768 research outputs found
Competitive Environments and Protective Behaviour
The class of two-person competition games is introduced and analyzed.For any game in this class the set of Nash equilibria is convex, equilibrium strategies are exchangeable, and all Nash equilibria lead to the same payoff vector. Competition games are compared to other competitive environments such as unilaterally competitive games and rivalry games.Moreover, protective behaviour within competitive environments is analyzed.For matrix games it is known that protective strategies pro¯les exactly correspond to proper equilibria.It is shown that this result can be extended to the class of unilaterally competitive games.competitive environments;unilaterally competitive games;rivalry games;competition games;protective strategies
On Properness and Protectiveness in Two Person Multicriteria Games
This paper extends the concepts of proper equilibria, protective behaviour and prudent behaviour to multicriteria games.Three types of proper equilibria based on different types of domination are introduced.It is shown that protective behaviour coincides with prudent behaviour.Possible relations and existence are analyzed.Multicriteria games;proper;protective;prudent
Deposit Games with Reinvestment
In a deposit game coalitions are formed by players combining their capital. The proceeds of their investments then have to be divided among those players. The current model extends earlier work on capital deposits by allowing reinvestment of returns. Two specific subclasses of deposit games are introduced. It is seen that each term dependent deposit game possesses a core element. Capital dependent deposit games are also shown to have a core element and even a population monotonic allocation scheme if the revenue function exhibits increasing returns to scale. Furthermore, it is shown that all superadditive games are deposit games if one allows for debt.cooperative game theory;deposit games;core elements;population monotonic allo- cation schemes;superadditive games
Transfers, Contracts and Strategic Games
This paper analyses the role of transfer payments and strategic con- tracting within two-person strategic form games with monetary pay- offs. First, it introduces the notion of transfer equilibrium as a strat- egy combination for which individual stability can be supported by allowing the possibility of transfers of the induced payoffs. Clearly, Nash equilibria are transfer equilibria, but under common regularity conditions the reverse is also true. This result typically does not hold for finite games without the possibility of randomisation, and transfer equilibria for this particular class are studied in some detail. The second part of the paper introduces, also within the setting of finite games, contracting on monetary transfers as an explicit strategic option, resulting in an associated two-stage contract game. In the first stage of the contract game each player has the option of proposing transfer schemes for an arbitrary collection of outcomes. Only if the players fully agree on the entire set of transfer proposals, the payoffs of the game to be played in the second stage are modified accordingly. The main results provide explicit characterisations of the sets of payoff vectors that are supported by Nash equilibrium and virtual subgame perfect equilibrium, respectively.monetary transfer scheme;transfer equilibrium;contract game;virtual subgame perfect equilibrium;Folk theorems
Characterizing Cautious Choice
The class of maximin actions in general decision problems is characterized.Maximin actions;Decision problems
Effects of turbulence and rotation on protostar formation as a precursor to seed black holes
Context. The seeds of the first supermassive black holes may have resulted
from the direct collapse of hot primordial gas in K haloes,
forming a supermassive or quasistar as an intermediate stage.
Aims. We explore the formation of a protostar resulting from the collapse of
primordial gas in the presence of a strong Lyman-Werner radiation background.
Particularly, we investigate the impact of turbulence and rotation on the
fragmentation behaviour of the gas cloud. We accomplish this goal by varying
the initial turbulent and rotational velocities.
Methods. We performed 3D adaptive mesh refinement simulations with a
resolution of 64 cells per Jeans length using the ENZO code, simulating the
formation of a protostar up to unprecedentedly high central densities of
cm, and spatial scales of a few solar radii. To achieve this
goal, we employed the KROME package to improve modelling of the chemical and
thermal processes.
Results. We find that the physical properties of the simulated gas clouds
become similar on small scales, irrespective of the initial amount of
turbulence and rotation. After the highest level of refinement was reached, the
simulations have been evolved for an additional ~5 freefall times. A single
bound clump with a radius of AU and a mass of ~ M is formed at the end of each simulation, marking the onset
of protostar formation. No strong fragmentation is observed by the end of the
simulations, regardless of the initial amount of turbulence or rotation, and
high accretion rates of a few solar masses per year are found.
Conclusions. Given such high accretion rates, a quasistar of
M is expected to form within years.Comment: 18 pages, 7 figures, fixed typos, added references and clarified some
details; accepted for publication in A&
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