Game Theory
Introduction
For some it’s a challenge they’ve always wanted to take, for others it’s a daunting task. Regardless of which group you resonate with, one thing's for sure - game theory doesn't leave anyone indifferent.
You may have your doubts about it, about its potential limitations, its obscure formulas at times, but game theory has been analyzed by the best minds and has been applied by the brightest. That alone speaks a lot about it.
That said, we want to “bring” this discipline closer to people by stripping it of its complexities and obscurities. In other words, we’ll cover the basics of game theory in a manner that will allow you to connect with it much more meaningfully.
So, let’s see what the fuss is all about!
What Is Game Theory?
To keep things simple here’s a relatively straightforward definition of game theory:
Game theory is the process of modeling the strategic interaction between two or more players in a situation containing set rules and outcomes. While used in a number of disciplines, game theory is most notably used as a tool within the study of economics. The economic application of game theory can be a valuable tool to aid in the fundamental analysis of industries, sectors and any strategic interaction between two or more firms.
In general, game theory is the science of strategy - it tries to logically determine the possible actions “the players” (or rather, participants) can take in order to secure the best possible outcomes for everybody concerned. The “games” (situations) in question have one thing in common: interdependence, meaning that the outcomes will depend on the decisions made by all players (so it’s not enough for one player to opt for the best strategy - each player’s move affects the other ones).
Game theory helps us understand other people’s moves and why we make decisions the way we do, that is, what we take into account before deciding, what determines our next move, and which outcome motivates us to actually make our next move at all.
Plus, when it comes to these games, they aren’t made in a “neutral environment”, and here’s what we mean by it: when a lumberjack needs to chop wood, the wood won’t fight back, so we say that the lumberjack’s environment is neutral. On the other hand, if there’s a general who tries to think of ways to attack his enemy, he will surely come across some resistance from his soldiers.
We dig deeper into such examples in the following section.
Game Theory Examples
Although we’re talking about game theory, it’s a discipline applied in practice, so let’s see what that looks like.
The next sections contain four game theory examples, which illustrate the purpose behind this discipline. And although, for you, these examples may not appear like “typical games”, they most certainly are in the eyes of experienced game theorists.
Example 1: Planning a party
Someone’s planning an outdoor party and they’re worried if it will rain or not. Here’s what the probabilities for each scenario look like:
Nature’s states:
Rain No rain
(p=⅓) (~p=⅔)
Party Outside: 1 3
planner’s
possible Inside: 2 2
scenarios:
This scenario belongs to “games against nature”, and so the expected utility of action A about an uncertain state S can be expressed in the following manner: S = Probability(S|A)*Utility(S|A) + Probability(not S|A)Utility(not S|A).
Action A can be seen as the outcome, and plus, the probability of each state can depend on the agent’s course of action (although in the above-given example, it really doesn’t).
So, in terms of the party problem, here’s how we can illustrate it:
EU(Outside) = (1/3)(1) + (2/3)(3) = 2.33;
EU(Inside) = (1/3)(2) + (2/3)(2) = 2.
That said, Outside is the course of action with the higher expected utility.
Example 2 - Friends hoping to see each other
Let’s imagine two friends who wish to see each other - we’ll call them Chris and Kim. Both players enjoy spending time in each other’s company, but they’re not in a position to communicate prior to deciding whether they’ll stay at home or go to the beach in the afternoon. In the first case, they definitely won’t be able to see each other and in the latter, they could potentially meet.
Plus, both Chris and Kim prefer going to the beach rather than staying at home, and also each person prefers being in the company of the other instead of being on their own. This scenario is known as noncooperative game theory, when a decision includes more than one agent, however, each is expected to act independently (that is, there are no binding agreements).
Here’s how we can represent this scenario:
Kim
Home Beach
Chris Home (0,0) (0,1)
Beach (1,0) (2,2)
So, each play basically has the same set of “strategies” available to them: home and beach. If we were to specify one strategy (i) for Chris, who is the row player, and strategy (j) for Kim, the column player, it brings us to the following outcome: we have a pair of payoffs (Rij, Cij), in which case Rij is the utility which the row player gets, and the other one, Cij, the one which applies to the column player.
Therefore, in this specific example, the act of going to the beach ends up being a dominant strategy for both players, as it will always provide the best possible outcome (irrespective of what the other player does). In other words, beach-beach is what’s called a dominant strategy equilibrium for this particular game.
Finally, Chris and Kim (if both act rationally and logically) don’t need to make any agreements ahead of time. Each of them should freely follow their preferred interest, and the best scenario will occur for both of them.
Example 3 - "Friends" with asymmetric preferences
Now, this scenario differs from the previous one, as it deals with people with distinct preferences. Or more specifically, we have Betty and John; John is fond of Betty, however, Betty isn’t really that much into John. Both players know this, and so neither really wants to call one another before deciding what to do this particular afternoon (to stay at home or go to their neighborhood's swimming pool). Here’s what the normal form looks like:
John
Home Pool
Betty Home (2,0) (2,1)
Pool (3,0) (1,2)
In this scenario, Betty’s best option is to first see what John does. However, if she assumes what he’ll do, she is likely to come to the realization that he probably won’t stay at home (because going to the pool is a dominant strategy for John). Keeping this in mind, she may decide to stay at home (since 2>1). This is known as iterated dominance, and Pool-Home (3,0), Home-Pool (2,1), and Pool-Pool (1,2) are called Pareto optimal outcomes. Betty is the one who gets higher utility than John as a result of their relative preferences.
Example 4 - Prisoners' dilemma
The prisoners’ dilemma is probably one of the most well-known examples in game theory. It’s actually the representative example when it comes to understanding game theory in a more practical manner.
Let’s imagine two prisoners (Stan and Leland) and each has been offered a deal to “betray” the other prisoner. Initially, they’ve agreed to not testify against each other, however, the tables have turned and now they have to make different choices. Also, they’re not allowed to communicate so they have no idea what the other person is planning to do.
Here are the rules: if both remain in solidarity, each will get a minor punishment. If one defects then he will be released, but the other one gets punished. If both defect, however, each gets a longer prison sentence. Here’s what that outcome looks like:
Leland
Solidarity Defection
Stan Solidarity (3,3) (1,4)
Defection (4,1) (1,1)
Of course, the most favorable strategy would be for both of them not to confess. That said, as neither knows what the other will do, it’s very likely that both will confess and receive the longer sentence. In other words, both players will probably stick to the option which is best for them on an individual level, however, worse on a collective one. This is an example of a social dilemma, a scenario in which, as the article suggests, “each agent’s autonomous maximization of self-utility leads to an inefficient outcome”.
Finally, there are many articles that explain the prisoners’ dilemma with much more concrete options:
- If both confess, they will each receive a five-year prison sentence.
- If Prisoner 1 confesses, but Prisoner 2 does not, Prisoner 1 will get three years and Prisoner 2 will get nine years.
- If Prisoner 2 confesses, but Prisoner 1 does not, Prisoner 1 will get 10 years, and Prisoner 2 will get two years.
- If neither confesses, each will serve two years in prison.
That said, both explanations lead to the same outcome: not confessing is the most favorable option. There’s a lot to be discussed regarding this example, which is why we’ve also included it in our online course too.
Game Theory Definition
Game theory is:
- a discipline that has its roots in mathematics;
- a problem-solving approach;
- very detailed and specific;
- a “tool” used across a wide range of disciplines (as we’ll explain later on);
- a very significant theoretical framework used to work out issues between competitors;
- concerned with analyzing economic and social situations and the strategies that pop up within those situations in order for the players involved to be able to solve them;
- an interaction between two, or even multiple people, or as game theory refers to them - players, and each player’s payoff is affected by others;
- full of a bunch of “fancy” terms such as nash equilibrium, determined game, dominated outcome, finite game, pareto efficiency, zero-sum game, solved game, and so many others (we actually explain some of the most significant ones later on in this article, so make sure to read on);
- strategic interaction between players and the potential outcomes of a game;
- something that takes time to fully grasp and apply in practice;
- optimally responding to what the other person (player) is doing;
- noticing recurring strategies and patterns and understanding how to act upon them;
- reaching a clear outcome (winning or losing);
- clearly knowing all the rules before you get to play (this refers to all the players);
- for rational, sensible, and well-informed people;
- opting for the solution that provides the most benefits;
- challenging (while you know your own options and your own strategies you don’t know your opponent’s);
- making a lot of assumptions (especially when it comes to what the other player may or may not do and/or choose);
- intellectual guesswork and rationalizing all aspects of the game;
- a multi-layered process (you’re not only guessing the other player’s move, you also need to guess what the other person’s guesses are about you too);
- tricky, and yet that’s what makes it so attractive.
Game theory isn’t:
- a random type of game;
- only for those who are naturally good at it (it actually requires a lot of practice and experience);
- simply about taking a random guess;
- predictable;
- something people are sometimes consciously aware of;
- a bunch of theory (it’s actually a very practical discipline);
- as complicated as you may initially think, but it also isn’t as simple as game theorists describe it to be;
- so daunting after you’ve had some experience and feel comfortable with the discipline;
- for procrastinators;
- for those who aren’t willing to take risks;
- for those running away from making decisions;
- always applicable to all real-life situations (if you want to learn more about this, along with some of the potential limitations connected to game theory, head over to our FAQ section and take a look at the third question).
The History of Game Theory
The appearance of game theory as a unique and separate field is first noted in John von Neuman’s paper On the Theory of Games of Strategy in 1928. We talk about John von Neuman a great deal in our FAQ section, so for now we’ll just say that the initial stages of game theory were a result of the need to come up with a new mathematical model to assist the process of decision making. Game theory was extensively developed by many scholars throughout the 1950s, but it wasn’t until a bit later on that it became widely embraced as a result of some events (such as Reinhard Selten receiving the Nobel Prize for Economics in 1994 for further developing game theory in relation to economics).
Originally, game theory was applied to parlor games such as bridge, poker, and chess. Today, game theory is applied across a wide range of disciplines including behavior sciences, computer science, political science, sociology, military science, and so on.
There are different game types including cooperative and non-cooperative games, symmetric and asymmetric games, zero-sum and non-zero-sum games, simultaneous and sequential games, discrete and continuous games, and so on.
Why Is Game Theory Important?
Game theory isn’t only important as a strategy - it has a lot of other benefits and implications for those engaging in it as well. In fact, according to Brian Martin, here are some of the main advantages of studying game theory:
(1) Game theory is very recent, so that its diversification, transformation, and institutionalization in scientific theory and practice have not proceeded as far as in the case of other branches of mathematics and science.
(2) Game theory is almost solely the creation of one person - John von Neumann - and so stands relatively coherent and free from doctrinal conflict.
(3) Game theory is concerned with an area - conflict situations - in which there is no accepted framework of relevant evidence and interpretation; therefore the impact of a new theory on the direction of scholarly attention is clearer.
Here’s why we believe game theory is important:
- Game theory helps you understand rational behavior.
- It has brain-boosting benefits.
- It helps you become a better decision-maker.
- It allows you to take a walk in other people’s shoes (especially when anticipating others’ moves).
- It shows you how well you can read others (and also how well others can read you, that is, it shows whether you’re an open book or not).
- Game theory teaches us to leave our emotions aside, and devote ourselves to fully “rationalizing” a specific issue.
- Game theory is important because it shows us where we stand in terms of knowledge, intelligence, speed of response, decisiveness, and so on.
- It illustrates how significant models of thinking are and how deeply they affect human psychology and the overall patterns of thinking we have.
- Game theory forces you to consider different perspectives by teaching you patience, as one needs to “wait” and play for some time before a final decision has been made.
- It helps you consider all the twists and turns that can occur during a specific game and what implications this may hold for the game’s outcome.
- Game theory helps you win at life (but also learn to accept losses).
- It forces us to consider many different strategies and solutions, although we may have been fixated on the one we feel most comfortable with.
- Game theory helps individuals deal with consequences and teaches them how to accept failure (when it occurs).
- It makes you feel comfortable with mathematical ways of thinking, and basic probability theory.
- It’s a subtle indicator of what happens when players decide to “collaborate” unknowingly in order to reach a better outcome.
- Game theory simply shows how interconnected we all are, as we can’t make changes in our lives without affecting others (and vice versa, other people’s life decisions also impact ours - no matter how small that change may be).
How To Develop Game Theory Skills?
Some argue that game theory wasn’t popular and so mainstream until it gained recognition through the movie A Beautiful Mind where Rusell Crowe played John Nash, and it made viewers wonder: “What’s game theory?”, “How do I apply it?”, “Why does it matter?”, and more importantly “How do I develop the proper skills to engage in game theory?”.
So, naturally, questions were asked and answers were sought. Now how does one “master” this game of theory? There are many ways to work on your game theory skills, but here are the most common ones:
Focus on strategic thinking.
Become a strategic thinker. “Now how does one do that?”, you may ask. First of all, be more reflective when making decisions, meaning analyze your thinking process, denote your performance metrics, double-check sources, and so on, before you settle on a plan of action.
According to a Forbes article, here are ten questions a strategic thinker needs to take into account when making decisions:
- Why do I/we need to care about this issue? Or, what prompted the need for this decision to be made?
- What happens if I/we don’t decide on this issue? Is the status quo acceptable? Why or why not?
- What outcomes are we trying to achieve? Who cares about them and why?
- What are my/our biases, prejudices, interests, or values? Are they congruent with the defined decision options?
- Whom will this decision mostly affect? How?
- What are the positive and negative consequences of this decision? What is this based on?
- Who are the short-term and long-term beneficiaries? Who gets to define them?
- What is the worst result this decision can bring? Can I/we live with that?
- What are forces for or against this decision? Do I/we care? Why or why not?
- What is the second choice/option or fallback position? Is it viable, and how do I/we know?
Get to know others.
It’s not just about knowing yourself and your moves and plans - you need to pay attention to others too. What are their thinking patterns? How do they react when they’re angry? Are they thinking only about themselves when making decisions? How do you know if you can trust someone?
Also, are the people you’re dealing with rational or emotional? Open or closed? Approachable or not? This is important because when you’re dealing with game theory, understanding your opponent is as important as planning your next move.
Try to get experience.
This one is pretty much straight forward. The more you engage in game theory, the better you are at it. The thing here is to understand that you may make mistakes, you may feel insecure, and you may feel others are better than you. It’s all part of the learning process. The faster you realize this, the easier your journey of learning game theory becomes.
Be open to the unknown.
When you’re dealing with game theory, it’s important to keep an open mind and simply stay open to the unknown, and this may manifest in various ways. For instance, you may come up with a solving strategy you have never considered before for your specific issue, you could get an idea from a person when you least expect it.
This may sound weird, and you may wonder “How is this relevant when it comes to developing my game theory skills?”, but it is. Staying open keeps you on the edge, doesn’t allow you to fall into routine or any comfort zones, and forces you to take into consideration things you may otherwise decide to neglect. This will change the way you perceive your world and the overall environment.
As Brandenburger and Nalebuff put it:
Game theory is a different way of looking at the world. In game theory, nothing is fixed. The economy is dynamic and evolving. The players create new markets and take multiple roles. They innovate. No one takes products or prices as given. If this sounds like the free-form and rapidly transforming marketplace, that's why game theory may be the kernel of a new economics for the new economy.
Examples of Game Theory in Everyday Life
Economics
Did you know that twenty game theorists have received the Nobel Memorial Prize Award in Economic Sciences for their contribution to the discipline? This alone probably seems much more than what we can cover in this whole section devoted to economics. But we’ll try.
Economics is probably the most important field when it comes to using game theory because this is why game theory was created in the first place - to provide a fresh way of solving problems in economics.
One common way economists tend to use game theory is to understand oligopoly firm behavior. For instance, this is especially helpful when it comes to price-fixing.
All companies want to achieve maximum profit, increase sales, and ensure their customers are happy, but they can’t neglect their competition. It’s only natural. So, when it comes to deciding whether to introduce a new product (or retire a new one), opt for a new marketing campaign, and or lower prices, companies can’t help but see where their competitors stand.
Let’s take a look at a very simple example with Apple and Samsung as players engaging in a so-called “game of advertising”:
As both firms have a stable market reputation, the advertising costs are a direct drain on the net corporate profits. If both do not advertise, their profits will remain the same (with many simplistic assumptions, including that there are no other competitors). But advertising budgets are assigned in both the firms so that they do not lose market share to the competitor (spending on advertising is a good strategy for both irrespective of the decision taken by the competitor).
There’s a lot to be said about business and economics and their connection to game theory, but the important thing is that game theory brought about a fresh perspective in these fields and has certainly kept employees on their toes.
After all, knowing what game theory means now and the implications that it has it seems all businesses engage in it, whether knowingly or unknowingly. So, it’s that important and that impactful.
How to approach this?
- Do I apply game theory in my everyday business life? Why (not)?
- Am I the type of person who analyzes my opponent's every move, thought, action or idea? If yes, am I discreet about it?
- What are some of the most important things to ensure the success of a business deal? Make a list.
- How willing am I to take risks when I know I have a boss I answer to? And vice versa, how willing am I to take risks when I know all the responsibility falls on my shoulders?
- Do I have an entrepreneurial mindset? How can I tell for sure? Could I maybe benefit from improving my entrepreneurial skills?
- Do I re-evaluate how my workday went, what happened during the meeting with my colleague and the people I ran across during my coffee break, and so on? Do I wish I had reacted differently in some of these situations? Why?
- When it comes to work decisions, do I have any regrets? Maybe I should have asked for a promotion? I should have chosen a different company? Opted for a different job position altogether? Do I think about all these things?
- Do I feel others try to outsmart me? If yes, why do I allow this to happen? What changes can I make?
- What types of strategies am I comfortable with when it comes to persuading others to cooperate with my company/ accept our offer/ buy our products, and so on?
- Do I need to know what my colleagues think about a specific issue before I can make up my mind about it?
- Do I take initiative? Why (not)?
- Do I think about my workday and how it went even after I’ve left my job, or I feel free to relax and do something else in the evening? If I think about it, is it due to having regrets and feelings that something could’ve been done differently, or due to feeling proud of my achievements and decisions that day?
Decision making
We make decisions each day from the moment we open our eyes, to the moment we go to bed. And then we repeat the same the next day.
However, each of us has different values, priorities, beliefs, and approaches to solving problems, which may be problematic when it comes to making important decisions. Plus, what makes decision-making difficult is that oftentimes there’s another person on the other side of the “problem” and we may need to compromise (or at least consider their point of view).
Let’s take the following example: you are buying a car from a car dealership and here’s what this looks like from both perspectives.
The dealer wants to sell the car, and has a fixed price beyond which he cannot drop without making a loss. You want to buy the car, but get the best price. The car dealer bases his negotiating tactics on the fact that you want the car, that he could sell the car to another customer, that he'll win praise for selling the car, and the break-even point beyond which he cannot negotiate down.
You base your negotiating on the fact that the dealer wants to sell the car, that there is a profit margin into which you can haggle to bring down the car's price, and are mindful that the dealer knows your presence in his office means you want to buy a car.
So, making decisions isn’t only about ourselves. They impact others the same way others’ decisions impact us. Game theory is said to be an effective way of assisting individuals (or groups) in making better decisions. This is especially true for strategic situations where we may observe certain competitive behaviors (such as auctions, product decisions, supply chain design, bargaining activities, negotiations, stocks and shares, employer-employee talks, and so on).
Overall, game theory is supposed to offer a neat methodology for reasonable decision-makers, and those who wish to challenge themselves.
How to approach this?
- How do I make decisions? Can I make a decision right away, or I need time to come up with possible solutions? Do I overthink or I have no problem reacting quite quickly?
- Do I share my decisions with others before I act on them? Do I rely on what they’ll say? Why (not)?
- Is it more stressful for me to make decisions at work or at home? Why is that so? Think of one problem you had at work and another one at home and try to analyze how you came up with the solutions and which option was harder.
- Do I allow emotions to outweigh my logical reasoning when making decisions?
- Do we make choices all the time or simply life happens to us and we have no say in it?
- How can I make better choices and better decisions starting today? Also, what patterns of thinking and behavior do I want to get rid of?
- Are there any limiting thoughts blocking me from coming up with better solutions?
- Can I focus my attention on more problems (that is, can I multitask), or I’m able to do one thing at a time? Do I consider this (whichever option you identify with) to be an issue?
- Have I ever made a decision based on tossing a coin? If yes, what has that taught me? Will I ever do it again? Why (not?)
- “The more I think about a problem, the bigger the problem becomes”. Yes or no?
- “I make the best decisions under pressure”. Yes or no?
- “I’ve never made a wrong decision in my entire life”. Yes or no?
- “Others don’t know what’s best for me, therefore, I can’t go to others for advice.” Yes or no?
- “I put in the effort to think only about important matters in life such as money, family, work, and friends; more basic stuff such as food, travel, and random activities aren’t worth stressing over.” Yes or no?
Human Psychology
The fascinating thing about game theory and the way it affects human psychology is that it shows how individual decisions and behaviors may potentially result in harmful consequences for society as a whole. Consider the following examples:
In sports, all professional athletes would be better off if no one used performance-enhancing drugs. The problem is that when no one uses these drugs, an individual athlete is tempted to use them in order to perform better than everyone else [...]. This then leads everyone to consume performance-enhancing drugs, and any athlete who decides not to consume these drugs would suffer from a major comparative disadvantage.
This also applies to environmental policies regarding CO2 emissions. The world as a whole needs to stop climate change, but each country individually has an economic interest in emitting CO2 for their industrial production, which leads to global inaction.
This is known as the Nash equilibrium, or in simple words, the act of doing what’s best for you. It’s in human nature to want what’s best for us - it’s almost as if we were wired that way. That said, some may argue that that’s pure ego and selfishness, others simply accept it as such.
However, an interesting aspect when it comes to human psychology is that oftentimes we make decisions based on current emotions and feelings (this is especially true if we're very attached to a specific outcome or we’re simply biased). Yet, game theory highlights utmost rationality, logic, and balanced thinking. Overall, it seems it’s up to us (and our individual psychology) to choose how we’d handle this.
But, it’s important to understand that sometimes our unconscious behaviors can outweigh our conscious efforts. For instance, even measurements of participants’ gazes and pupillometry can be informative for understanding potential deception in a game theory decision making task.
How to approach this?
- How can I contribute better: to my family, my society, my workplace, and the people around me?
- When is the last time I’ve acted selfishly? Why? What caused my reaction? Will I react differently the next time?
- Do I always know who I’m impacting with my actions?
- Do I understand my behavior in all situations? How do I react when I’m sad vs. happy; calm vs. triggered; angry vs. calm?
- When was the last time I lost control over my actions? What happened? Will I allow for it to happen the next time too? What steps can I take to make sure I react better?
- How would I react if somebody told me I’ve hurt them (verbally)?
- How would I describe human awareness?
- The way I see it, the most important thing about human psychology is _________ (fill in the blank).
- I’m not aware about my ___________, ____________, _____________(fill in the blanks).
- What bothers me about people is that they __________, ___________, __________, (fill in the blanks).
- What I like about people is that they ___________, ____________, ____________ (fill in the blanks).
- If I had the chance to apologize to someone I’ve hurt, will I do it? Why (not)?
- Is pride an important part of how I communicate with others?
- How do I usually solve conflicts? Is there anything problematic about my approach?
- Do I tend to lie about the small stuff (white lies)? If I do, how exactly do I think such behavior is helping me? On the other hand, how do I react if I know I’m the one I’ve been lied to?
- Am I afraid to confront others?
- What do I think about commitment?
- What are some emotions I’m not comfortable with? Why? Is it because I’ve never felt them before, or because I have but never dealt with them?
Famous Quotes about Game Theory
“The actual rewards that come from arguing with other people have nothing to do with winning and losing. A good argument helps us refine our own ideas and discover where our reasoning is the weakest. Other people's opposition can help us turn our own half-formed ideas into clear assertions backed by solid reasoning. And setting our ideas and opinions against someone else's helps us know each other better, which makes us better friends. We get these benefits from arguments when we collaborate with a partner. We do not get them when we try to destroy an enemy. That is how non-zero-sum games work.”
“If changing strategies doesn't help, you can try to change the game. And if that's not possible, you can at least exercise some control about which games you choose to play. The road to hell is paved with intractable recursions, bad equilibria, and information cascades. Seek out games where honesty is the dominant strategy. Then just be yourself.”
“The Game gives you a Purpose. The Real Game is, to Find a Purpose.”
“Love is like organized crime. It changes the structure of marriage game so that the equilibrium becomes the outcome that works for everybody.”
“All reality is a game. Physics at its most fundamental, the very fabric of our universe, results directly from the interaction of certain fairly simple rules, and chance; the same description may be applied to the best, most elefant and both intellectually and aesthetically satisfying games. By being unknowable, by resulting from events which, at the sub-atomic level, cannot be fully predicted, the future remains makeable, and retains the possibility of change, the hope of coming to prevail; victory, to use an unfashionable word. In this, the future is a game; time is one of the rules. Generally, all the best mechanistic games - those which can be played in any sense "perfectly", such as a grid, Prallian scope, 'nkraytle, chess, Farnic dimensions - can be traced to civilisations lacking a realistic view of the universe (let alone the reality). They are also, I might add, invariably pre-machine-sentience societies.”
“[G]ame theory has an essential role in the analysis of rationality. It helps us define a kind of rationality. Or one kind of rationality. But mathematical analysis of abstract games is not the same as philosophical understanding of rationality.”
“Danny: You can be as morally righteous as you want—in a vacuum—but throw in a second entity and you gotta start acting in response to the other.”
“For us the chief point of interest is the place where the game is played. Generally it is a simple circle, dyutamandalam, drawn on the ground. The circle as such, however, has a magic significance. It is drawn with great care, all sorts of precautions being taken against cheating. The players are not allowed to leave the ring until they have discharged their obligations. But, sometimes a special hall is provisionally erected for the game, and this hall is holy ground. The Mahabharata devotes a whole chapter to the erection of the dicing hall - sabha - where the Pandavas are to meet their partners. Games, of chance, therefore, have their serious side. They are included in ritual.”
Frequently Asked Questions (FAQ)
Who invented game theory?
Game Theory has initially been developed by John von Neumann, an American mathematician, and his colleague Oskar Morgenstern, an economist, to solve problems in the field of economics.
In their book The Theory of Games and Economic Behavior (1944), both Morgenstern and Neumann argue that the mathematics which was created for the physical sciences wasn’t an adequate model for economics. Instead, they observed that economics resembled a game, where players try to anticipate each other’s moves, which poses the need for a new type of mathematics. And this new type of mathematics is what they called game theory.
For many, the term game theory may be slightly misleading, as some may associate it with games in the traditional sense of the word, but for those who fully understand the concept, and more importantly, are familiar with the work of Neumann and Morgenstern, this isn’t the case.
John von Neumann treated game theory as a separate mathematical discipline. Back in 1928, he managed to prove this minimax theorem. The theorem basically established that in zero-sum games with perfect information (meaning each player is aware of all the “moves” that have occurred so far), there’s a possible pair of strategies available to both players and they allow each of them to minimize their maximum losses. So, when considering each strategy, the player should consider all the possible responses of his opponent too. Then, the player will opt for the strategy which will bring about minimization of their maximum loss. The strategies which minimize the maximum loss for each player are called optimal strategies.
What are some important terms in game theory?
As if the concept of game theory isn’t complex enough, there are a bunch of game theory terms that denote different aspects of the theory. That said, the terms aren’t there to further confuse you. In fact, once you know the terms and are comfortable with their meaning, we guarantee you’ll understand the basics of game theory even better.
So, here are the most significant ones:
- Payoff matrix: refers to the matrix whose elements represent all amounts the row player has either lost or won;
- Saddle point: denotes the amount in a playoff matrix, which is the smallest in a specific row, but at the same time it’s also the largest in its column (please note that not all matrices have saddle points);
- Strictly determined game: denotes a game that has a saddle point;
- Fair game: denotes a game with a value 0;
- Strategy: represents the move(s) chosen by the player(s);
- Optimal strategy: the strategy that will be the most beneficial to the player;
- Pure strategy: when the player chooses the same row or column all the time;
- Mixed strategy: when the player changes their choice of column or row with different plays or turns;
- Value (expected value) of game: the amount which represents the results when both players play the best possible strategy;
- Zero-sum game: refers to a situation during the game when one player’s gain is equivalent to the other player’s loss; basically, what one player wins, the other one loses.
What are the limitations of game theory?
While we’re fond of game theory and the implications it holds for the individual, it’s only fair to acknowledge some of its limitations too. After all, even game theorists have openly spoken about this. Take Ariel Rubinstein, for instance.
What baffled many is that Ariel Rubinstein, who is well known in the game theory world, had doubts about it having any practical usage whatsoever. As he explained,
The choice of the name “theory of games” was brilliant as a marketing device. The word “game” has friendly, enjoyable associations. It gives a good feeling to people. It reminds us of our childhood, of chess and checkers, of children’s games. The associations are very light, not heavy, even though you may be trying to deal with issues like nuclear deterrence. I think it’s a very tempting idea for people, that they can take something simple and apply it to situations that are very complicated, like the economic crisis or nuclear deterrence. But this is an illusion. Now my views, I have to say, are extreme compared to many of my colleagues. I believe that game theory is very interesting. I’ve spent a lot of my life thinking about it, but I don’t respect the claims that it has direct applications.
Other examples
Also, game theory presumes that each player has a firm understanding of all the strategies (that is, it presumes that each player is a rational and knowledgeable human being), which may not always be the case. So, this may end up being a highly unrealistic assumption in the long run.
What’s more, not all strategies and scenarios are fully applicable to all real-life situations. And not all decisions we make on a daily basis can be “calculated” or analyzed using these strategies. A lot of times our issues and problems go far beyond Nash equilibrium, payoff, information set, and so on.
Finally, Brain Martin puts the following into perspective too:
Many defenders of game theory would say that many or most of its applications (and certainly its ex post facto use as a legitimization of policies) in practice constitute 'misuses' of the theory: the theory was not designed for these purposes. These defenders can go to great lengths to spell out when game theory is appropriate and when it is not. But from the point of view of game theory's value-laden concepts and selective usefulness, these 'misuses' are not due so much to fault of users as to the bias in the theory itself: the theory lends itself to 'misuse'.
Suggestions for Further Reading
Let’s be honest - game theory is for the curious and the knowledgeable ones. It’s for those willing to constantly work on keeping a sharp mindset and stay open to new ideas.
One of the best ways to educate yourself about game theory is to read what others have written about it. By reading about their experiences, suggestions, opinions, and thoughts, you’re upgrading yours. You’re opening yourself up to a higher perspective, which is what the ultimate purpose of game theory is, anyway.
We’ve chosen highly acclaimed books; books that will not only expand your current knowledge but also make you re-evaluate everything you’ve known so far.
We hope you’ll enjoy them!
- Theory of Games and Economic Behavior, by John von Neumann and Oskar Morgenstern
- The Art of Strategy: A Game Theorist's Guide to Success in Business and Life, by Avinash K. Dixit and Barry J. Nalebuff
- The Evolution of Cooperation: Revised Edition, by Robert Axelrod
- The Infinite Game, by Simon Sinek
- The Joy of Game Theory: An Introduction to Strategic Thinking, by Presh Talwalkar
- Thinking Strategically: The Competitive Edge in Business, Politics, and Everyday Life, by Avinash Dixit and Barry Nalebuff
- Prisoner's Dilemma: John von Neumann, Game Theory, and the Puzzle of the Bomb, by William Poundstone
- Rock, Paper, Scissors: Game Theory in Everyday Life, by Len Fisher
- Game Theory: A Very Short Introduction, by Ken Binmore
- Game Theory: A Nontechnical Introduction, by Morton D. Davis
- The Predictioneer's Game: Using the Logic of Brazen Self-Interest to See and Shape the Future, by Bruce Bueno De Mesquita
- Winning Ways for Your Mathematical Plays: Volume 1, by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy
Final Thoughts
To sum up, game theory is a complex discipline with many “branches” and subcategories, but it all unravels perfectly for the patient and the curious ones. It’s not a discipline you master overnight, which is precisely what makes it so exciting and appealing to learn.
And if you think we’ve told you everything there is to know about game theory here, you’re wrong! There are so many other details and other fun stuff to learn!
Of course, you can learn a lot on your own (also by going through the books we’ve shared with you), and/or you can join our amazing online course on game theory. Here’s what other game theory areas you can expect to learn about:
- the assumptions of game theory;
- repeated games and the tit-for-tat strategy;
- details about the Nash equilibrium;
- board games and game theory;
- reciprocity and conventions;
- chance and game theory.
There’s so much more, and we can’t wait to share all of it with you!
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