives, but their (monetary) outcome is dependent on the decisions of other players as well. Game theory is a mathematical tool to analyze the interactive decision-making process, generally paired with a method to ‘resolve’ the conflict situation. The way in which players interact in such a situation is commonly divided in two categories, distinguishing between cooperative and competitive (non-cooperative) behavior. This dissertation first studies two models within a cooperative framework, starting with the definition and analysis of a new influence measure for general, collaborative projects. The second model applies to situations where players cooperate on the construction of a new joint infrastructure, with a specific focus on cost allocation for CO2 transport infrastructure. Next, two-stage models are considered, in which a noncooperative first stage is followed by a cooperative second stage. Subsequently, social welfare loss in auctions with a corrupt auctioneer is studied. Finally, a new solution concept is presented that refines the notion of Nash equilibria for a general class of non-cooperative games

Fall Back Equilibrium

Fall back equilibrium is a refinement of the Nash equilibrium concept. In the underly- ing thought experiment each player faces the possibility that, after all players decided on their action, his chosen action turns out to be blocked. Therefore, each player has to decide beforehand on a back-up action, which he plays in case he is unable to play his primary action. In this paper we introduce the concept of fall back equilibrium and show that the set of fall back equilibria is a non-empty and closed subset of the set of Nash equilibria. We discuss the relations with other equilibrium concepts, and among other results it is shown that each robust equilibrium is fall back and for bimatrix games also each proper equilibrium is a fall back equilibrium. Furthermore, we show that for bimatrix games the set of fall back equilibria is the union of finitely many polytopes, and that the notions of fall back equilibrium and strictly fall back equilibrium coincide. Finally, we allow multiple actions to be blocked, resulting in the notion of complete fall back equilibrium. We show that the set of complete fall back equilibria is a non-empty and closed subset of the set of proper equilibria

Fall back equilibria

Fall back equilibrium is a refinement of the Nash equilibrium concept. In the underlying thought experiment each player faces the possibility that, after all players decided on their action, his chosen action turns out to be blocked. Therefore, each player has to decide beforehand on a back-up action, which he plays in case he is unable to play his primary action. In this paper we introduce the concept of fall back equilibrium, and discuss the relations with other Nash equilibrium refinements, in particular proper equilibrium. Furthermore, we show that for bimatrix games fall back equilibrium is a strict concept. We also consider the structure of the set of fall back equilibria for bimatrix games

Fall Back Equilibrium for 2 X n Bimatrix Games

Abstract: In this paper we provide a characterisation of the set of fall back equilibria for 2 x n bimatrix games. Furthermore, for this type of games we discuss the relation between the set of fall back equilibria and the sets of perfect, proper and strictly perfect equilibria. In order to do this we reformulate the existing characterizations for these three equilibrium concepts by the use of refinement-specific subgames.