In a

matrix game, own object as player A has the ability to use [s.sub.0] different pure strategies, and J objects representing player B have [s.sub.J] different pure strategies.

In this paper we deal with fuzzy goals in multi-objective

matrix game, assuming that each player has a fuzzy goal of the payoffs.

Created specifically for the Intel AIC 2013, which challenged contestants to "Dream up an interactive entertainment experience that helps make the all-in-one an endless adventure," Paint Your Music (PYM) combines multi-touch, multi-player-enabled interaction with a musical

matrix game board, virtual "paint balls," and a scoring mechanism to create a unique, fun-to-play virtual musical instrument/game.

Among the topics are analyzing power supply maintenance in transport telematics systems, creating terrain maps for unmanned ground platforms, experimental research on the directional stability of articulated tractors, a reliability model of motorway emergency communication systems, an automatically controlled anti-collision maneuver and its numerical simulation with disturbances, predicting the spatial orientation of a ship by means of neural networks, characterizing the

matrix game sensitivity of the safe passing of ships at sea, analyzing parameters of the impact of a traveling wave on the speed of a biomimetic underwater vehicle, and evaluating he stiffness of fire rescue robot suspension with hydropneumatic components.

(2008) include proving that mediation helps by at most a factor of 4/3 in a

matrix game with two players and two strategies, and proving that mediation can help by an unbounded factor even in congestion games with few players and strategies.

Restrictions =SUMPRODUCT(B22:E22;B$27:E$27) <= 1 =SUMPRODUCT(B23:E23;B$27:E$27) <= 1 =SUMPRODUCT(B24:E24;B$27:E$27) <= 1 Value of objective function: =MAX(SUMPRODUCT (B27:E27;B20 :E20)) Optimal mixed strategy of Player II =B27/$J$25 =C27/$J$25 =D27/$J$25 Therefore,

matrix game given by the matrix M admits equilibrium in mixed strategies.

The sufficient conditions for the structure of an optimal stationary policy of player 1 and player 2 that achieves the supremum and infimum in the

matrix game [V.sub.[gamma]](v ) = [T.sub.[gamma]][V.sub.[gamma]](v ).

The game theory can be used for sustainable decision-making; many authors have applied game theory to solve problems in construction engineering and management; i.a.: Peldschus and Zavadskas (2005) investigated fuzzy

matrix game in construction, Lo et al.

As shown in Table 1, it can be observed that there are two pure Nash equilibria, given by ([p.sub.1l], [p.sub.2l]) and ([p.sub.1h], [p.sub.2h]) in this

matrix game.

The situation ([i.sup.*], [j.sup.*]) in

matrix game [[GAMMA].sub.F] with payoff matrix F(t) is called a saddle point (or a solution) if exists such positive number [t.sub.0] [member of] [0,1], that for every [t.sub.0] [member of] [0, [t.sub.0]] the following inequalities will take place

(2004) solved construction technology and management problems; Peldschus and Zavadskas (2005) investigated fuzzy

matrix game in construction; Su et al.

Neo accomplishes his goals because he believes that he is the One and because his powers increase exponentially as he achieves the next level of knowledge and physical challenges in The

Matrix game. Simultaneously, The Oracle raises Neo's consciousness and his confidence.