Narrow Results

Results of our recent studies concerning possible effects of Λ > 0 for equilibrium positions of spinning test particles and stationary configurations of perfect-fluid tori are presented.

This paper deals with the qualitative analysis of a class of bilinear systems of equations describing the dynamics of individuals undergoing kinetic (stochastic) interactions. A corresponding evolution problem is formulated in terms of integro-differential (nonlocal) system of equations. A general existence theory is provided. Under the assumption of periodic boundary conditions and the interaction rates expressed in terms of convolution operators two classes of equilibrium solutions are distinguished. The first class contains only constant functions and the second one contains some nonconstant functions. In the scalar case (one equation) under suitable scaling, related to the shrinking of interaction range of each individual, the limit to the corresponding "macroscopic" equation is studied. The limiting equation turns out to be the (nonlinear) porous medium equation.

Well-balanced or asymptotic preserving schemes are receiving an increasing amount of interest. This paper gives a precise setting for studying both properties in the case of Euler system with friction. We derive a simple solver which, by construction, preserves discrete equilibria and reproduces at the discrete level the same asymptotic behavior as that of the solutions of the continuous system. Numerical illustrations are convincing and show that not all methods share these properties.

We deal with n-player coordination games with vanishing actions, which are repeated games where all non-diagonal entries yield zero-payoffs, and where, moreover, at any stage beyond r_i any player i loses any action that she has not used during the previous r_i stages of play. For these games we examine the set of equilibrium rewards, where we treat the two-player case and the more player case separately. Folk-theorem like results are established.

Infinite multistage games G with games Γ(·) played on each stage are considered. The definition of path and trajectory in graph tree are introduced. For infinite multistage games G a regularization procedure is introduced and in the regularizied game a strong Nash Equilibrium (coalition proof) is constructed. The approach considered in this paper is similar to one used in the proof of Folk theorems for infinitely repeated games. The repeated n-person "Prisoner's Dilemma" game is considered, as a special case. For this game a strong Nash Equilibrium is found.

The purpose of this paper is to present some simple properties and applications of dynamic games with discrete time and a continuum of players. For such games relations between dynamic equilibria and families of static equilibria in the corresponding static games, as well as between dynamic and static best response sets are examined and an equivalence theorem is proven. The existence of a dynamic equilibrium is also proven. These results are counterintuitive since they differ from results that can be obtained in similar games with a finite number of players.

The theoretical results are illustrated with examples describing voting and exploitation of ecological systems.

In this paper we consider dynamic games with continuum of players which can constitute a framework to model large financial markets. They are called semi-decomposable games.

In semi-decomposable games the system changes in response to a (possibly distorted) aggregate of players' decisions and the payoff is a sum of discounted semi-instantaneous payoffs. The purpose of this paper is to present some simple properties and applications of these games. The main result is an equivalence between dynamic equilibria and families of static equilibria in the corresponding static perfect-foresight games, as well as between dynamic and static best response sets. The existence of a dynamic equilibrium is also proven. These results are counterintuitive since they differ from results that can be obtained in games with a finite number of players.

The theoretical results are illustrated with examples describing large financial markets: markets for futures and stock exchanges.

We analyze the global stability of the equilibria in Bertrand and Cournot duopolies. Assuming a set of sufficient conditions for the global stability of the Bertrand duopoly equilibrium, we derive additional conditions which are sufficient for the global stability of the Cournot duopoly equilibrium. We use the relationships among the first and second order partial derivatives of the ordinary and inverse demand functions in deriving our results.

A formula is presented for computing the equilibrium payoffs in a generic finite two-person game when the support of the equilibrium is known.

A dynamic normal formulation for differential games is introduced and the "pedestrian principle" is discussed as a means of dynamically implementing the equilibrium strategy in a single game. Our formulation emphasizes the distinction between a player's rational prediction and the actual evolution of the game dynamics. To model the free will of players, a randomized strategy is introduced which serves as the justification of mixed strategies and the bridge from a static analysis to a dynamic one. Existence of Nash equilibrium in the class of mixed strategies is proved for non-cooperative deterministic differential games.

In this paper we study and compute E-points in an explicit way for diagonal games of three, four, five and n-players.

In this paper we study and compute E-points in an explicit way for a special general kind of 3k + 1 and 3k + 2 players.

In this paper, we establish the existence of Berge's strong equilibrium for games with n persons in infinite dimensional space in the case where the payoff function of each player is quasi-concave. Moreover, we study the continuity of Berge's strong equilibria correspondence and essential games.

This paper presents a new systematic review of N-person social dilemma games using a new approach based on dynamic properties of the corresponding system. Traditionally N-person social dilemma games are classified by relative orders of magnitude of payoff parameters. Without border-line cases 24 are identified. The new approach introduced in this paper categorizes the social dilemma games in cases with different number and asymptotic properties of the equilibria. In these cases the solution structure or the trajectory of the percentage of cooperators is readily apparent. These cases also provide the modeler with additional information concerning the impacts of the model parameters on the game outcomes. The example of a simple cartel illustrates this methodology.

We consider service providers (e.g., contractors) who bid for undertaking a large project — reverse auctions. As there is a risk that the lowest bidder will not be able to complete the project on budget or time, the customer, often a government agency, wishes to incorporate prior information on the bidders reliabilities into the choice of winning bid. We consider the use of official ratings of bidders, which are common knowledge. The customer is assumed to select the bidder for which the ratio of bid to rating is the lowest. A bidder assumes that each other bidder’s bid is the sum of its private value, the ratio of this value to its rating and the inverse of the rating. We characterize the equilibrium bids of two bidders, of $n$ symmetric bidders and of three nonsymmetric bidders, and provide comparative statics and examples. We also discuss a scenario where all ratings are known only to the customer, and each bidder knows only its own rating.

The properties of Cournot mixed oligopoly consisting of one public firm and one or more than one private firms have mostly been analyzed for simple cases on the basis of numerical calculations of the equilibrium values for a linear market demand function and linear or quadratic cost functions. In this paper, after proving the existence of a unique equilibrium in Cournot mixed oligopoly under general conditions on the market demand and each firm’s cost function, we derive conditions ensuring the existence of a unique Nash equilibrium for the mixed oligopoly where one public firm and at least one of the private firms are active in a general model of Cournot mixed oligopoly with one public firm and several private firms.

One of the key features which promote growth of industrial clusters is collaboration among firms within such clusters. Collaboration among firms leads to the formation of networks. Stability of these networks is vital to the sustainability of the particular firms. In this paper, we model a supply chain network where a set of downstream firms (players) source inputs from upstream firms (players) who manufacture goods, add value to the products and resell them. The upstream firms produce identical goods and compete on quantities to sell these goods to the downstream firms. The upstream firms procure goods from the downstream firms and sell them. Additionally, upstream firms network among themselves so as to reduce their costs. We model this setting as a two-stage $n$-player strategic network formation game. Firms decide their links before competing on quantities in the second stage of the game. Using the defined model, we derive equilibrium quantities and profits as a function of the network structure and number of firms. Following which we analyze the conditions under which different stable network emerge. Our analysis brings forth several interesting insights such as higher connections among downstream players lead to increased profits for upstream manufacturers. From the network stability perspective, we obtain the conditions under which regular, star, etc. network structures are pairwise and bilaterally stable. Furthermore, we also find the conditions under which core–periphery network structures emerge and are stable.

Scanning a large bandwidth of radio spectrum for anomalous signals is a fundamental challenge that must be addressed in building a secure spectrum sharing system. When designing a bandwidth scanning algorithm, the system engineer faces a problem of which band to scan and how long to scan each band. Traditionally, in such a problem, the adversary is considered as one who wants to achieve a malicious goal, e.g., to sneak usage of a particular band while being undetected. In this paper, we deal with a new type of adversary, called a sophisticated adversary, who, besides the basic goal of being malicious and undetected, also has a secondary goal to achieve the basic goal in the most unpredictable way. As a metric for such unpredictability we consider the entropy associated with the adversary’s strategy. The problem is modeled by a two-player game between an Intrusion Detection System (IDS) and the adversary. The equilibrium is found in closed form. Finally, weighting coefficients for the basic and secondary goals of the adversary are optimized via proportional fairness criteria.

This paper is devoted to the biological equilibrium of a stochastic nonlocal PDE population model with state-selective delay. By an improved dissipativity method and a delicate analysis of interaction of stochastic terms and delay terms, we obtain a unique equilibrium, which mixes exponentially. In order to check the validity of the model, we also investigate its stochastic stability.

In this paper, we study a quantum Boltzmann equation with a harmonic oscillator for isotropic gases of bosons and fermions, respectively. This model comes from physics literatures (see, e.g., [M. Holland, J. Williams and J. Cooper, Bose–Einstein condensation: Kinetic evolution obtained from simulated trajectories, Phys. Rev. A 55 (1997) 3670–3677]). The distribution function, i.e. the solution, is discrete in the energy variable. We give the classification of equilibria of the equation for bosons and fermions, respectively, and prove the global existence, uniqueness and the strong convergence to equilibrium for solutions of the equation.