The Games Economists Play - Implications of Economic Game Theory for the Study of Computer Games

Source : gamestudies.org

by : Jonas Heide Smith

Abstract
It is a source of confusion that economists for decades have worked on "game theory" while studying economic behaviour. However, while not focused on games in the recreational sense this perspective does provide a highly meticulous complementary framework for the understanding of computer game structure and player behaviour. This article attempts to extract useful analytic concepts and insights from economic game theory and to give suggestions for how these might be put to concrete use in the study of computer games. A non-technical introduction is given, the framework is applied to computer games, a brief case study is performed and finally ideas for future research are presented.
Introduction
Studying games, as Jesper Juul (2001) puts it, is a "repeatedly lost art." There are those, however, who for the last many decades have devoted careers to the study of games in a somewhat special sense. These individuals, known to their peers as game theorists, can be said to have placed computer game theorists in a hard spot. Since the label is occupied, it is only by risking confusion that the term game theory can be used as a label for work on electronic entertainment of the ludic persuasion. What, then, do these economic game theorists do?
Imagine, for instance, two children sharing a cake. The rule is that the one who does not cut the cake gets to choose first. Now, assume that the cutter wants to maximize his share of cake and that he expects the other child to share this preference. He will do his best to cut the cake exactly in half.
Such an analysis, although extremely simple, implies a game theoretical perspective. We assume that the people involved desire the best possible personal outcome and are aware (on some level) of the perspectives of the other participants. By "game" we are not referring to any recreational sense of the word but to strategic interaction between agents ("game theory," henceforth, refers to this special perspective).
Phrased in such general terms, game theory is as old as social theory. In an informal version, but one logically akin to modern thinking, it found application in the study of human behaviour among the so-called contract theorists Thomas Hobbes (1588-1679), John Locke (1632-1704) and Jean-Jacques Rousseau (1712-1778) as they discussed the rationale behind individuals drawing up a "social contract." And it has seen use among a variety of writers attempting to analyse successful gambling strategies.
More formally, we can think of game theory as the systematic study of the relationship between rules, choice and outcome in competitive situations. Two main branches exist. Analytical game theory is the analysis of games played by non-empirical players; that is "ideal" players who may be endowed with any characteristics, which can be modelled. These players need not accurately correspond to real-world people and such work is only open to critique to the extent that the math involved is wrong. They are experiments in logic, not models of the real world. On the other hand, behavioural game theory is the study of actual human players as they are confronted with precisely defined games. In this branch, researchers study how people make choices and navigate social conflicts (Camerer, 2003). The birth of game theory in its modern form is commonly said to be the publication of Johan Von Neumann and Oskar Morgenstern's Theory of Games and Economic Behaviour in 1944. The ideas put forth in this volume relied on complex mathematics with the ambitious goal of providing a solid scientific foundation for the discipline of economics. This work was expanded upon in the years to follow, reaching political science in the late 1960s and evolutionary biology in the early 1970s.
This article is split in three parts. First, key issues and concepts in game theory are introduced. Second, the general implications of applying a game theoretical framework to games are presented and discussed. And finally, a case study of the strategy game Age of Kings (1999) is made, exemplifying how game theory may be applied in the analysis of games.
Key Concepts in Game Theory
This section introduces game theory focusing on those issues, which are most relevant to computer game studies. The format here is informal in the attempt to impart the logic of the perspective rather than the exact details. The next section will relate the issues to computer games.
Game theorists attempt to provide precise descriptions of situations of conflicting interests in order to study the behaviour that such a conflict would (or, in some cases, should) elicit from rational agents. Players are assumed to consider the position and perceptions of other players while forming their strategies. Alternatively, players may be seen as merely thoughtlessly adapting their strategies over time. The latter is assumed when games are played between non-human actors (algorithms, bacteria, etc.). The games studied by game theorists are usually those in which players are unable to enter into binding agreements. This branch is known as non-cooperative game theory and constitutes by far the larger portion of the entire field.
Technically, a strategy here is a plan for dealing with all possible actions of other players. I will return to the concept of strategy below in the discussion of how game theoretical concepts map onto computer games. As opposed to less sophisticated conceptions of human behaviour, game theory is decidedly social. In human conflict situations there is rarely one context-independent best strategy. What works well depends on the actions of others. And since these actions depend on perceptions, game theory takes into account that agents expect each other to have certain interests, and to do their best to attain them.
In order not to confuse issues, there is an important distinction to be made between payoff (measured in points, dollars or the like) and the personal joy gained through a game. The game theoretical concepts described in the following make sense in relation to game-internal payoff only. When considering pay-off in a broader sense, things become much more complex. For instance, one may consider it quite a victory to last for 30 moves against a Chess grandmaster. Or imagine introducing a favourite board game to a child. In this case, one may actually want to lose the first round in order to encourage the child's interest. Also, in darkened arcades many Space Invaders players will have considered their scores highly gratifying even though the game may be technically impossible to win.
Thus, when trying to explain and predict actual player behaviour one may have to examine the personal motivations of players for doing what they do. A somewhat simplistic way of understanding the scope of (analytical) game theory as regards computer games would be to say that it applies to the extent that players try to achieve the goals presented by the game. It is crucial to remain aware that the "rationalism" implied in the approach is at best a useful approximation and that the accompanying assumptions about player behaviour are non-trivial.
Four characteristics of games are of particular interest: 1) The number of players, 2) the sum type, 3)whether the game is repeated and 4) the existence and type of equilibria.
Number of Players
Game theory works with either two-person games or games with more than two players, termed n-player games. An important difference between the two types, apart from the complexity of the mathematics involved, is the fact that coalitions may form between players of n-person games affecting the game dynamics. Since we are concerned with opposing interests, a player in this perspective needs not be a single person but can be a nation, a football team or a pair of Bridge partners.
In certain cases, game theory addresses situations where a single agent is effectively playing against the environment or "nature." In these so-called parametric models or "games against nature," the player is trying to optimize his or her outcome against an opponent who is oblivious to the player's choices. However, such situations are only indirectly thought of as within the domain of game theory as they are the subjects of standard economics.
The most famous among the key two-person games is "The Prisoner's Dilemma"-- "the game that launched a thousand studies" (Kollock, 1998 p.185; see also Axelrod, 1984 ; for a popular account see Poundstone, 1992). The game, explained below, is often considered a fundamental model for the study of conflict and its simplicity and potential scope has earned it a place in textbooks within a truly wide range of fields (Smith, 2002). Briefly, the Prisoner's Dilemma is a situation in which two people are faced with a temptation to act in their personal interest disregarding the interest of the other person. However, if they both choose this (individually rational) course of action they will both be worse off than if they had cooperated.
This well-known game is illustrated below. Each player, let's call them Bob and Alice, must choose between one of two options: Cooperate or defect.