Concepts needed in the definition of difference game problems are first studied in detail. Solutions for a general class of deterministic linear quadratic two-player nonzero-sum difference games are then developed. Nash and Stackelberg solutions for open-loop and zero-memory information structure are considered. An augmentation techniques and a dynamic programming approach are applied to obtain...

Formalization of a 2 Person Zero-Sum Game 1. There are two players, P1 and P2. 2. P1 has a set A = {a1, a2, . . . , am} of m pure strategies (or actions). 3. P2 has a set B = {b1, b2, . . . , bn} of n pure strategies (or actions). 4. Each player has a utility for each (ai, bj) pair of actions. The utility for P1 is denoted U1(ai, bj) and the utility for P2 is denoted U2(ai, bj). Since this is a...

We consider a statistical decision problem faced by a two player organization whose members may not agree on outcome evaluations and prior probabilities. One player is specialized in gathering information and transmitting it to the other, who takes the decision. This process is modeled as a game. Qualitative properties of the equilibria are analyzed. The impact of improving the quality of avail...

In 1967 Aumann and Maschler presented their celebrated model for games with incomplete information, see [1] and references therein. The game they consider consists in a set of, say I, standard discrete time two person zero-sum games. At the beginning one of these zero-sum games is picked at random according to a probability p. The information which game was picked is transmitted to Player 1 onl...

In game theory and in particular in the theory of stochastic games, we encounter systems of polynomial equalities and inequalities. We start with a few examples. The first example relates to the minmax value and optimal strategies of a two-person zero-sum game with finitely many strategies. Consider a twoperson zero-sum game represented by a k ×m matrix A = (aij), 1 ≤ i ≤ k and 1 ≤ j ≤ m. The n...

In this paper a noncooperative, two person, zero sum, stochastic differential game is formulated and solved that is described by a linear stochastic system and a quadratic cost functional for the two players. The optimal strategies for the two players are given explicitly using a relatively simple direct method. The noise process for the two player linear system can be an arbitrary square integ...

A class of nonzero-sum symmetric stochastic games of capital accumulation/resource extraction is considered. It is shown that Nash equilibria in the games with some natural constraints are also equilibrium solutions in unconstrained games and dominate in the Pareto sense an equilibrium leading to exhausting the entire resource stock in the first period of the game. One example is given to ilust...

for all mixed strategies Al, . ., ,, and i = 1, . . ., n in an n-person game r for all possible assignments of the pay-offfunction h is that r have total recall. Theorem 1 generalizes the theorem of von Neumann which asserts that a zero-sum two-person game with perfect information is strictly determined. It is proved by the same inductive device with a slight variation due to the absence of the...