In this paper, a new iteration approach is derived to solve the optimal strategies for quadratic zero-sum game of finite-horizon continuous-time nonaffine nonlinear system. Through iteration algorithm between two sequences which are a sequence of state trajectories of linear quadratic zero-sum games and a sequence of corresponding Riccati differential equations, the optimal strategies for the n...

Strictly competitive games are a class of 2-player games often quoted in the literature to be a proper generalization of zero-sum games. Other times it is claimed, e.g. by Aumann, that strictly competitive games are only payoff transformations of zero-sum games. But to the best of our knowledge there is no proof of such claim. We shed light to this point of confusion in the literature, showing ...

The classic video game Tetris can be represented as an optimization problem that can be maximized to produce an efficient player. In this problem, a player picks moves by generating future game states and computing a weighted sum of features for each state. The player picks the move for the state with the largest weighted sum. The values for these weights are optimized through a genetic algorit...

Table 1: Coordination Game Note that in the case of the coordination game, we also have bBa. However, for the game described by Table 2 statement aBb is true, but bBa is false. The main focus of this paper is functional dependence in multiplayer games. For example, consider a “parity” game with three players a, b, c. Each of the players picks 0 or 1, and all players are rewarded if the sum of a...

A probabilistic framework is developed in which one can analyze both the classical and the quantum games. We suggest exploiting peculiar probabilities involved in the Einstein-Podolsky-Rosen (EPR) experiments to construct quantum games. In our framework a game attains classical interpretation when probabilities are factorizable and a quantum game corresponds when probabilities cannot be factori...

A probabilistic framework is developed that gives a unifying perspective on both the classical and quantum versions of two-player games. We suggest exploiting peculiar joint probabilities involved in Einstein-Podolsky-Rosen (EPR) experiments to construct a quantum game when the corresponding classical game is obtained from factorizable joint probabilities. We analyze how nonfactorizability chan...

We show that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for existence are provided. We point out that the class of symmetric two-player zero-sum games coincides with ...

The paper focusses on optimal control issues arising in semi-active vehicle suspension motivated by the application of continuously controllable ERF-shock absorbers. Optimality of the damping control is measured by an objective consisting of a weighted sum of criteria related to safety and comfort which depend on the state variables of the vehicle dynamics model. In the case of linear objective...