Zero forcing is a combinatorial game played on a graph with a goal of changing the color of every vertex at minimal cost. This leads to a parameter known as the zero forcing number that can be used to give an upper bound for the maximum nullity of a matrix associated with the graph. A variation on the zero forcing game is introduced that can be used to give an upper bound for the maximum nullit...

We propose a single loop diagram and use it to devise matrix method computationally solve the Penney-Ante game. This avoids nuances of repeated conditional probability Markov chain representations. remove limitations Conway’s trick as applied fair coin generalize where is allowed be biased. A uniform random number generator used simulate game formulate implicit mathematical relations explore no...

We present a new algorithm for polynomial time learning of optimal behavior in single-controller stochastic games. This algorithm incorporates and integrates important recent results of Kearns and Singh 5] in reinforcement learning and of Monderer and Tennenholtz 7] in repeated games. In stochastic games, the agent must cope with the existence of an adversary whose actions can be arbitrary. In ...

where B is a real matrix with m rows and n columns, x ranges over the set of row vectors with m components, all non-negative and adding up to one, y ranges over the corresponding set of «-component column vectors, and the pay-off, (x2?, y), indicates the inner product of the two vectors xB and y. One device which may simplify a game computation is that of "dominance" or "majorization" [vNM, p. ...

In this section, we will first prove that any 2-player zero-sum finite game has a Nash equilibrium of mixed strategies (a special case of Nash’s theorem), and a Nash equilibrium can be found through solving linear programs. We will further show how to prove lower bounds on randomized complexity of Las Vegas algorithms using this result. A 2-player game is a zero-sum game if the sum of the payof...

By Shapley’s (1964) theorem, a matrix game has a saddle point whenever each of its 2 × 2 subgames have one. In other words, all minimal saddle point free (SP-free) matrices are of size 2 × 2. We strengthen this result and show that all locally minimal SP-free matrices are of size 2× 2. In other words, if A is a SP-free matrix in which a saddle point appears after deleting an arbitrary row or co...

This paper, presents an adapted serious game for rating social ability in children with autism spectrum disorder (ASD). The required measurements are obtained by challenges of the proposed serious game. The proposed serious game uses reinforcement learning concepts for being adaptive. It is based on fuzzy logic to evaluate the social ability level of the children with ASD. The game adapts itsel...

In social situations with which evolutionary game is concerned, individuals are considered to be heterogeneous in various aspects. In particular, they may differently perceive the same outcome of the game owing to heterogeneity in idiosyncratic preferences, fighting abilities, and positions in a social network. In such a population, an individual may imitate successful and similar others, where...