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

Group Decisions

To pursue and Ipad/Iphone style game incorporating a platform style of play or a shooter that breaks the conventional standards. Primary focus will be set on platform play as we want to show a strong character followed by as strong storyline. This is because typical shooter games during present day times follow the first person shooter theme demonstrating no need to show the characters which is something we aim to avoid so we can produce a character with signs of developmental process visual to people.
Currently we are thinking of following a 2.5-dimensional style of play common to Angry Birds.
The reasoning behind this decision was understanding that although this is an growing market it is still quite unexplored in possibilities which was something we believed to be interesting enough and worth the exploration.
Also, there are functions available where people can touch and tilt the actual object followed by networking possibilities for unique Multiplayer play.
Also it is possible to explore Nash Equilibrium using this platform with implications of co-operative play while it can apply to Conflict Theory as well due to Ipad/Iphones playing a vastly growing role on society today with availability towards social interaction.

Group Roles

Today we assigned each other the respective group roles.

Ron Quizon - Environment Designer/Modeller/Leader
Robin Tey - Character Designer/Modeller
Ma'ake Manu'Atu - Interface Designer
Daniel Lee - Character Designer/Modeller
Amir Yousef - Environmental Programmer
Jack Yang - Primary Researcher

As a group we discussed topics that we all researched.
Social Interaction exists not as a game theory but rather a subject based off the broad entirety of game theory. Therefore, the validity is difficult to ensure as it doesn't follow the leading concerns of what game theory is within multiplayer game theories. Therefore research will only return broad material as a loose source of relevant information and appear in scarce amounts.

Possible game genres from remaining game theories:
Nash Equilibrium- Platform, Puzzle/Logic, Ipad/Iphone style, Role Playing Game/Adventure and Defense.

Conflict- Platform, Ipad/Iphone Style, Action, Role Playing Game/Adventure, Fighting and Defense.

Research - Game Theories

Today after a discussion we had a deeper talk with the group after we decided are organizing our project in a more tidier manner.
Therefore we developed our game in greater depth.
Main Theme: Multiplayer Play
Topics: Game Theory - Nash Equilibrium, Conflict, Social interaction.

Nash Equilibrium - A set of strategies available of each player where no player holds the desire to alter their set strategy. Should a player decided to change strategies with the result of a smaller end result then equilibrium has occurred.
Reference:
http://www.gametheory.net/dictionary/NashEquilibrium.html

Conflict- Multiplayer games contain social issues where although some games surround direct conflict a vast majority of games are subject to destructive social dynamics, this can also be referred to as grief play. This comes into play when implicit rules are simply ignored to achieve player advantage for the team, against the team or solely for one's self. This is where labels of cheating and so forth are applied towards players creating the socially destructive play.
Reference:
Playing Dirty - Understanding Conflicts in Multiplayer Games, Paper presented at the 5th annual conference of the Association of Internet Researchers, The University of Sussex, 19-22nd September 2004.
Jonas Heide Smith (Smith @itu.dc), PhD candidate, Center for Computer Games Research Department of Digital Aesthetics and Communication, The IT University of Copenhagen.

Social Interaction: Game theories and gaming in general has played on impacting the role on direct social interaction by playing as a model for social issues present in the virtual world. Putting forawrd issues such as social norms, co-operation, social order, stability or even trust falling in to the realms of transactions of an economic standing.
Research:
Game Theory and Society: Models of Social Interaction in Sociological Research.
International Conference at ETH Zurich, Swiss Federal Institute of Technology, July 27th to July 30th, 2011
Organizing Committee: Andres Diekmann, Dirk Helbing, Ryan O. Murphy.
Conference Office: Stefan Wehrli
http://www.socio.ethz.ch/workshop2011

These are my personal sources of individual research.

Research Day

Our group is called JusPlay is comprised of six members.
Myself Robin Tey, Ron Quizon, Ma'ake Manu'atu, Daniel Lee, Amir Yousef and Jack Yang.
In order to collect a stronger basis of gaming in general we were sent to research five separate games that we could bring back to the group the next day.
My first games of choice were Pokemon and the Legend of Zelda: Ocarina of Time.

Pokemon: Publisher, Nintendo - Year, 1995:
Qualities of the Pokemon industry that push it forward annually is the feeling of success provided to players. Repetition is avoided because of the varying options available from capturing Pokemon, capturing rare and specific Pokemon for the team you desire, or even catching them all to fill perfectionist needs. Directly after catching one comes a whole new set of possibilities. Leveling them up to evolve them or not as you see fit, building teams with them or trading them for the team you want and battling others in game characters or real life friends through the game. However the 'I don't know what to do next' factor never settles in because a challenge is always present. You can explore the island through means of air, water, feet and bike. You have your own in game rival and gyms to challenge and beat to advance in the game. Strategies of in game battle can be applied as well by understanding type advantages and disadvantages such as, fire Pokemon having dominance over grass Pokemon, Grass over water, and water over fire. Also one favorite features is the choice of starting Pokemon every game that determines how difficult things may run.