Two players engage in a repeated game with incomplete information on one side, where the underlying stage-games are zero-sum. In the case where players evaluate their stage-payoffs by using different discount factors, the payoffs of the infinitely repeated game are typically non zero-sum. However, if players grow infinitely patient, then the equilibrium payoffs will sometimes approach the zero-...

In this paper, we consider an interval matrix game with interval valued payoffs, which is the generation of the traditional matrix game. The “saddle-points”of this interval matrix game are defined and characterized as equilibrium points of corresponding non-zero sum parametric games. Numerical examples are given to illustrate our idea. These results are extended to the fuzzy matrix games. Also,...

My primary research interest is social behavior for software agents to achieve cooperation in general-sum normal form games. An agent can easily be programmed to constantly cooperate in a normal form game, but such an agent is not suitable for environments with potentially hostile opponents. For a rational agent, the main reason to cooperate is to induce reciprocation therefore it is necessary ...

It is known that the value of a zero-sum infinitely repeated game with incomplete information on both sides need not exist [1]. It is proved that any number between the minmax and the maxmin of the zero-sum infinitely repeated game with incomplete information on both sides is the value of the long finitely repeated game where players’ information about the uncertain number of repetitions is asy...

In 1954, O.G. Haywood used game theory to analyze the military decisions used in the Battle of the Bismarck Sea, a battle fought during the World War II. Haywood analyzed the Battle of the Bismarck Sea by using a two-person zero-sum game [1]. This paper discusses the fundamental concepts of the two-person zero-sum game and some Nash Equilibrium dominance ideas as well as the strategies applied ...

Among the secondary detection effects in gamma-ray spectroscopy with HPGe detectors that reduce the peak area and must be properly taken into account in accurate measurements, the less well known is counting loss by beta and gamma-ray sum coincidence. The fraction of lost counts was estimated assuming that a photon detection event can sum either with the coincident beta-ray or its bremsstrahlun...

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...

In this paper, a gentle introduction to Game Theory is presented in the form of basic concepts and examples. Minimax and Nash’s theorem are introduced as the formal definitions for optimal strategies and equilibria in zero-sum and nonzero-sum games. Several elements of cooperative gaming, coalitions, voting ensembles, voting power and collective efficiency are described in brief. Analytical (ma...