Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring twoplayer-two strategy (2 × 2) dilemma containing classical games into quantum realm, dilemmas can be resolved in quantum pure strategies if entanglement is distributed between ...

This paper proposes a multi-agent Q-learning algorithm called meta-game-Q learning that is developed from the meta-game equilibrium concept. Different from Nash equilibrium, meta-game equilibrium can achieve the optimal joint action game through deliberating its preference and predicting others’ policies in the general-sum game. A distributed negotiation algorithm is used to solve the meta-game...

Given any $$\alpha \in [0,1]$$ , an $$ -constant-sum game (abbreviated as -CS game) on a finite set of players, N, is function that assigns real number to coalition $$S\subseteq N$$ such the sum worth S and its complementary $$N\backslash S$$ times grand coalition. This class contains constant-sum games Khmelnitskaya (Int J Game Theory 32:223–227, 2003) (for = 1$$ ) threats (Kohlberg Neyman, Ga...

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...

Kalmar [2, 1928-9] proved that Chess is strictly determined. Von Neumann-Morgenstern [5, 1944] proved the same for any finite two-person zero-sum perfect-information (PI) game. The latter result yields a minimax theorem for (finite) non-zero-sum PI games. Fix a PI, and a player, Ann. Convert this game to a two-person zero-sum game between Ann and the other players (considered as one player), in...

One of the earliest solution concepts considered in game theory are saddle points, combinations of actions such that no player can gain by deviating (see, e.g., von Neumann and Morgenstern, 1947). In two-player zero-sum games, every saddle point happens to coincide with the optimal outcome both players can guarantee in the worst case and thus enjoys a very strong normative foundation. Unfortuna...

We consider competition between two decentralized supply chains network under demand uncertainty. Each chain consists of one risk-averse manufacturer and a group of risk-averse retailers. These two chains present substitutable products to the geographical dispensed markets. The markets’ demands are contingent upon prices, service levels, and advertising efforts of two supply chains. We formulat...