I analysed ‘Phoenix Wright: Ace Attorney’ for my essay last semester on game theory. I decided to post this up on my blog to get some more insight from anyone reading or hopefully enlighten someone on a bit of basic game theory.. I am in no way an expert on the subject and donot claim to be. Would love to hear your feedback and comments.
Game Theory
Introduction
The game under analysis is Phoenix Wright: Ace Attorney for the Nintendo DS. This game provides the player with multiple episodes with different storylines but recurring characters and mechanics. The particular episode under review will be the very first episode, “Episode One – The first turnabout”. This means characters are introduced in the game as if the player has never met them before, and introduces the player to the various game play elements without being too complex which will make it easier to unearth the kinds of theories which can be paralleled with the game. This game also has shown elements of being what is known as an ‘interactive novel’ with the engagement of dialogue with other characters to discover and discuss information being a large portion of the game play. Without the player interaction, the textual machine ceases to work thus not making it a game anymore (Nitsche, 2008) therefore game theory models must be put in place in computer games through which the player interacts.
Overview of Relevant Game Theories
There are a large amount of game theories that are used to model decisions, consequences and pay-offs in a given situation (Duffy, 2010). It is widely used in economics and business to understand the types of transactions that can occur between people in a given situation. Game Theory umbrellas multiple approaches, one of which is known as Decision Theory. It focuses on what decisions are available to players in the face of uncertainty and how the player is going to make that decision based on a rational and justified course of action (North, 1968). These models show how a decision can get the most reward out of a situation where the player might not have all the information of the situation (imperfect information). This concept can be paralleled with the iterated Prisoner’s Dilemma. The Prisoner’s Dilemma is a model of the decision between cooperation or defection between two players in order to get the best outcome individually when neither have perfect information about what the other player will do (Le & Boyd, 2006). An example of this is the television game show ‘Golden Balls’. Utility theory is also relevant, and the first stage in understanding decisions. It assigns mathematical value to the finite amount of outcomes a situation has to be analysed to create a strategy. Utility can be represented in two different forms – extensive form (situation tree) or a matrix (normal form). Games can therefore be represented by their utilities in either extensive form or normal form. Utility theory is relevant because “it is more general because it allows for the possibility of goods
without monetary value” (Bartha, 2001) which is applicable in Phoenix Wright.
Critical Review of Phoenix Wright: Ace Attorney, Episode One ‘The First Turnabout’
The player interacts with other characters using cheap talk tactics. Communication happens between characters constantly through first-person dialogue scenarios. It is how the player gains spoken information which motivates the player to then bargain. However, because of the amount of spoken information the player obtains through these one-on-one dialogue scenarios, the player must use data reduction methods to determine what information will be relevant. This means the player often suffers from the curse of dimensionality – the often large amount of characters in each episode of Phoenix Wright means the player is presented with a variety of perspectives and bias on the situation.
The spoken information does not become valuable until it has been manifested in the form of an item which can be presented at court during the court phases. The presentation of these items is the key to victory. Items can be obtained in two ways – through individual exploration of a crime scene which can be paralleled to the Princess and Monster search game model where the item is hidden until the player finds it and that particular game ends. In the traditional Princess and Monster search game model, the Princess has the ability to move locations and a time limit is present (Garnaev, 1992). The items (the Princess) only have one location in any given episode, and occasionally the player cannot further the game until the item has been uncovered. It is sometimes obtained through bargaining methods with other characters (other ‘players’ in traditional models). This bargaining method is somewhat limited due to the game mechanics of only being able to talk with other characters and having a finite amount of conversation topics and dialogue options. If the game designers opened up opportunity for the player to engage in more extensive conversation and the characters to have more nodes and responses to players it would make the game a little more engaging and intimate for the player, typical of the style shown in RPGs such as Neverwinter Nights. The bargaining model assumes there is a varying pay-off for each player if they cooperate which provides a motivation for the players. This creates a strategic equilibrium (Nash, 1950) and shows the utilities of the other characters – sometimes it is reward enough to help their friend Phoenix.
During the court case phases in Phoenix Wright, the hawk-dove approach is apparent. The ultimate victory and preferable utility for the player is to make sure the defendant gets a ‘not guilty’ verdict. The utility which means loss for the player is a guilty verdict, which the opposing ‘player’ – the prosecution – is aiming for. This means Phoenix Wright is a zero-sum game, where the victory of the prosecution means a loss for the player and visa verse. In order to obtain these utilities, bargaining and ultimatum techniques are applied. The prosecution often offers Phoenix an ultimatum to prove to the court the innocence of his client after Phoenix makes a point (a point the player does not have control over but has to deal with the consequences). This interaction with the prosecution means it becomes a one-shot game and the player has to choose the correct item to present to the court in order not to lose to the prosecution. Each item in the player’s inventory can have its own situation tree applied to it. Only one item can be the correct item in any ultimatum situation in Phoenix Wright so the utility of all items bar one provide player loss. This means the player must use data reduction on each item to determine whether it would back up the point Phoenix made previously and the player must also try to recall the cheap talk that happened with characters throughout the episode thus far to justify the item choice and make a rational decision in order not to lose. If the game designers made better use of this technique, they could add additional nodes and utilities to each item to provide more responses from the court when the player presents an item rather than making the item choice decision so risky. This situation in the game is very binary – it is either win or lose, whereas in a real court situation the defence lawyer would have a chance to explain why a certain item is relevant and make further points rather than relying on the often spontaneous responses Phoenix comes out with which leaves the player in a bad position.
Critical Reflection
Looking at this game using superficial analysis, it is apparent which areas are covering a very basic interaction between two players. For example, the bargaining ultimatum game that occurs between the prosecution and defence is very black and white. The player either presents an item from the inventory which causes them to lose the argument or win it – there is no grey area, making it very binary. This can be frustrating for a player who has used data reduction methods to decide that that particular item has been referenced by characters in conversation previously. It may be better for game designers to add more nodes of utility for the items to cause the court to respond differently to each one and perhaps steer the player in the right direction. This binary model seems quite archaic when it’s compared to modern day games such as Dragon Age which has multiple nodes attached to the smallest decisions (such as choosing a dialogue option).
As Phoenix Wright is a single-player game, the other characters will be programmed with a number of information sets, and that is obvious by the binary structure the game takes on when the player is tackled with the ultimatum challenge. Therefore, the latest artificial intelligence theories and research can be used to improve this style of game to make it less one-dimensional and transparent to the very simple game underneath. Research by (Floridi, 2010) on the philosophy of information shows the importance of improving the way cybernetics and artificial intelligence interact dynamically to provide innovative approaches to how information is given and how information theory can be studied.
Phoenix Wright shows the importance of utility theory in extensive form trees however. Many of the character’s motivations in providing Phoenix with information and items stem from their emotional relationship with Phoenix, something that can’t have a mathematical value attached to it unlike the Prisoner Dilemma approach where the outcomes are represented as a matrix rather than a tree.
References
Bartha, P. (2001, September). Probability and Decision. Retrieved December 14, 2010, from University of British Columbia, Philosophy: http://faculty.arts.ubc.ca/pbartha/p321f01/p321ovh4.pdf
Duffy, J. (2010, April). Introduction to Game Theory. Retrieved December 14, 2010, from Game Theory: http://www.pitt.edu/~jduffy/econ1200/Lect01_Slides_files/v3_document.htm
Floridi, L. (2010). What is the Philosophy of Information? Oxford: Oxford University Press.
Garnaev, A. Y. (1992). A Remark on the Princess and Monster Search Game. International Journal of Game Theory , 269-276.
Le, S., & Boyd, R. (2006). Evolutionary Dynamics of the Iterated Prisoner’s Dilemma. Journal of Theoretic Biology , 258-267.
Nash, F. J. (1950). Equilibrium Points in N-Person Games. Proceedings of the National Academy of Sciences of the United States of America 36 (pp. 48-49). Princeton University: JSTOR.
Nitsche, M. (2008). Video Game Spaces. Massachusetts Institute of Technology: MIT Publishing.
North, D. W. (1968). A Tutorial Introduction to Decision Theory. Transactions on System Science and Cybernetics , 200-210.
- Emma
















