Define parallel play

Parallel play Definition & Meaning

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noun

a form of play in which a very young child plays independently in the presence of another child or other children.

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Words nearby parallel play

parallel of altitude, parallel of latitude, parallelogram, parallelogram law, parallelogram rule, parallel play, parallel port, parallel postulate, parallel processing, parallel projection, parallel resonance

Dictionary. com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2023

How to use parallel play in a sentence

Have there been discussions with FX regarding an Archer movie, and how do you think that would play out?
‘Archer’ Creator Adam Reed Spills Season 6 Secrets, From Surreal Plotlines to Life Post-ISIS|Marlow Stern|January 8, 2015|DAILY BEAST
Father Joel Román Salazar died in a car crash in 2013; his death was ruled an accident, but the suspicion of foul play persists.
Mexico’s Priests Are Marked for Murder|Jason McGahan|January 7, 2015|DAILY BEAST
He plays an aging punk rocker and I play the drummer from his old band.
Coffee Talk with Fred Armisen: On ‘Portlandia,’ Meeting Obama, and Taylor Swift’s Greatness|Marlow Stern|January 7, 2015|DAILY BEAST
When fathers hold and play with their children, oxytocin and prolactin kick in, priming them for bonding.
How Good Dads Can Change the World|Gary Barker, PhD, Michael Kaufman|January 6, 2015|DAILY BEAST

Ironically, the play deals with the ‘management’ of information by the Establishment.
Harry’s Daddy, and Diana’s ‘Murder’: Royal Rumors In a New Play|Tom Sykes|January 4, 2015|DAILY BEAST
I assure you, no matter how beautifully we play any piece, the minute Liszt plays it, you would scarcely recognize it!
Music-Study in Germany|Amy Fay
But I hope at least to play to him a few times, and what is more important, to hear him play repeatedly.
Music-Study in Germany|Amy Fay
To fill up the time till Liszt came, our hostess made us play, one after the other, beginning with the latest arrival.
Music-Study in Germany|Amy Fay
Again the sallow fingers began to play with the book-covers, passing from one to another, but always slowly and gently.
Bella Donna|Robert Hichens
Her attachment to impressionism leads this artist to many experiments in color—or, as one critic wrote, "to play with color."
Women in the fine arts, from the Seventh Century B.C. to the Twentieth Century A. D.|Clara Erskine Clement

What Is Parallel Play And How Does Your Baby Benefit From It?

| What Is Parallel Play | Examples | Why Is Parallel Play Important |

If you’ve taken your baby to a playdate only to find that they sit near other children but never join in the fun, you may be just a bit concerned.

Does this mean your baby is anti-social at such a tender age?

Is the reluctance to engage in social interaction a sign of something more serious?

You can relax.

Your baby isn’t holding anything back. They are engaging in parallel play. They’re doing exactly what they should be doing at this age and right on cue.

What Is Parallel Play

Parallel play takes place when two toddlers play near one another, usually with the same material, without interacting directly. Parallel play is quite common in young children from 18 months old to age two. ¹

During parallel play, some children observe their playmates and mimic their behavior. While this can be considered as social behavior, there’s still a noticeable lack of full-on interaction².

Examples Of Parallel Play

Parallel play is often seen on the playground among young children.

When two toddlers play in the sandbox near each other, they may both grab handfuls of sand and watch it sift through their fingers. Or they both use a bucket to build a sand castle. Each one is engaged with the process but not with each other.

If a playmate is playing with a doll, for example, the other child is likely to start playing with a doll as well.

Why Is Parallel Play Important

Every type of play contributes to a child’s cognitive development and social development, and parallel play is no exception³.

But the importance of this type of play is divided into two schools of thought.

Stages of play

Parten (1932) described parallel play as a stage children pass through as they develop from solitary players to social ones. She believed that the six stages of play – unoccupied, onlooker, solitary, parallel, associative, cooperative – were ordered, representing increasing levels of social participation.

As a result, parallel play is important because it represents a milestone in a child’s development of social skills. With age, this type of play will decrease⁴.

Strategy of play

Although Parten’s study proposed six categories of play as “stages”, other scientists have found that children sometimes do not go through these stages sequentially or at all.

While one child can progress from solitary play to parallel play and then to group play, another can go directly from solitary play to group play⁵.

Parallel play is also found to not vary much with age.

Sugarman-Bell (1978), believed that children developed person-oriented and object-oriented interactive abilities separately, resulting in two major modes of play – alone play and group play.

As the first year progresses, these two abilities begin to work together. Children begin integrating people into their physical activity of object manipulation and objects into their social environment in a systematic way.

Adding a social focus or an object focus is done one at a time, not simultaneously.

Children who are playing alone may desire to play with other children but may not have the skills to engage in group play immediately. Parallel play is a step or strategy to bring them closer to group play. It is an optional state that arises momentarily as needed. It provides a child opportunities to play with others.

Parallel play is therefore important because it initiates group play rather than being a developmental stage as previously believed⁶.

Final thoughts on parallel play

Playing, regardless of the types of play, is important in a child’s healthy development. It challenges and socializes a child through activities. Help them develop connections with people by setting up playdates for your child with children their age.

References

1.
Anderson-McNamee JK, Bailey SJ. The importance of play in early childhood development. Montana State University Extention. 2010;4(10):1-4.
2.
Grusec JE, Abramovitch R. Imitation of Peers and Adults in a Natural Setting: A Functional Analysis. Child Development. Published online June 1982:636. doi:10.2307/1129374
3.
Milteer RM, Ginsburg KR, Mulligan DA, et al. The Importance of Play in Promoting Healthy Child Development and Maintaining Strong Parent-Child Bond: Focus on Children in Poverty. Pediatrics. Published online January 1, 2012:e204-e213. doi:10.1542/peds.2011-2953
4.
Smith PK. A longitudinal study of social participation in preschool children: Solitary and parallel play reexamined. Developmental Psychology. Published online 1978:517-523. doi:10. 1037/0012-1649.14.5.517
5.
Robinson CC, Anderson GT, Porter CL, Hart CH, Wouden-Miller M. Sequential transition patterns of preschoolers’ social interactions during child-initiated play: Is parallel-aware play a bidirectional bridge to other play states? Early Childhood Research Quarterly. Published online March 2003:3-21. doi:10.1016/s0885-2006(03)00003-6
6.
Bakeman R, Brownlee JR. The Strategic Use of Parallel Play: A Sequential Analysis. Child Development. Published online September 1980:873. doi:10.2307/1129476

About Pamela Li

Pamela Li is a bestselling author. She is the Founder and Editor-in-Chief of Parenting For Brain. Her educational background is in Electrical Engineering (MS, Stanford University) and Business Management (MBA, Harvard University). Learn more

View all posts by Pamela Li | Website

Game theory and its application in life / Sudo Null IT News

Hello, reader!

Some of you have seen the "qwerty" set of letters. Qwerty is a keyboard layout. Look at your keyboard. You will see the letters "q" "w" "e" "r" "t" "y" in the top row. And for what reason are we interested in the keyboard layout?

A long time ago, when people used typewriters, they typed quite quickly. This created problems: the heads of the typewriter, hitting the paper and printing letters on it, clung to each other, which led to breakage. A qwerty layout was created, in which letters standing next to each other were placed at the maximum possible distance from each other. Thus the problem was solved. nine0003

No one has been using typewriters for a long time, and the problem of contact between the print heads has disappeared. The fact that we stopped using the uncomfortable keyboard layout is logical. But, there is a catch - this fact does not exist, people are used to typing on the qwerty layout and do not want to relearn.

You can now switch the keyboard layout to "dvorak" by going into settings. Printing will speed up at times, while training will take only a week. Unfortunately, it is not beneficial for anyone to be the only one who has relearned, because it will be inconvenient to work on any computer other than a personal one. And also, unfortunately or fortunately, people are too lazy to relearn. Although together, with effort and retraining, we could increase the typing throughput by several times. nine0003

To sum it up: in the mass use of "qwerty", the transition of an individual player to "dvorak" is not effective, although the transition of the society to "dvorak" is effective.

The concept of "Game Theory"

Game theory is the study of conflicts between two or more parties, called games. The games themselves, the strategies used in the games, as well as the behavior patterns in the games fall under the study. The behavior of players is conditioned by strategies. The strategies inherent in the players are called "behavior patterns". nine0003

Let's take an example:

There is an automaton that reacts to your actions. If you put a coin in it, your opponent will get three coins - and vice versa, if your opponent puts a coin in the machine, you will get 3 coins.

In this case, there are 2 players in the game - "Naive" and "Strategist". They can trust the opponent, therefore put a coin or cheat and not put a coin.

What will happen? If the first player and his opponent trust, then the first player will receive 3 coins by giving 1 and his opponent will receive 3 coins by giving 1. If player number 1 trusts and the opponent cheats, then the player will not receive anything by giving 1 coin. If the first player cheats and the opponent trusts, then the player will receive 3 coins without spending any. If both participants try to cheat, they will get nothing. nine0003

For convenience, let's denote player 1 as I1 and player 2 as I2.

Table:

On the table we clearly see the possible options for the development of games, then we will build a lot of similar tables. What conclusions can we draw from the table?

Let's try to find the most profitable strategy - the plan, following which we will get the greatest benefit. So which strategy is the most profitable?

If the opponent trusts, I1, choosing the strategy "Deceive", will receive the highest win. If the enemy deceives us, then the "Deceive" strategy also wins. Although it is cruel, the strategy of cheating is always the best. nine0003

What are patterns of behavior? These are strategies that certain players constantly use. Let's remember the names of our players - "Strategist" and "Naive". Perhaps their names were given based on the strategies they use? Yes it is. And here are the strategies used by the players: "Strategist" looks at the opponent's previous action and analyzes it, "Naive", in turn, always trusts.

It is also necessary to mention the Nash equilibrium. Nash equilibrium is a situation in which no participant can increase the payoff by changing his strategy if the other participants do not change their strategies. Remember the intro? Namely the game “qwerty”. If all gadget users were retrained to dvorak, society would be better off, but by no means, retraining only a few players is not profitable - this is the Nash equilibrium. nine0003

Terms and types of games

Game theory is a branch of mathematical economics. Studying conflicts and their resolution.

A game is a conflict between two or more parties, in which each party pursues its own personal interests.

The outcome of the game is a win, a loss or a draw, as well as the reward received.

Strategy - the conclusions from which the choice of actions in the game proceeds.

Behavior pattern - a player's inherent strategy or strategies.

Nash equilibrium — This is the name of a set of strategies in a game for two or more players in which no participant can increase the payoff by changing his strategy if the other participants do not change their strategies. Often in games with equilibrium, changing the strategy of all participants will lead to an increase in payoff, but it is unprofitable for each individual participant in the game to change the strategy. nine0003

Cooperative and non-cooperative. The game is called cooperative when players can unite in groups, make commitments to other players and coordinate their actions. Unlike cooperative games, non-cooperative games are games where everyone has to play only for themselves. Hybrid games include elements of cooperative and non-cooperative games. This means that each player will pursue the interests of his group and at the same time try to make a personal profit.

Symmetrical and asymmetrical. The game is symmetrical when the players will have respectively the same rewards. In other words, if the players change places, they will receive payoffs for the same moves as without changing places. Many of the studied games for two players are symmetrical.

Zero-sum and non-zero-sum. Zero-sum games are games with a constant game fund, the available resources of the game cannot become more or less. In this case, the sum of all wins is equal to the sum of all losers for each move. An example of such a game is poker. In non-zero-sum games, a win for one player does not necessarily mean a loss for another player. The result of such a game can be less than or greater than zero. nine0003

Parallel and series. In parallel games, all players can take an action in a given time interval. All parties make their move in a given period of time, without knowing the actions of their opponents, until the end of the game. In sequential games, participants can make moves in a predetermined or random order, but in doing so they receive some information about the previous actions of others.

With complete or incomplete information. In a game with complete information, the participants know all the moves made up to the current moment, as well as the possible strategies of opponents. Complete information is not available in parallel games. In a game with incomplete information, players have only partial information about the opponent. nine0003

Games with an infinite number of steps. Infinite Step Games, as the name suggests, have no limit on the number of steps. Games with a finite number of steps are the exact opposite, they are limited by the number of them.

Discrete and continuous games. Discrete games are games with a limited number of steps, events, outcomes. Continuous games are games that continue for an infinite amount of time.

Game analysis

Ultimatum game

Play 1 time. There are 2 players. The former may divide the sum of 200 decillion francs between himself and the enemy. The opponent can agree with the decision of the first player - to divide the winnings, or refuse. In case of refusal, no one gets anything.

Let's classify the game!

This is a non-cooperative game because cannot join groups. This is not a symmetrical game, because 1 and 2 players have different actions in the game. This is a non-zero-sum game, because all winnings can be lost. This is a sequential game, as decisions are made in turn - 1, and then 2 player. This is a game of complete information, as the second player has access to information about the actions of the first player. This is a game with a non-infinite number of steps - only 2 steps. This is a discrete game, because the number of actions is limited. nine0003

We are playing as 1 player. How to choose a strategy? Imagine possible developments.

n > 0: Any reasonable player will agree to share the winnings, because no one will refuse to become the second or even the first richest person on our planet.

n = 0: The player can either agree or refuse.

Thus, the optimal strategy for 1 player is to offer the opponent 1 decillion francs, taking the remaining 199 for himself.

Deer hunting game

The essence of the game - a group of hunters of 2 people went hunting for a deer in the region with a very large number of hares. The goal of the hunters is to kill the deer. The goal of each player is to kill prey. Although the highest benefit for all players is the deer, each of the hunters can kill the hare for personal gain, but frightening the deer. nine0003

Classification.

This is a cooperative game - players can form groups. This is a symmetrical game, because players have the same choice of actions. This is a non-zero-sum game because the entire payoff varies. This is a parallel game, because decisions are made in the same interval, arbitrarily. This is a game of complete information, as both players have access to information about each other's actions. This is a game with a non-infinite number of steps - only 1 step is available. This is a discrete game, because. the number of actions is limited. nine0003

Let's build a scheme:

The reward for the deer is definitely higher, but the chance of being left with nothing is high. Playing with a reliable partner you can trust, you can arrange to kill a deer. Otherwise, it is better to choose the Hare strategy.

Botto game

2 players play. Each of them can write 3 digits, but not in descending order. The sum of the digits must equal 6. The player whose 2 digit positions exceed the opponent's 2 digit positions wins.

Classification.

This is a non-cooperative game - players cannot form groups. This is a symmetrical game, because players have the same choice of actions. This is a zero-sum game because all winnings are fixed. This is a parallel game, because decisions are made in the same interval, arbitrarily. This is a game of incomplete information, as both players do not have access to information about the opponent's action. This is a game with a non-infinite number of steps - only 1 step. This is a discrete game, because the number of actions is limited. nine0003

Strategy selection.

There are 3 options for each player (the game is symmetrical):

(2-2-2) or (1-2-3) or (1-1-4).

(1-1-4) against (1-2-3) results in a draw.

(1-2-3) against (2-2-2) results in a draw.

(2-2-2) hits (1-1-4).

Thus (2-2-2) is the optimal strategy.

This game also has Our equilibrium: any combination of strategies (2-2-2) and (1-2-3).

Princess and the Beast Game

In a dark, dark cave... A dark, dark night... A dark, dark monster... Looking for a dark, dark princess... A dark, dark cave had dark, dark borders known to dark, dark players...

Simply put, the princess and the monster appeared in a cave whose boundaries are known to both the princess and the monster. The goal of the monster is to capture the princess, and the goal of the princess is to survive as long as possible. The monster can grab the princess at a small distance relative to the size of the cave. Both players have freedom of movement.

Game classification

This is a non-cooperative game - players cannot form groups. This is not a symmetrical game, because players do not have the same choice of actions. This is a zero-sum game because all winnings are fixed. This is a parallel game, because decisions are made in the same interval, arbitrarily. This is a game of incomplete information, as both players do not have access to information about each other's actions. This is a game with an infinite number of steps - the steps are not limited. This is a game with an infinite number of steps. the number of actions is not limited. nine0003

Game solution

This game was not solved until the late 1970s. But later a strategy was found. The strategy for the princess is as follows: the princess goes to a random point and waits at that point for a certain amount of time, neither too short nor too long. The princess then moves to another random point, and so on.

An optimal search strategy is proposed for the monster, in which the whole room is divided into many small rectangles. The monster randomly selects a rectangle and searches it, then randomly selects the next rectangle, and so on. nine0003

By the way, the obvious strategy of starting at a random end and zigzag cutting off the escape route is suboptimal.

Guess 2/3 Average Game

In 2005, a Danish newspaper called "Politiken" invited its readers to play the following game: anyone could send a real number from 0 to 100 to the publisher, the sender of the number closest to 2/3 of the arithmetic mean of the submitted numbers won 5,000 DKK.

This game demonstrates the difference between completely rational behavior and the real actions of the players. nine0003

Imagine that all participants in the game act rationally and know that all other participants are rational. What is the optimal number in this situation?

It obviously doesn't make sense to say a number greater than 66. (6) because two-thirds of the arithmetic mean cannot be greater. However, if all players think this way, all numbers will be at most 2/3*66.(6) = 44.(4). Repeating this reasoning infinitely many times, we will come to the conclusion that the only correct move is the number 0. Therefore, if all players are rational, they should all choose the number 0.

However, the situation is different in real life. Even if the player is rational, he knows that many of his opponents are not rational, which means that he will have to take into account that their numbers will be greater than 0. It can be assumed that the majority will send more or less random numbers, then the average will be 50, two-thirds of 50 is approximately equal to 33. If we go further and assume that quite a lot of people guess the number 33, then we can choose two-thirds of 33, i.e. 22. Further iterations will give ~15, ~10, etc., but it seems unlikely that a sufficiently significant number of players will calculate this far. nine0003

Volunteer's Dilemma Game

The Volunteer's Dilemma game models a situation in which each player can either make a small sacrifice that benefits everyone, or instead wait in the hope of benefiting from someone else's sacrifice.

One example is a scenario in which the power went out for the entire area. All residents know that the electric company will not solve the problem until it calls and notifies at least one person about what happened, paying for the call. If no one wants to call, all participants will receive a negative payoff. If any person decides to volunteer, the rest will benefit, of course, if they don't volunteer. nine0003

In this game, the players themselves decide whether to sacrifice themselves for the benefit of the group. If no one sacrifices something voluntarily, everyone loses.

No matter how hard we try, we cannot find a winning strategy when playing with rational players. But what will happen in life? After all, not all people are rational!

History of Game Theory

Already in the 18th century, optimal solutions and strategies for mathematical modeling were proposed. Some tasks were considered in 19century by Augustine Augustine Cruneau and Joseph Louis Francois Bertan.

At the beginning of the 20th century, Emmanuel Lasker, Ernst Firidrich Gemelo and Ferdinand Felix Eduard Justin Emil Borel put forward the idea of a mathematical theory of conflict of interest.

Mathematical game theory comes from neoclassical economics. The mathematical aspects and applications of the theory were first presented in John von Neumann and Oskar Morgenstern's classic 1944 book Game Theory and Economic Behavior. nine0003

This area of mathematics has found some reflection in public culture. The American writer and journalist Sylvia Nazar published a book about the fate of John Forbes Nash in 1998, and in 2001 the film A Beautiful Mind was made based on the book.

After graduating from Carnegie Polytechnic Institute with two bachelor's and master's degrees, John Nash entered Princeton University, where he attended lectures by John von Neumann. In his writings, Nash developed the principles of "control dynamics". John Nash earned his PhD in game theory at 1949 and was awarded the Nobel Prize in Economics.

The first concepts of game theory analyzed antagonistic games, when there are losers and players who won at their expense. Nash develops methods of analysis in which all participants either win or lose.

These situations are called "Nash equilibrium" or "non-cooperative equilibrium" when the parties use the optimal strategy, which leads to the creation of a stable equilibrium. Players benefit from maintaining this balance, as any change will worsen their situation. nine0003

Nash's work has made a significant contribution to the development of game theory, and mathematical tools for economic modeling have been revised. Nash shows that Adam Smith's classical approach to competition, when every man for himself, is not optimal. Strategies are more profitable when everyone is trying to benefit themselves and do better for others.

Although game theory originally considered economic models, it remained a formal theory within mathematics until 1950s. But already in the 1950s, attempts were made to apply the methods of game theory not only in economics, but also in biology, cybernetics, technology and anthropology.

During the Second World War and immediately after it, the military became seriously interested in game theory, who saw it as a powerful tool for the study of strategic decisions.

In the years 1960-1970, interest in game theory waned, despite the significant mathematical results achieved by that time. From mid 19In the 1980s, the active practical application of game theory began, especially in the field of economics and management.

Over the past 20-30 years, the importance of game theory and interest in it has increased significantly. Some areas of modern economic theory cannot be expounded without the application of game theory.

A number of well-known scientists have been awarded the Nobel Prize in Economics for their contributions to the development of game theory, which describes socio-economic processes. John Nash, through his research in game theory, became one of the leading experts in the field of Cold War, which confirms the enormity of the tasks that game theory deals with. nine0003

Alfred Nobel Prize in Economics for achievements in game theory and economics: Robert Aumann, Reinhard Selten, John Nash, John Harsanyi, William Vickrey, James Mirrlees, Thomas Schelling, George Akerlof, Michael Spence, Joseph Stiglitz, Leonid Hurwitz, Eric Maskin, Roger Myerson, Lloyd Shapley, Alvin Roth, Jean Tyrol.

Application of Game Theory in life

Game "Trap" The cork from a bottle of champagne shot so hard that it flew to the phone with the navigator open.

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Let's imagine that you have a choice: either drive on a highway during a traffic jam, or take an empty detour that is 2 times longer than the highway. The maximum allowable speed in a traffic jam is 3 times less than the maximum allowable speed, without it.

Everything is simple here. The length of the path is x, the speed is y.

Cork - 1 x / 1 y
Empty road - 2 x / 3 y
Let's try to substitute numbers.

Cork - 50 / 10 = 5
Empty road 100 / 30 = 3.3
Let's try others, different from the previous numbers.

Cork - 100 / 320 = 0.3
Empty road - 200 / 960 = 0.2
According to the results, we can conclude that in any case, an empty road will be faster.

But that's not all, this experience has a continuation. Many people, without knowing it, will use game theory and choose an empty road, which in turn will become busy. With this in mind, you may choose the first option by analyzing some factors: the average arrival of cars, the capacity of the roads, the time it takes to form a traffic jam and the time to approach the fork in the road. nine0003

Mafia Game

You and your friends play Mafia. Remain alive: "Civilian", "Mafia" and "Maniac". What are the chances of a peaceful win? It would seem - none.

As we can see, if:

the Mafia kills the Maniac, and the Maniac kills the Mafia, Mirny wins.

Mafia will kill Maniac and Maniac will kill Peaceful - Mafia will win.

Mafia will kill Peaceful and Maniac will kill Mafia - Maniac will win.

Mafia will kill Peaceful and Maniac will kill Peaceful - Draw. nine0003

If the decisions are spontaneous and random, the chances of a peaceful one are 25%

a chance to either lose or win better. Consequently, the choice to kill a civilian is excluded. Consequently, the Mafia will kill the Maniac and the Maniac will kill the Mafia - Mirny will win.

Movie Game

Imagine - after a long day at work, you return home, hoping to go to bed immediately after arrival. The trip will last 1 hour 50 minutes. All of a sudden you have a desire to watch a movie, and the streaming service has one last movie coupon left. You have a choice of 2 films: one of them is The Matrix, which runs for 2 hours, the second is The Hateful Eight, which runs for 3 hours. Also, the last one you really wanted to see. nine0003

So, let's try to understand what to watch. It is important to note that you will receive the next movie coupons only in a week.

Your interest in the Hateful Eight is very great, but, unfortunately, we cannot translate the interest and the desire to sleep into one value and compare them, because it is very personal and depends on many factors, such as: the desire to sleep, the time of waking up, the importance of tomorrow's affairs, the possibility of watching a movie at a different time, the battery level of the phone, etc. nine0003

Fortunately, the human brain can process a huge amount of information. But the creation of a universal solution, even for such a simple task for us, is very difficult and requires a lot of time and resources.

Unfavorable Monopoly Game

Perhaps this is one of the most common games in the world of economics. Recall that game theory is a branch of mathematical economics.

Microsoft, Sony, Disney… Guess what these corporations have in common? Each of them, to one degree or another, is a monopolist in its market. Microsoft, namely Windows in the field of operating systems. Sony, to be more precise - Play Station, in the field of game consoles. Disney in the field of entertainment films. nine0003

All 3 companies control most of the market by regulating and setting standards. Once they made a coup, produced what became the pinnacle of possibilities. We can think of some Microsoft operating systems, Play Station 2 and The Last of Us, Disney cartoons that are popular all over the world.

But corporations are primarily interested in profit. Having conquered the market and secured their status, they began to produce rather mediocre products and services. Windows 8 and Windows 10 issues, Play Station Vita, Avengers are mediocre products that don't deserve their status. nine0003

Customers, united, can force companies to change their strategy - to start producing better products. By abandoning the company's services and products, customers could shrink the market, forcing the company to find ways to reclaim the market.

But, unfortunately, people, unlike birds and some other creatures, are not endowed with the ability to unite so productively and harmoniously.

The chances of the above situation are very slim. And the players understand this.

It is not profitable for each participant in the game to give up Windows, because most players are used to it and it will be difficult for them not only to understand and not only install Linux, but also to understand the differences between Linux Kali and Linux Ubuntu. nine0003

It is not profitable for each participant in the game to refuse a particular product, because he knows that he will not benefit personally.

This game is based on the "Nesh Equilibrium" with which we are already familiar. But let's update our possibly distorted memories!

Nash equilibrium is a set of strategies in a game for two or more players in which no participant can increase the payoff by changing his strategy if the other participants do not change their strategies.

Of course, we can imagine a situation in which the previous customers of the above companies have abandoned the products of our companies. nine0003

In this case, Microsoft, Sony, Disney would create products of the quality and capabilities that are necessary for the return of the market.

Perhaps they would be: “Windows Infinity open source”, “games not only with Keanu Reeves and Norman Reedus, but with all of Hollywood, in addition to Quentin Tarantino as a director”, “Avengers with meaning and a good story ".

Alas, but this is not achievable. This Nesh equilibrium of 100 million participants is very difficult to solve. nine0003

I would also like to note some details:

Not only "our trinity" has such a position. Hundreds and hundreds of companies are playing this game.

There are different types of this game. Sometimes a corporation does not occupy a monopoly position, but has a circle of "loyal" customers, or only their products provide certain opportunities. An example of this is Apple.

Bertrand Model Game

Is it profitable for stores to reduce the price of a product? Obviously not, but it's not that simple. nine0003

Let's imagine a game - 2 stores sell the same product with a markup of 20%, buying it from the manufacturer at the same price. Same price = same demand = same earnings.

Suddenly one of the shops lowers the price. What will happen? He will have more demand and, consequently, more earnings. This is why lowering the price is sometimes profitable.

Narrow Road Game

X and Ygrik are driving towards each other along a narrow road. In order not to crash into each other, both need to pull over to the side of the road. nine0003

The game consists in choosing the side of the turn. Each player must choose a side that does not match the opponent's side. What to choose? To solve such a game, rules of the road have been created.

Application of Game Theory

Why is game theory needed? In the "History" section, you could observe the development of game theory and references to its application. So let's find out why game theory is needed, where it is used, and even how game theory can be useful to you!

Biology

To begin with, it should be noted that animal behavior is largely determined genetically, and some behaviors are more appropriate for the situation than others.

The partly incorrect idea “survival of the fittest” is widespread, no less than the highest criterion of biological fitness is not survival, but reproductive success.

Animals pass on their genes to the next. Then, the more adaptable phenotype becomes relatively larger in the next generation than the less adaptable phenotype. It is this selection process that changes the combination of genotype and phenotype and may eventually lead to the formation of a stable state. nine0003

New genetic mutations occur from time to time, spontaneously. Many of them create a phenotype that does not fit well with the environment and therefore disappears. However, sometimes mutations can lead to new phenotypes, making them more adaptive to their environment.

The number of more adapted animal mutations will increase while the unadapted ones may disappear, and mutations that are not currently part of this population may try to capture it. nine0003

Similar situations are used in game theory. Behavior can be seen as a strategy for how animals interact with other animals. The only difference is that in animals, the choice of strategy is not carried out with the help of purposeful decisions.

Sociology and psychology

Game theory is applied in sociology to understand, explain and control games with a social component. In turn, in psychology, game theory studies the actions of each individual isolated player. In one form or another, game theory is used by psychologists, sociologists, politicians, marketers and many other people. nine0003

Sociologists try to understand the reasons for the actions of groups of players and use the knowledge gained. They simulate games, conduct research to find the most profitable strategy.

Policy

In politics, game theory is used to analyze situations and interactions of players (usually countries), to solve games and to find the best strategies. Countries have a number of conflicts: territories, trade, alliances… Game theory helps to reach a compromise.

The same game theory is applied in voting - candidates resort to different strategies to increase the chances of winning. nine0003

Economy

In economics, game theory is ubiquitous. Earlier you met the game "Unfavorable Monopoly", this is a very good example of a game. Economic games - auctions, monopoly and oligopoly models, markets and much more.

In the economy, there are models that characterize certain games and are universal - and can be applied in all games that fit the characteristics.

Unconscious use

Often, we apply game theory without even realizing it. We build logical chains, analyze situations and come up with strategies using game theory, but without knowing it. Above are the games "Film", "Jam" and some others in which players play constantly. nine0003

Our brain analyzes games without realizing it. This statement raises the question: can knowledge of game theory be useful to an ordinary person?

Benefits of knowing Game Theory

Game Theory is useful to many different specialists, but is Game Theory useful to the average person?

There is no practical universal application of game theory for the average person. In real life, analyzing a game while standing with a leaf and a pen in front of a cookie counter, choosing a product, is not a good idea, because you can cope with this task without applying the methods of game theory. nine0003

Game theory is useful when:

Important decisions. There are situations in our lives that require very thoughtful choices that can change a lot of things. In such situations, game theory can be extremely useful and even necessary.
Logical thinking, the ability to think one step ahead. Game theory shows that our intuition is not always correct. It can teach us to think logically and test even the most obvious situations. Also, game theory can teach you to think in a longer term and take into account more details. Remember the game "Cork"? Toward the end of the text, it said: "A lot of people, without knowing it, will use game theory and choose an empty road, which in turn will become busy." This is thinking a few moves ahead. nine0358
Expanding horizons. Game theory can be interesting, besides, game theory broadens one's horizons. Any knowledge is useful, and multifaceted knowledge is extremely useful. Game theory, being no exception, is just as useful and interesting.

Sources

«Chapters | Evolutionary games” — scientific journal PostNauka ( bit.ly/2HrN02a )
Game Theory - Wikipedia (bit.ly/2Oz6Ltj)
"Guess 2/3 of the average, %username%" - Habr website ( bit.ly/3dJIxWL )
"Game Theory: An Introduction" - Habr website (bit.ly/35XcPmc)
"Game Theory" - scientific journal PostNauka (bit.ly/2T0PhHW)
"List of game theory games" - Wikipedia (bit.ly/2DrUOPF)
"Understood in 12 Minutes: When Game Theory Beats Common Sense" - Science Channel (bit.ly/3fPLJBZ)
“10 Facts About Game Theory” — University of Chicago and HSE Professor Konstantin Sonin ( bit.ly/2y4XBPK )
“Games that Economists Study” – a lecture by the National Research University Higher School of Economics ( bit. ly/2T2fHcc )
"Game Theory" - a course of lectures by Doctor of Sciences Alexei Savvateev (bit.ly/3fR2o8j)
“What is our life: 10 examples of why economists need game theory” - scientific journal PostNauka ( bit.ly / 2WZjuIu )

Game Theory: An Introduction / Habr

What it is and what it is eaten with.

Game theory is a branch of mathematical economics that studies conflict resolution between players and the optimality of their strategies. The conflict can relate to different areas of human interest: most often it is economics, sociology, political science, less often biology, cybernetics, and even military affairs. A conflict is any situation in which the interests of two or more participants, traditionally called players, are affected. Each player has a certain set of strategies that he can apply. Intersecting, the strategies of several players create a certain situation in which each player receives a certain result, called a payoff, positive or negative. When choosing a strategy, it is important to take into account not only getting the maximum profit for yourself, but also the possible moves of the enemy, and their impact on the situation as a whole. nine0003

Brief history of development.

The foundations of game theory originated in the 18th century, with the beginning of the Age of Enlightenment and the development of economic theory. The mathematical aspects and applications of the theory were first presented in the classic 1944 book by John von Neumann and Oskar Morgenstern, Game Theory and Economic Behavior. The first concepts of game theory analyzed antagonistic games, when there are losers and players who won at their expense. Despite the fact that game theory considered economic models, until the 50s of the 20th century it was just a mathematical theory. After, as a result of a sharp jump in the US economy after the Second World War, and, as a result, more funding for science, attempts begin to put the theory of games into practice in economics, biology, cybernetics, technology, and anthropology. During World War II and immediately after it, the military became seriously interested in game theory, who saw it as a powerful tool for investigating strategic decisions. In the early 50s, John Nash (pictured) develops methods of analysis in which all participants either win or lose. These situations are called "Nash equilibrium". According to his theory, the parties must use the optimal strategy, which leads to the creation of a stable equilibrium. It is beneficial for the players to maintain this balance, since any change will worsen their position. These works of Nash made a serious contribution to the development of game theory, the mathematical tools of economic modeling were revised. John Nash shows that A. Smith's classical approach to competition, when it's every man for himself, is suboptimal. More optimal strategies are when everyone tries to do better for themselves while doing better for others. Over the past 20 - 30 years, the importance of game theory and interest has been growing significantly, some areas of modern economic theory cannot be stated without the use of game theory. A great contribution to the application of game theory was the work of Thomas Schelling, Nobel Laureate in Economics in 2005 "Strategy of Conflict". nine0003

How it works

It seems to me that the meaning of game theory is best explained by the Prisoner's Dilemma, the classical formulation of which is:

Two criminals, A and B, were caught at about the same time on similar crimes. There is reason to believe that they acted in collusion, and the police, having isolated them from each other, offer them the same deal: if one testifies against the other, and he remains silent, then the first is released for helping the investigation, and the second receives the maximum term imprisonment (10 years). If both remain silent, their act passes under a lighter article, and they are sentenced to 6 months. If both testify against each other, they receive a minimum sentence (2 years each). Each prisoner chooses whether to remain silent or testify against the other.

However, neither of them knows exactly what the other will do. What will happen? nine0397

Representing the game as a matrix, we get:

	Criminal B Silence strategy	Criminal B Betrayal strategy
Criminal A Silence strategy	Half a year each	10 years of criminal A Release criminal B
Criminal A Betrayal strategy	10 years old criminal B Release criminal A	2 years each

And now let's imagine the development of the situation, putting ourselves in the place of prisoner A. If my accomplice is silent, it is better to hand him over and go free. If he speaks, then it is also better to tell everything, and get only two years, instead of ten. Thus, if each player chooses what is best for him, both will turn each other in and get two years, which is not an ideal situation for both. If everyone thought about the common good, they would only get half a year. nine0003

Game types

Co-op/non-co-op game

A cooperative game is a conflict in which players can communicate with each other and unite in groups to achieve the best result. An example of a cooperative game can be considered the card game Bridge, where the points of each player are counted individually, but the pair with the largest amount wins. Of the two types of games, non-cooperative ones describe situations in great detail and produce more accurate results. Cooperatives consider the process of the game as a whole. While the two are opposites, it is possible to combine strategies that can be more beneficial than following either one. nine0003

Zero-sum and non-zero-sum

A zero-sum game is a game in which one player's gain equals the other's loss. For example, a banal dispute: if you won the amount N, then someone lost the same amount N. In a game with a non-zero sum, the total price of the game can change, thus benefiting one player without taking its price away from another. Chess is a good example here: By queening a pawn, player A increases the total sum of his pieces, while not taking anything away from player B. In non-zero-sum games, losing one of the players is not a prerequisite, although such an outcome is not excluded. nine0003

Parallel and series

A parallel game is a game in which the players move at the same time, or the move of one player is unknown to the other until the general cycle is completed. In sequential play, each player has information about his opponent's previous move before making his choice. And it is not at all necessary that the information be complete, which leads to the next type.

Complete or incomplete information

These types are a subset of sequential games, and their names speak for themselves. nine0003

Metagames

These games are the "lemmas" of game theory. They are useful not by themselves, but in the context of any conflict, expanding its set of rules.

In any conflict, the types are combined, thus defining the rules of the game, whether it is a zero-sum cooperative sequential game or an incomplete information metagame.

Application problems

Of course, one should also point out the existence of certain limits for the application of the analytical tools of game theory. In the following cases, it can only be used if additional information is obtained. nine0003

First, this is the case when the players have different ideas about the game they are playing, or when they are not sufficiently informed about each other's capabilities. For example, there may be unclear information about a competitor's payments (cost structure). If not too complex information is characterized by incompleteness, then the experience of similar cases can be applied, taking into account certain differences.

Secondly, game theory is difficult to apply to many equilibrium situations. This problem can arise even during simple games with simultaneous choice of strategic decisions. nine0003

Thirdly, if the situation of making strategic decisions is very difficult, then players often cannot choose the best options for themselves. For example, several enterprises may enter the market at different times, or the reaction of enterprises already operating there may be more complex than aggressive or friendly.

It has been experimentally proved that when the game is expanded to ten or more stages, the players are no longer able to use the appropriate algorithms and continue the game with equilibrium strategies. nine0003

Unfortunately, real-world situations are often very complex and change so quickly that it is impossible to accurately predict how competitors will react to a change in tactics. However, game theory is useful when it comes to identifying the most important factors to consider in a competitive decision-making situation.