An Introduction To Game Theory: The Basics And Key Concepts

Game Theory is the analysis (or science) of rational behavior in interactive decision-making. It is therefore distinguished from individual decision-making situations by the presence of significant interactions with other ‘players’ in the game. Even though Game Theory has a mathematical origin, it is being used in fields such as economics, business, political science, psychology, computer science and even biology. For practical purposes, Game Theory can be used to help explain past events and situations, predict and forsee what actions players will take in future games, and advice clients in what actions they will have to take in interactions with other players in order to achieve the outcome that will best serve their interests. This article will go into the basics of Game Theory and provide a strong foundation from which to further build on.

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Key Concepts in Game Theory: Games, Strategies, Players, Outcomes, Payoffs and Equilibria

In order to understand Game Theory better, it is important to be familiar with some of the basic concepts, key terminology and background assumptions. The word ‘game‘ itself for example might already cause some confusion. Game Theory has nothing to do with games for entertainment such as Cards or video games. In addition, Game Theory goes beyond gambling games or even sports. Game Theory is about ‘Games of Strategy’ in which the strategic interactions of players are being examined in order to decide on the optimal strategy (set of choices) that will lead to the outcome that serves in the best interest of a certain player. It can therefore be a useful tool in business settings that deal with fierce competitors. Or it might be used to establish coalitions among politicians or bilateral relationships between countries in international trade. You therefore always need at least two parties (players) – whether they are competitors, politicians or countries – in order to call it a game. For the interaction to become a strategic game, however, these players need to be aware of each others’ presence and the effect of their decisions on the other players. Only then you can react to certains actions and forestall the bad effects of it in the future.

Outcomes and Payoffs

During a game, players have multiple actions to choose from. In business for example: will competitors raise prices or lower them? In politics: will political parties fight each other or collaborate? Each of these choices (which are part of a strategy) will eventually lead to a certain outcome. Lowering prices for example might result in more customers or a price war depending on what your competitor’s reaction is. The number associated with each possible outcome will be called that player’s payoff for that outcome. Higher payoff numbers usually stand for a more desired outcome for a certain player. By using numbers, the game gets quantified, which helps when performing calculations.

Rationality

An assumption in Game Theory is that all players in the game are considered ‘rational’ beings. Being rational in this context means a number of things. First of all, it is important that players think carefully before they act. Secondly, players are completely aware of their own objectives, preferences, limitations or constraints on their actions. Finally, they are able to perform the calculations needed that will lead to the outcome that best serves their interests. Being rational however does NOT mean that players are selfish, have no emotions or that all players have the exact same values and moral standards. It is part of the strategy to figure out what your opponent’s values are and what he or she finds important.

Equilibrium

Game theorists refer to the solution of a game as an equilibrium. This happens when a player uses the strategy that is the best response to the strategies of the other players. This does NOT necessarily mean that the player will get its preferred payoff. It simply gets the best payoff considering the choices that the other players have made. The so called Nash Equilibrium is reached when none of the players could improve their payoff, given the strategies of all other players in the game, by changing to another strategy. Or in other words: if each player has chosen a strategy and none of the players can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategic choices and the corresponding payoffs constitutes a Nash Equilibrium.

Types of Games

Games of Strategy arise in many different contexts and can therefore have many different features or characteristics. The most well-known classfications of different games are summarized below.

Sequential or Simultaneous

Sequential games entail strategic situations in which there is a strict order of play: players take turns in making there moves and they know what the other players have done. This for example happens in Chess. The player with the white pieces start and the player with the black pieces has the next turn, and so on. Furthermore, since they are both playing on the same chessboard, they can both see what the other player has done before deciding on their next move. With simultaneous games, the player has a trickier task of figuring out what the opponents is likely going to do right now. A game however is also considered simultaneous when players choose their actions in isolation and have no information on what other players have done or will do. Players therefore have to move without knowledge of what their rivals have chosen to do. The distinction between sequential and simulatenous games is important, because the two types of games require different types of interactive thinking.

Figure 1: Sequential-Move Game (Game Tree)

 

Figure 2: Simultaneous-Move Game (Payoff Matrix)

Cooperative or Non-Cooperative

Game Theory uses a special terminology to capture the distinction between strategic situations in which agreements are enforceable and those in which they are not. Games in which predetermined joint-action agreements are enforceable are called cooperative games. Agreements are for example enforceable when all players have to make their decisions in the presence of the others or when there is some third independent party that can punish a player when the agreement is violated. The Court of Justice is such a third party in society. However, most of the times games exist in situations in which individual actions are not observable nor enforceable by an external independent third party. Games in which such enforcement is not possible and individual players must be allowed to act in their own interest are called non-cooperative games.

Zero-Sum or Positive-Sum

Some games are constructed in such a way that one player can only win if the other player looses. You can for example see this in Chess or football. In these situations, the players’ interests are in complete conflict so to speak. These kind of games are called zero-sum games. More formally speaking, a zero-sum game is a mathematical representation of a situation in which each player’s gain or loss is exactly balanced by the losses or gains of the other player. Fortunately, most economic or social games are NOT zero-sum games and allow players to make deals that benefit everyone. These games can be called positive-sum games or win-win situations. Companies often do this by cooperating with competitors through Joint Ventures, alliances or strategic partnerships. Political parties can do this by forming coalitions. These parties’ interests might not be fully aligned but because of some overlap in their interests, they might still be able to cooperate in order to grow the total pie and benefit all to some extant.

Perfect or Imperfect and Complete or Incomplete Information

Before players move in a game, they are either perfectly informed about the ‘history’ of the game or not. A game where players are informed about all the events that have previously occured (moves previously made by all other players) are called games of ‘perfect information’. Most games however are imperfect-information games. Hence, this simply means that players are unaware of the actions chosen by other players. In addition, you can have games of complete and incomplete information. With complete information, each player knows the other players’ preferences (payoffs) and possible strategies. In such a case, there is so called ‘common knowledge’ among the players. Inversely, in a game with incomplete information, players do not possess full information about their opponents. Some players possess private information, a fact that the others should take into account when forming expectations about how those players will behave. In the real world, we most often encounter games of incomplete information, since people usually tend to keep some crucial information about them to themselves.

Solving the Games: Finding the Nash Equilibrium

Now you are familiar with some of the key concepts of Game Theory, the next step is to learn how to solve each game. Each type of game however has its own method of solving it. A sequential-move game for example requires a completely different way of solving than a simultanious-move game. We will therefore cover these methods in separate articles.

Further readings:

  • Dixit, A., Skeath, S. & Reiley, D.H. (2015). Games of Strategy. Norton. 4th Edition
  • Samuelson, L. (2016). Game Theory in Economics and Beyond. Journal of Economic Perspectives.
  • Dixit, A. (2006). Thomas Schelling’s Contribution to Game Theory. Scandinavian Journal of Economics.
  • https://plato.stanford.edu/entries/game-theory/