The referee has responsibility for control of players' behaviour during competitive football and implementing the rules of the game. To do this, the referee and the two assistant referees are obliged to keep up with play. Referees cover 10,000 m on average during a game, mean heart rate is about 160 - 165 beats . min(-1) and oxygen uptake is close to 80% of maximum (VO(2max). Assistant referees...

The domination game on a graph G (introduced by B. Brešar, S. Klavžar, D.F. Rall [1]) consists of two players, Dominator and Staller, who take turns choosing a vertex from G such that whenever a vertex is chosen by either player, at least one additional vertex is dominated. Dominator wishes to dominate the graph in as few steps as possible, and Staller wishes to delay this process as much as po...

It often results in sublevel grey full rank square matrix to become non-feasible solution square matrix when there are null-strategy variables and redundancy constraints in the grey matrix solving method of grey matrix game. We can not directly find the optimum grey game solutions in the non-feasible solution square matrix. However, we define concepts of nullstrategy variables and redundancy co...

In order to analyze the effect of a six-week intervention with an activitypromoting video game on muscle strength in elderly subjects (> 60 years) a controlled pretest-posttest study was conducted. The intervention group performed a 20-minutes session playing Wii bowling, twice a week for a total of six weeks. Data was analyzed by use of an ANCOVA. When comparing the results with the control gr...

A zero sum game is a simultaneous move game between 2 players. Such a game is represented by a matrix A ∈ Rm×n. The strategies of the “row” (resp. “column”) player are the rows (resp. columns) of A. If the row player plays strategy i ∈ [m] and the column player plays j ∈ [n] then the outcome is Aij . 1 Interpret this as that the row player pays Aij amount of money to the column player, therefor...

1 Persuasion mechanisms In this paper we study a particular game where Sender chooses a signal π whose realization is observed by Receiver who then takes her action. In Subsection 2.3 we made an observation that Sender's gain from persuasion is weakly greater in this game than in any other communication game. In this section of the Online Appendix we provide a formal statement and proof of this...

A game of group pursuit in which players move on a plane with bounded velocities is considered. The game is supposed to be a nonzerosum simple pursuit game between an evader and m pursuers acting independent of each other. The case of complete information is studied. In other words, each player, choosing control variables at each time instant t > 0, knows the moment t and his own as well as all...

In the game Knock ’m Down, tokens are placed in N bins. At each step of the game, a bin is chosen at random according to a fixed probability distribution. If a token remains in that bin, it is removed. When all the tokens have been removed, the player is done. In the solitaire version of this game, the goal is to minimize the expected number of moves needed to remove all the tokens. Here we pre...

We consider the new game of Cops and Attacking Robbers, which is identical to the usual Cops and Robbers game except that if the robber moves to a vertex containing a single cop, then that cop is removed from the game. We study the minimum number of cops needed to capture a robber on a graph G, written cc(G). We give bounds on cc(G) in terms of the cop number of G in the classes of bipartite gr...