Data-free quantization (DFQ) recovers the performance of quantized network (Q) without accessing real data, but generates fake sample via a generator (G) by learning from full-precision (P) instead. However, such generation process is totally independence Q, specialized as failing to consider adaptability generated samples, i.e., beneficial or adversarial, over resulting into non-ignorable loss...

We have seen that Nash equilibria in two-player zero-sum games (and generalizations thereof) are polynomial-time tractable from a centralized computation perspective. We have also seen that the payoff matrix of a zero-sum game determines a unique value for the row player and a unique value for the column player (summing to zero), which specify their payoffs in all equilibria of the game. In thi...

While the idea of a matching pennies game may seem contrived, it is merely the simplest example of a general class of zero-sum games, where the total payoff of the players is constant regardless of the outcome. Consequently gains for one player can only come from losses of the other. For this reason, zero-sum games will rarely have a pure strategy Nash equilibrium. Examples would be chess, or m...

The linear quadratic zero-sum dynamic game for discrete time descriptor systems is considered. A method, which involves solving a linear quadratic zero-sum dynamic game for a reduced-order discrete time state space system, is developed to nd the linear feedback saddle-point solutions of the problem. Checkable conditions, which are described in terms of two dual algebraic Riccati equations and a...

We study the complexity of solving succinct zero-sum games, i.e., the games whose payoff matrix M is given implicitly by a Boolean circuit C such that M(i, j) = C(i, j). We complement the known EXP-hardness of computing the exact value of a succinct zero-sum game by several results on approximating the value. (1) We prove that approximating the value of a succinct zero-sum game to within an add...

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...

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 ...

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,...

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...