Different mutation operators have been proposed in evolutionary programming. A mixture of various mutation operators may be more efficient than a single one. This paper presents a game-theoretic approach for designing evolutio nary programming with a mixed mutation strategy. The approach is applied to design a mixed strategy using Gaussian and Cauchy mutations. The experimental results show the...

This note studies the following question: If a researcher is given a finitely supported mixed strategy for each player over a continuous strategy space, does there exist a game whose unique Nash equilibrium is given by these mixed strategies? This note finds that any set of finitely supported mixed strategies on metric spaces can be represented as the unique Nash equilibrium to a separable game...

We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). While not every two-person zero-sum finite game has an equilibrium in the set of pure strategies, von Neumann showed that there is always an equilibrium at which each player follows a mixed strategy. A mixed strategy deviating from the...

Based on the unidirectional conversion model, we investigate a practical buy-and-hold trading problem. This problem is useful for long-term investors, we use competitive analysis and game theory to design some trading rules in the securities markets. We present an online algorithm, Mixed Strategy, for the problem and prove its competitive ratio 1+ (n−1)t 2 , where n is the trading horizon and t...

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an nxn payoff matrix. Players can use mixed strategies, which are given by the vector (p(1),...,p(n)). Each entry specifies the probability to use the corresponding pure strategy. The sum over all entri...

The complexity of algorithms that compute strategies or operate on them typically depends on the representation length of the strategies involved. One measure for the size of a mixed strategy is the number of strategies in its support the set of pure strategies to which it gives positive probability. This paper investigates the existence of "small" mixed strategies in extensive form games, and ...

This study examines the influence of the organizational strategy used to structure opening statements and closing arguments on presentation effectiveness in a simulated civil trial. Two organizational structures, a narrative and a legal-expository format, were manipulated to produce a 2 (plaintiff organizational strategy) x 3 (defense organizational strategy) experimental design. Results indica...

Consider a two-person general-sum game on n × n payoff random matrices A and B with iid continuous entries, for large n. It is shown that the probability that there exists a pure strategy Nash equilibrium that is not pure Pareto optimal remains bounded away from 0 and 1 as n increases. We also consider the number of mixed strategy Nash equilibria: It is shown that for a mixed strategy Nash equi...