Nash Equilibrium

Nash Equilibrium is our chosen strategy to explore.
In definition it is a strategy implemented in games that maps down a players decision theoritically in Multiplay. It focuses on the available strategies that are possible through assessing the situation to gather which option has the most payoff and incentive to follow through with. Typically this is compacted within a matrix.

		PLAYER 2
		Option 2	Option 1
PLAYER 1	Option 2	3, 3	0, 2
	Option 1	2, 0	1, 1

What happens here is the numbers represent the achieved result. The higher the number, the stronger the payoff and incentive. Therefore this matrix is a direct strategy in comparison to determine which strategy would be the most successful to use.

PLAYER 2 Option 2 PLAYER 1 Option 2 '3','3' Option 1 2, 0

In this particular case if player two chooses 'option 2' player 1 should also choose 'option 2' as '3' provides a greater payoff than 2.

		PLAYER 2
			Option 1
PLAYER 1	Option 2		0, 2
	Option 1		'1', '1'

However, in this situation if player 2 chooses 'option 1' player 1 should 'option 1' as well because '1' gives a greater payoff than 0.

Therefore, this speaks of where players choose strategies where they believe they are better off at times compared to the opposing player in the game.
Solidified Definition:
- Nash Equilibrium occurs when no player in the game has incentive to deviate from his strategy given the strategies all other player are playing.
- That is, everyone is playing their own "best response" to what all other players are doing in terms of strategies.
-At least one Nash Equilibrium exists in all finite games.

So by examining the given matrix we can determine if Nash Equilibrium exists.

		PLAYER 2 Option 2	Option 1
PLAYER 1	Option 2	'3', '3'	0, 2
	Option 1	2, 0	1, 1

At this point player 1 benefits more from 'option 2' with a payoff of '3' as opposed to choosing 'option 1' only to receive a payoff of 2. Therefore, Player 1 would not change strategies from 'option 2' provided player 2 initially chooses 'option 2'.
Should Player 1 initiate with 'option 2' player 2 would then remain on 'option 2' as well as it has a payoff of '3' compared to a payoff of 2 from option 1. Thus, player 2 would want to maintain this same strategy.
*This means that 'option 2' to 'option 2' is a Nash Equilibrium however, there is always a possibility of more than one Nash Equilibrium present in a game therefore, exploration is necessary to a further extent.

		PLAYER 2
		Option 2	Option 1
PLAYER 1	Option 2	3, 3	0, 2
	Option 1	2, '0'	1, 1

In the case that player two uses 'option 2' and player 1 uses 'option 1' it is necessary to assess if a strategy change is required purely based on what the opposing player chooses as their strategy. For player 2, choosing 'option 2' when player 1 initially decides on 'option 1' will give player 2 the lower payoff of '0', therefore player 2 should and will deviate to picking 'option 1' as well to receive a better payoff of 1 so a strategy change will occur here. This suggests that 'option 1' to 'option 2' is not a Nash Equilibrium.

		PLAYER 2
		Option 2	Option 1
PLAYER 1	Option 2	3, 3	'0', '2'
	Option 1	2, o	1, 1

Now we visit the strategy play of 'option 2' to 'option 1'. Therefore if player 2 initially chooses to follow through with 'option 1' player 1 would want to deviate and choose 'option 1' as well as 'option 2' would only provide a payoff of '0'in this particular case compared to the payoff of 1 received from choosing 'option 1'. This immediately declares that 'option 2' to 'option 1' is of course not a Nash Equilibrium.

		PLAYER 2
		Option 2	Option 1
PLAYER 1	Option 2	3, 3	0, 2
	Option 1	2, 0	'1', '1'

Now, it is the final combination of 'option 1' to 'option 1'. As demonstrated through previous assessments of the past outcomes should any player choose 'option 1' as the initial choice no plaer would demonstrate any incentive to deviate and change strategies as 'option 1' in this case will always have the highest payoff of '1'compared to the alternative of 0. Therefore, this is also a Nash Equilibrium.

Therefore from the matrix we can gather that this game has two existent Nash Equilibrium. However, of course option 2's payoff of 3 is dominant over 'option 1's' payoff of 1. But should any player begin with 'option 1' it is obvious no change should take place.

Upon discussion despite considering the fact that conflict was definitely a valid theory confined within gaming in Ipad/Iphone games. Some areas demonstrated difficulties and limitations. Although Ipads and Iphones are a current boom on the market it doesn't distract consumers from the fact that it is still expensive regardless. Therefore it's more than clear that not everyone would own either Ipad or Iphone which immediately suggests that the possible social issues we are delivering attention onto is constrained to a somewhat richer market of people. Therefore, limiting the social concerns present to a smaller demographic. Also due to the Iphone and Ipad market primarily focusing on Monetary gain it can be deduced that the games created weren't entirely designed or dedicated to addressing any such social concern or conflict. Also, a main pivotal fact presented in the idea of social concerns and conflict is that it plays largely on simultaneous large pools of player all at one time which requires a leading talent in networking and the understanding of it. Typically multiplay through Ipads and Iphones is limited to perhaps wi-fi through neighboring players, using the same Ipad and Iphone or a direct internet connection where unlike the internet of the PC games, Ipad and Iphone games have yet to reach the standard where within social interaction the entire multitude of players are visible to players. Therefore as a group based on these findings it was decided that conflict in games although valid, had many cons visible to us in comparison to Nash Equilibrium in games.

Research:
Game theory 101: Stag hunt and Pure Strategy Nash Equilibrium
http://www.youtube.com/watch?v=C85jOlRt_88