Unique Nash Equilibrium Point Research Articles

Dynamic scheduling model of computing resource based on MAS cooperation mechanism

Allocation of grid resources aims at improving resource utility and grid application performance. Currently, the algorithms proposed for this purpose do not fit well the autonomic, dynamic, distributive and heterogeneous features of the grid environment. According to MAS (multi-agent system) cooperation mechanism and market bidding game rules, a model of allocating allocation of grid resources based on market economy is introduced to reveal the relationship between supply and demand. This model can make good use of the studying and negotiating ability of consumers’ agent and takes full consideration of the consumer’s behavior, thus rendering the application and allocation of resource of the consumers rational and valid. In the meantime, the utility function of consumer is given; the existence and the uniqueness of Nash equilibrium point in the resource allocation game and the Nash equilibrium solution are discussed. A dynamic game algorithm of allocating grid resources is designed. Experimental results demonstrate that this algorithm diminishes effectively the unnecessary latency, improves significantly the smoothness of response time, the ratio of throughput and resource utility, thus rendering the supply and demand of the whole grid resource reasonable and the overall grid load balanceable.

Buffered Cross-Bar Switches, Revisited: Design Steps, Proofs and Simulations Towards Optimal Rate and Minimum Buffer Memory

Regarding the packet-switching problem, we prove that the weighed max-min fair service rates comprise the unique Nash equilibrium point of a strategic game, specifically a throughput auction based on a ldquoleast-demanding first-servedrdquo principle. We prove that a buffered crossbar switch can converge to this equilibrium with no pre-computation or internal acceleration, with either randomized or deterministic schedulers, (the latter with a minimum buffering of a single-packet per crosspoint). Finally, we present various simulation results that corroborate and extend our analysis.

Dynamics of the Nash map in the game of Matching Pennies

An iterative procedure for the game of Matching Pennies is examined in which players use Nash's map to respond to mixed strategies of the other players. It is shown that even though the game of Matching Pennies has a unique Nash equilibrium point, the iterative procedure does not lead to convergence to the Nash equilibrium. In fact we find that if the game is played using this iterative procedure then the successive plays of the game will follow an orbit around the equilibrium point. This orbit has period eight and it is the only periodic orbit other than the equilibrium point.

The Existence and Uniqueness of Nash Equilibrium Point in an m-player Game “Shoot Later, Shoot First!”

We consider the following "silent duel" of m players with a possible economic interpretation. Each player has one "bullet", which she can shoot at any time during the time interval (0,1). The probability that the i-th player hits the "target" at moment t is given by an increasing accuracy function fi(t) .T he winner is the player who hits the target first. Under natural assumptions on the functions fi(t) we prove the existence and uniqueness of a Nash equilibrium point in this game, and we provide an explicit construction of this equilibrium. Thisconstructionallowsustoobtainexactsolutionsformanyspecificexamples. Some of them are presented.