A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the linear. Each players has a quadratic functional on its own disposal, which should be minimized. case where weight matrices in control costs one player are singular both functionals studied. Hence, under consideration singular. novel definition Nash equilibrium this (a sequence) proposed. solved by appl...

The digital revolution of the information age and in particular the sweeping changes of scientific communication brought about by computing and novel communication technology, potentiate global, high grade scientific information for free. The arXiv for example is the leading scientific communication platform, mainly for mathematics and physics, where everyone in the world has free access on. Wh...

Matching Pennies is a well-known example of a two player, zero-sum game. In this game, each of the players, the matcher and the mismatcher, flips a coin, and the payoffs are determined as follows. If the coins come up matching (i.e., both heads or both tails), then the matcher wins, so the mismatcher pays the matcher the sum of $1. If the coins do not match (i.e., one head and one tail), then t...

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 ...

Since the seminal paper of Nash [7] game theoretic literature has focused mostly on equilibrium and not on maximin (minimax) strategies. We study the properties of these strategies in 2-player non-zero-sum strategic games, whose Nash equilibria are only mixed.

This paper is concerned with two-person non-zero-sum game versions of the secretary problem. A remarkable feature of our models compared with previous ones is that Nash equilibrium strategies are different for two players, i.e. one player should behave more hastily, and the other less hastily, than in the secretary problem.

warranty as a kind of service contract today plays a role key in business and legal transactions. in this paper, we present a manufacturer, an agent and a customer's model under different service contracts suggestions. the manufacturer's profit is maximized by determining sale price, warranty period and warranty price. in addition we obtain optimal maintenance cost or repair cost for ...