Game Theory
Definition 1 (courtesy of wikipedia.org)
Game theory is a branch of applied mathematics that uses models to study interactions with formalised incentive structures ("games"). A definitive feature of game theory that distinguishes it from decision theory whose main subject is also studying formalized incentive structures is that game theory encompasses decisions that are made in an environment or states of the world in which strategic interaction between various players occurs. It has applications in a variety of fields, including economics, international relations, evolutionary biology, political science, and military strategy. Game theorists study the predicted and actual behaviour of individuals in games, as well as optimal strategies. Seemingly different types of interactions can exhibit similar incentive structures, thus all exemplifying one particular game.
Definition 2 (courtesy of indiainfoline.com)
The theory of making the best choice form among available strategies given imperfect information.
Game Theory allows us as designers to understand the interactions, influence and impact of player actions upon opposing players in a game. Using mathematics we can calculate the optimal strategies and make optimal choices to better position ourselves in a game as players. While chances are that no one would attempt to calculate these types of calculations during game play, it can over time allow players to make better choices upon repeated playing of a game.
With game theory we gain concepts such as extensive and normal form, zero-sum games, non-zero-sum games, cooperative games, Utility Theory and the MiniMax Theorem. All of these are useful tools for assessing the decisions, payoffs and outcomes available to players in our games. And as designers these tools allow us check our games for possible flaws, lack of optimal strategy, or even asses the depth of a game.
Zero-sum and Non-zero-sum games
When the additions of winnings and the subtraction of losses is the sum of zero for every set of strategies in the game, it is considered a zero-sum game.
If there exists even a single strategy that yields a sum greater or less than zero, the game is no longer zero sum, or otherwise known as Non-zero-sum game.
A useful tool to represent or depict zero-sum games is the pay-off matrix. It will allow for us to show what payoffs are available to each player at the outcome of a game. Of course the outcome will be dependent on the actions of all players. (for more information on pay-off matrix visit wikipedia.com)
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The topic is Game Theory? Why?
I will refer you to an article I found on the net at (http://plato.stanford.edu/entries/game-theory/#Games), which states
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All situations in which at least one agent can only act to maximize his utility through anticipating the responses to his actions by one or more other agents is called a game. Agents involved in games are referred to as players. If all agents have optimal actions regardless of what the others do, as in purely parametric situations or conditions of monopoly or perfect competition (see Section 1 above) we can model this without appeal to game theory; otherwise, we need it.
We assume that players are economically rational. That is, a player can (i) assess outcomes; (ii) calculate paths to outcomes; and (iii) choose actions that yield their most-preferred outcomes, given the actions of the other players. This rationality might in some cases be internally computed by the agent. In other cases, it might simply be embodied in behavioral dispositions built by natural, cultural or economic selection.
Each player in a game faces a choice among two or more possible strategies. A strategy is a predetermined ‘programme of play’ that tells her what actions to take in response to every possible strategy other players might use. The significance of the italicized phrase here will become clear when we take up some sample games below.
A crucial aspect of the specification of a game involves the information that players have when they choose strategies. The simplest games (from the perspective of logical structure) are those in which agents have perfect information, meaning that at every point where each agent's strategy tells her to take an action, she knows everything that has happened in the game up to that point. A board-game of sequential moves in which in which both players watch all the action (and know the rules in common), such as chess, is an instance of such a game…
So what does this tell us?
To me is says that we are the ones that 'program' what players can do, and as a result we are forcing players to interact 'the way we want' based on how we design the strategies and actions our our game.
Sounds pretty obvious, but really think about it. If your game design does not influence a players behavioral, economical, and moral rational (I am sure there is much more that could be added to this list), are you designing a *good* game?
As designers we are not just 'designing a game', we are molding an experience for our players. We need to interact with the minds of our players from multiple directions. Imagine a bidding game where players had no emotional attachment to *losing*. What would be the point?
(to be continued...)
