Graphical congestion games provide powerful models for a wide range of scenarios where spatially distributed individuals share resources. Understanding when graphical congestion game dynamics converge to pure Nash equilibria yields important engineering insights into when spatially distributed individuals can reach a stable resource allocation. In this paper, we study the convergence dynamics o...

In this paper we provide a logical framework for using computers to discover theorems in (two-person finite) games in strategic form, and apply it to discover classes of games that have unique (pure-strategy) Nash equilibria. We consider all possible classes of games that can be expressed by a conjunction of two binary clauses, and our program re-discovered Kats and Thisse’s class of weakly uni...

in this paper, we analyze the effect of lack of capital investment on energy projects using game theory in the guise of cooperative games. we focus on the energy projects in the provincial level as case study during 2010-2011. therefore, we design a theoretical model of the lack of capital investment as a factor influencing the implement of energy projects. in the experimental section, we deter...

We initiate a study of Nash bargaining games [Nas50] via combinatorial, polynomial time algorithms and we carry this program over to solving nonsymmetric bargaining games of Kalai [Kal77] as well. Since the solution to a Nash bargaining game is also the optimal solution to the corresponding convex program, this involves obtaining a combinatorial algorithm for the latter. This in turn can be vie...

A quantum version of the Minority game for an arbitrary number of agents is studied. When the number of agents is odd, quantizing the game produces no advantage to the players, however, for an even number of agents new Nash equilibria appear that have no classical analogue. The new Nash equilibria provide far preferable expected payoffs to the players compared to the equivalent classical game. ...

Consider an information network with harmful procedures called attackers (e.g., viruses); each attacker uses a probability distribution to choose a node of the network to damage. Opponent to the attackers is the system protector scanning and cleaning from attackers some part of the network (e.g., an edge or a path), which it chooses independently using another probability distribution. Each att...

We study a quantum game played by two players with restricted multiple strategies. It is found that in quantum game Nash equilibrium does not always exist which is totally different from that in classical game. This happens only when the initial state is in entangled state. At the same time, we find that when Nash equilibrium exists the pay off function is usually different from that in the cla...

Consider the N -person non-cooperative game in which each player’s cost function and the opponents’ strategies are uncertain. For such an incomplete information game, the new solution concept called a robust Nash equilibrium has attracted much attention over the past several years. The robust Nash equilibrium results from each player’s decision-making based on the robust optimization policy. In...

Multi-leader multi-follower games are a class of hierarchical games in which a collection of leaders compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the followers. The resulting equilibrium problem with equilibrium constraints is complicated by nonconvex agent problems and therefore providing tractable conditions for existence of global or even loca...

We apply existing, and develop new, zero-sum game techniques for designing polynomial-time algorithms to compute additive approximate Nash equilibria in bimatrix games. In particular, we give a polynomial-time algorithm that given an arbitrary bimatrix game as an input, outputs either an additive 1 3 -Nash equilibrium or an additive 1 2 -well-supported Nash equilibrium; and we give a polynomial...