There is limited formal mathematical analysis of one type of games — dynamic sequential games with large, or even infinitely large, planning horizons, from the point view of system controls. In this paper, we use a zero-sum game theoretical approach to address the disturbance attenuation analysis of state feedback Nash strategies for Dynamic Linear Quadratic Sequential Games (LQSGs) with uncert...

The strategic allocation of resources across multiple fronts has long been studied in the context of Blotto games in which two players simultaneously select their allocations. But many allocation problems are sequential. For example, a state trying to defend against a terrorist attack generally allocates some or all of its resources before the attacker decides where to strike. This paper studie...

We introduce generous, even-matched, and greedy strategies as concepts for analyzing games. A two person prisoner's dilemma game is described by the four outcomes (C,D), (C,C), (D,C), and (D,D). In a generous strategy the proportion of (C,D) is larger than that of (D,C), i.e. the probability of facing a defecting agent is larger than the probability of defecting. An even-matched strategy has th...

The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new spin: building nim. With given finite numbers of tokens and stacks, this two-player game is played in two stages (thus belonging to the same family of games a...

The solution is given here for the infinitely repeated two-person zero-sum,games of inr complete information characterized by 2 X 2 games, with information matrxces b for the ftrst game and( b ab)for the second game.

We consider two populations co-evolving with fitness defined by the payoff in a two-person zero-sum game. We show that such situations lead to spontaneous and sustained oscillations iff the optimal strategy of the game is mixed.

The function that assigns to each matrix game (i.e., the mixed extension of a finite zero-sum two-player game) its value is axiomatized by a number of intuitive properties.

Two important metrics for measuring the quality of routing paths are the maximum edge con-gestion C and maximum path length D. Here, we study bicriteria in routing games where eachplayer i selfishly selects a path that simultaneously minimizes its maximum edge congestion Ciand path length Di. We study the stability and price of anarchy of two bicriteria games:• Max games, where ...