Consequences of a Connection

The Matrix series, a blockbuster science-fiction, can aid reason about our real world interactions with virtual world. Primary concept of the series revolves around two parallel worlds: ‘The Matrix’ and real world. Many people live in such parallel lives. One such comparison can be drawn with hardcore game players, who live two lives: one in the real world, and second in the virtual game world. Analogous to The Matrix series there are consequences in the real world for the game players for their extensive involvement in their virtual world.

Neo, the lead character, and most of the other characters in the movie are all liberated from virtual world, called Matrix, to live their real life. Contrarily, a game player wants to get involved in the virtual world. They strive for extraordinary powers in this virtual world and achieve it through games.

In the movie there is a constant struggle going on both the worlds. It is a war between good and evil. Actions of one world have consequence in the other world. Though, direct not evident there is also a connection between the virtual world and the real world. It is the mind which also acts as connecter in the movie, and makes them real. When a player starts playing the game, he gets mentally involved. This connection makes his the virtual world a real world.

But there is a contradiction, yet analogy in the manner in which the series ends and manner in which the obsession of these hardcore game players ends. Neo fight against the evil program in the virtual world and dies in both worlds. Contradictorily, in video games the players never die and always emerge as winner. Games are designed to make everyone a winner. But, a player dies in real world. A player has invested a significant energy and time in playing this game. There are incidents wherein players gets so much involved in playing the game that they lose in real world, they lost their house, jobs, careers and friends in real world. All they are left is the virtual world which does no good to for them.

Even though, most hardcore game players would not agree with this, but there is a direct or indirect connection between their fantasied virtual world and the real world. There is a price attached to their involvement in virtual world; they will have to pay in real world. Neo fought and won an extreme battle in virtual world, yet he died in real world.

This entry was posted in General.

Coordination Games

Coordination game

Coordination is required in every aspect of day to day activities.  It can be coordination between husband and wife, for research activities, in politics and economics, or it can be for a choice of a computer technologies. All the players advantage by coordination.  For example, a situation of choosing sides on the road while driving. Consider the encounter of two vehicles on a narrow dirt road. Both drivers will successfully pass each other if they both choose different sides on the road; failure to do so will lead to an accident. Figure 1, shows a payoff matrix for such a game wherein each player receives a payoff of 5 for choosing the same side. Therefore, coordination is required for successfully crossing each other, and hence a coordination game is being played between the players.

Player 2
Player 1 Right Left
Left 5,5 0,0
Right 0,0 5,5

Figure 1: Choosing Sides

Technically, a coordination game is a game with multiple pure strategy Nash equilibriums, wherein players are better off selecting the same strategies. Payoff matrix in figure 2 represents the general form of 2 ×2 coordination game for which inequalities: a>c; d>b ,and w>y; z>x  hold. Here, {C, C}, and {D, D} are pure Nash equilibriums.

Player 2
Player 1 C D
C a, w b, x
D c, y d, z

Figure 2: Coordination game

Example of Coordination Game

Battle of the sexes is one of the most discussed coordination game. The story is about a couple trying to determine whether to go for a romantic or an action movie. General notion is that man would prefer going to an action movie, while female would prefer going to a romantic movie. Couple would still prefer going to the same movie rather than going to a different movie and spending time alone. Figure 3 shows a payoff matrix for Battle of sexes, where husband choose rows and wife choose columns. There are two pure strategy Nash equilibriums wherein both chooses a same place for going. The game represents an interesting scenario; one of the players consistently performs better than other.

Wife R A
R 3, 1 0,0
S 0,0 3, 1

Figure 3: Battle of sexes

Stag hunt, a coordination game, symbolizes conflict between individual satisfaction and social cooperation. Two hunters have decision to make, whether to hunt a stag or a hare. Hunting a hare is relatively easy, which makes a tasty but less satisfying meal. On the other hand, hunting a stag is difficult and requires coordination between hunters. Stag makes a large mean and is beneficial for the society on the whole, but requires its member to coordinate.  Figure 4 shows the payoff matrix for the stag hunt game. Again, there are two pure strategy Nash equilibriums in this game. General form of the game, based on figure 2, can be represented by inequalities a > c ≥ d > b and w > x ≥ z > y.

Player 1
Player 2 Stag Hare
Stag 4,4 0, 2
Hare 2, 0 1, 1

Figure 4: Stag Hunt

Finally, a pure coordination game is similar to the game of choosing sides. Again consider a couple trying to decide whether to go out for party or to stay home. Figure 5 shows a payoff matrix for such a game. There are two Nash equilibriums in the game, but both the payers prefer a single equilibrium over other i.e. {Party, Party}.  Such a game where a single equilibrium is preferred by all the players is called pure coordination game. With reference to figure 1, general form of the game is: a>d>b; a>d>c ,and w>z>y; w>z>x

Player 2
Player 1 Party Home
Party 15,15 0,0
Right 0,0 5,5

Figure 5: Pure Coordination game