Talking about Games

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Talking about Games

Game theory is a field of research that is quite prominent in Economics but rather unpopular in other scientific disciplines. However, the concepts used in game theory can be of interest to a wider audience, including data scientists, statisticians, computer scientists or psychologists, to name just a few. This article is the opener to a […]

In this article, I will explain the kinds of problems Game Theory deals with and introduce the main terms and concepts used to describe a game. We will see some examples of games that are typically analysed within game theory and lay the foundation for deeper insights into the capabilities of game theory in the later chapters. But before we go into the details, I want to introduce you to some applications of game theory, that show the multitude of areas game-theoretic concepts can be applied to.

Applications of game theory

Even french fries can be an application of game theory. Photo by engin akyurt on Unsplash

Does it make sense to vote for a small party in an election if this party may not have a chance to win anyway? Is it worth starting a price war with your competitor who offers the same goods as you? Do you gain anything if you reduce your catch rate of overfished areas if your competitors simply carry on as before? Should you take out insurance if you believe that the government will pay for the reconstruction after the next hurricane anyway? And how should you behave in the next auction where you are about to bid on your favourite Picasso painting?

All these questions (and many more) live within the area of applications that can be modelled with game theory. Whenever a situation includes strategic decisions in interaction with others, game-theoretic concepts can be applied to describe this situation formally and search for decisions that are not made intuitively but that are backed by a notion of rationality. Key to all the situations above is that your decisions depend on other people’s behaviour. If everybody agrees to conserve the overfished areas, you want to play along to preserve nature, but if you think that everybody else will continue fishing, why should you be the only one to stop? Likewise, your voting behaviour in an election might heavily depend on your assumptions about other people’s votes. If nobody votes for that candidate, your vote will be wasted, but if everybody thinks so, the candidate doesn’t have a chance at all. Maybe there are many people who say “I would vote for him if others vote for him too”.

Similar situations can happen in very different situations. Have you ever thought about having food delivered and everybody said “You don’t have to order anything because of me, but if you order anyway, I’d take some french fries”? All these examples can be applications of game theory, so let’s start understanding what game theory is all about.

Understanding the game

Before playing, you need to understand the components of the game. Photo by Laine Cooper on Unsplash

When you hear the word game, you might think of video games such as Minecraft, board games such as Monopoly, or card games such as poker. There are some common principles to all these games: We always have some players who are allowed to do certain things determined by the game’s rules. For example, in poker, you can raise, check or give up. In Monopoly, you can buy a property you land on or don’t buy it. What we also have is some notion of how to win the game. In poker, you have to get the best hand to win and in Monopoly, you have to be the last person standing after everybody went bankrupt. That also means that some actions are better than others in some scenarios. If you have two aces on the hand, staying in the game is better than giving up.

When we look at games from the perspective of game theory, we use the same concepts, just more formally.

A game in game theory consists of n players, where each player has a strategy set and a utility function.

A game consists of a set of players I = {1, .., n}, where each player has a set of strategies S and a utility function ui(s1, s2, … sn). The set of strategies is determined by the rules of the games. For example, it could be S = {check, raise, give-up} and the player would have to decide which of these actions they want to use. The utility function u (also called reward) describes how valuable a certain action of a player would be, given the actions of the other players. Every player wants to maximize their utility, but now comes the tricky part: The utility of an action of yours depends on the other players’ actions. But for them, the same applies: Their actions’ utilities depend on the actions of the other players (including yours).

Let’s consider a well-known game to illustrate this point. In rock-paper-scissors, we have n=2 players and each player can choose between three actions, hence the strategy set is S={rock, paper, scissors} for each player. But the utility of an action depends on what the other player does. If our opponent chooses rock, the utility of paper is high (1), because paper beats rock. But if your opponent chooses scissors, the utility of paper is low (-1), because you would lose. Finally, if your opponent chooses paper as well, you reach a draw and the utility is 0.

Utility values for player one choosing paper for three choices of the opponents strategy.

Instead of writing down the utility function for each case individually, it is common to display games in a matrix like this:

The first player decides for the row of the matrix by selecting his action and the second player decides for the column. For example, if player 1 chooses paper and player 2 chooses scissors, we end up in the cell in the third column and second row. The value in this cell is the utility for both players, where the first value corresponds to player 1 and the second value corresponds to player 2. (-1,1) means that player 1 has a utility of -1 and player 2 has a utility of 1. Scissors beat paper.

Some more details

Now we have understood the main components of a game in game theory. Let me add a few more hints on what game theory is about and what assumptions it uses to describe its scenarios.

We often assume that the players select their actions at the same time (like in rock-paper-scissors). We call such games static games. There are also dynamic games in which players take turns deciding on their actions (like in chess). We will consider these cases in a later chapter of this tutorial.
In game theory, it is typically assumed that the players can not communicate with each other so they can’t come to an agreement before deciding on their actions. In rock-paper-scissors, you wouldn’t want to do that anyway, but there are other games where communication would make it easier to choose an action. However, we will always assume that communication is not possible.
Game theory is considered a normative theory, not a descriptive one. That means we will analyse games concerning the question “What would be the rational solution?” This may not always be what people do in a likewise situation in reality. Such descriptions of real human behaviour are part of the research field of behavioural economics, which is located on the border between Psychology and economics.

The prisoner’s dilemma

Let us become more familiar with the main concepts of game theory by looking at some typical games that are often analyzed. Often, such games are derived from are story or scenario that may happen in the real world and require people to decide between some actions. One such story could be as follows:

Say we have two criminals who are suspected of having committed a crime. The police have some circumstantial evidence, but no actual proof for their guilt. Hence they question the two criminals, who now have to decide if they want to confess or deny the crime. If you are in the situation of one of the criminals, you might think that denying is always better than confessing, but now comes the tricky part: The police propose a deal to you. If you confess while your partner denies, you are considered a crown witness and will not be punished. In this case, you are free to go but your partner will go to jail for six years. Sounds like a good deal, but be aware, that the outcome also depends on your partner’s action. If you both confess, there is no crown witness anymore and you both go to jail for three years. If you both deny, the police can only use circumstantial evidence against you, which will lead to one year in prison for both you and your partner. But be aware, that your partner is offered the same deal. If you deny and he confesses, he is the crown witness and you go to jail for six years. How do you decide?

The game derived from this story is called the prisoner’s dilemma and is a typical example of a game in game theory. We can visualize it as a matrix just like we did with rock-paper-scissors before and in this matrix, we easily see the dilemma the players are in. If both deny, they receive a rather low punishment. But if you assume that your partner denies, you might be tempted to confess, which would prevent you from going to jail. But your partner might think the same, and if you both confess, you both go to jail for longer. Such a game can easily make you go round in circles. We will talk about solutions to this problem in the next chapter of this tutorial. First, let’s consider some more examples.

Bach vs. Stravinsky

Who do you prefer, Bach or Stravinsky? Photo by Sigmund on Unsplash

You and your friend want to go to a concert together. You are a fan of Bach’s music but your friend favors the Russian 20th. century composer Igor Stravinsky. However, you both want to avoid being alone in any concert. Although you prefer Bach over Stravinsky, you would rather go to the Stravinsky concert with your friend than go to the Bach concert alone. We can create a matrix for this game:

You decide for the row by going to the Bach or Stravinsky concert and your friend decides for the column by going to one of the concerts as well. For you, it would be best if you both chose Bach. Your reward would be 2 and your friend would get a reward of 1, which is still better for him than being in the Stravinsky concert all by himself. However, he would be even happier, if you were in the Stravinsky concert together.

Do you remember, that we said players are not allowed to communicate before making their decision? This example illustrates why. If you could just call each other and decide where to go, this would not be a game to investigate with game theory anymore. But you can’t call each other so you just have to go to any of the concerts and hope you will meet your friend there. What do you do?

Arm or disarm?

Make love, not war. Photo by Artem Beliaikin on Unsplash

A third example brings us to the realm of international politics. The world would be a much happier place with fewer firearms, wouldn’t it? However, if nations think about disarmament, they also have to consider the choices other nations make. If the USA disarms, the Soviet Union might want to rearm, to be able to attack the USA — that was the thinking during the Cold War, at least. Such a scenario could be described with the following matrix:

The matrix for the disarm vs. upgrade game.

As you see, when both nations disarm, they get the highest reward (3 each), because there are fewer firearms in the world and the risk of war is minimized. However, if you disarm, while the opponent upgrades, your opponent is in the better position and gets a reward of 2, while you only get 0. Then again, it might have been better to upgrade yourself, which gives a reward of 1 for both players. That is better than being the only one who disarms, but not as good as it would get if both nations disarmed.

The solution?

All these examples have one thing in common: There is no single option that is always the best. Instead, the utility of an action for one player always depends on the other player’s action, which, in turn, depends on the first player’s action and so on. Game theory is now interested in finding the optimal solution and deciding what would be the rational action; that is, the action that maximizes the expected reward. Different ideas on how exactly such a solution looks like will be part of the next chapter in this series.

Summary

Learning about game theory is as much fun as playing a game, don’t you think? Photo by Christopher Paul High on Unsplash

Before continuing with finding solutions in the next chapter, let us recap what we have learned so far.

A game consists of players, that decide for actions, which have a utility or reward.
The utility/reward of an action depends on the other players’ actions.
In static games, players decide for their actions simultaneously. In dynamic games, they take turns.
The prisoner’s dilemma is a very popular example of a game in game theory.
Games become increasingly interesting if there is no single action that is better than any other.

Now that you are familiar with how games are described in game theory, you can check out the next chapter to learn how to find solutions for games in game theory.

References

The topics introduced here are typically covered in standard textbooks on game theory. I mainly used this one, which is written in German though:

Bartholomae, F., & Wiens, M. (2016). Spieltheorie. Ein anwendungsorientiertes Lehrbuch. Wiesbaden: Springer Fachmedien Wiesbaden.

An alternative in English language could be this one:

Espinola-Arredondo, A., & Muñoz-Garcia, F. (2023). Game Theory: An Introduction with Step-by-step Examples. Springer Nature.

Game theory is a rather young field of research, with the first main textbook being this one:

Von Neumann, J., & Morgenstern, O. (1944). Theory of games and economic behavior.

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Denise Dubie is a senior editor at Network World with nearly 30 years of experience writing about the tech industry. Her coverage areas include AIOps, cybersecurity, networking careers, network management, observability, SASE, SD-WAN, and how AI transforms enterprise IT. A seasoned journalist and content creator, Denise writes breaking news and in-depth features, and she delivers practical advice for IT professionals while making complex technology accessible to all. Before returning to journalism, she held senior content marketing roles at CA Technologies, Berkshire Grey, and Cisco. Denise is a trusted voice in the world of enterprise IT and networking.

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At the end of October, Meta announced a joint venture with funds managed by Blue Owl Capital to finance, develop, and operate the previously announced “Hyperion” project, a multi-building AI megacampus in Richland Parish, Louisiana. Under the new JV structure, Blue Owl will own 80 percent and Meta 20 percent, though Meta had announced the project long before Blue Owl’s involvement was confirmed. The venture anticipates roughly $27 billion in total development costs for the buildings and the long-lived power, cooling, and connectivity infrastructure. Blue Owl contributed about $7 billion in cash at formation; Meta received a $3 billion one-time distribution and contributed land and construction-in-progress to the vehicle. Rachel Peterson, VP of Data Centers at Meta, noted that construction on the project is already well underway, with thousands of workers on-site. Structuring Capital and Control Media coverage from Reuters and others characterizes the financing package as one of the largest private-capital deals ever for a single industrial campus, with debt placements led by PIMCO and additional institutional investors. Meta keeps the project largely off its balance sheet through the joint venture while retaining the development and property-management role and serving as the anchor tenant for the campus. The JV allows Meta to smooth its capital expenditures and manage risk while maintaining execution control over its most ambitious AI site to date. The structure incorporates lease agreements and a residual-value guarantee, according to Kirkland & Ellis (Blue Owl’s counsel), enabling lenders and equity holders to underwrite a very large, long-duration asset with multiple exit paths. For Blue Owl, Hyperion represents a utility-like digital-infrastructure platform with contracted cash flows to a single A-tier counterparty: a hyperscaler running mission-critical AI workloads for training and inference. As Barron’s and MarketWatch have noted, the deal underscores Wall Street’s ongoing appetite for AI-infrastructure investments at

Microsoft will invest $80B in AI data centers in fiscal 2025

And Microsoft isn’t the only one that is ramping up its investments into AI-enabled data centers. Rival cloud service providers are all investing in either upgrading or opening new data centers to capture a larger chunk of business from developers and users of large language models (LLMs). In a report published in October 2024, Bloomberg Intelligence estimated that demand for generative AI would push Microsoft, AWS, Google, Oracle, Meta, and Apple would between them devote $200 billion to capex in 2025, up from $110 billion in 2023. Microsoft is one of the biggest spenders, followed closely by Google and AWS, Bloomberg Intelligence said. Its estimate of Microsoft’s capital spending on AI, at $62.4 billion for calendar 2025, is lower than Smith’s claim that the company will invest $80 billion in the fiscal year to June 30, 2025. Both figures, though, are way higher than Microsoft’s 2020 capital expenditure of “just” $17.6 billion. The majority of the increased spending is tied to cloud services and the expansion of AI infrastructure needed to provide compute capacity for OpenAI workloads. Separately, last October Amazon CEO Andy Jassy said his company planned total capex spend of $75 billion in 2024 and even more in 2025, with much of it going to AWS, its cloud computing division.

John Deere unveils more autonomous farm machines to address skill labor shortage

Join our daily and weekly newsletters for the latest updates and exclusive content on industry-leading AI coverage. Learn More Self-driving tractors might be the path to self-driving cars. John Deere has revealed a new line of autonomous machines and tech across agriculture, construction and commercial landscaping. The Moline, Illinois-based John Deere has been in business for 187 years, yet it’s been a regular as a non-tech company showing off technology at the big tech trade show in Las Vegas and is back at CES 2025 with more autonomous tractors and other vehicles. This is not something we usually cover, but John Deere has a lot of data that is interesting in the big picture of tech. The message from the company is that there aren’t enough skilled farm laborers to do the work that its customers need. It’s been a challenge for most of the last two decades, said Jahmy Hindman, CTO at John Deere, in a briefing. Much of the tech will come this fall and after that. He noted that the average farmer in the U.S. is over 58 and works 12 to 18 hours a day to grow food for us. And he said the American Farm Bureau Federation estimates there are roughly 2.4 million farm jobs that need to be filled annually; and the agricultural work force continues to shrink. (This is my hint to the anti-immigration crowd). John Deere’s autonomous 9RX Tractor. Farmers can oversee it using an app. While each of these industries experiences their own set of challenges, a commonality across all is skilled labor availability. In construction, about 80% percent of contractors struggle to find skilled labor. And in commercial landscaping, 86% of landscaping business owners can’t find labor to fill open positions, he said. “They have to figure out how to do

2025 playbook for enterprise AI success, from agents to evals

Join our daily and weekly newsletters for the latest updates and exclusive content on industry-leading AI coverage. Learn More 2025 is poised to be a pivotal year for enterprise AI. The past year has seen rapid innovation, and this year will see the same. This has made it more critical than ever to revisit your AI strategy to stay competitive and create value for your customers. From scaling AI agents to optimizing costs, here are the five critical areas enterprises should prioritize for their AI strategy this year. 1. Agents: the next generation of automation AI agents are no longer theoretical. In 2025, they’re indispensable tools for enterprises looking to streamline operations and enhance customer interactions. Unlike traditional software, agents powered by large language models (LLMs) can make nuanced decisions, navigate complex multi-step tasks, and integrate seamlessly with tools and APIs. At the start of 2024, agents were not ready for prime time, making frustrating mistakes like hallucinating URLs. They started getting better as frontier large language models themselves improved. “Let me put it this way,” said Sam Witteveen, cofounder of Red Dragon, a company that develops agents for companies, and that recently reviewed the 48 agents it built last year. “Interestingly, the ones that we built at the start of the year, a lot of those worked way better at the end of the year just because the models got better.” Witteveen shared this in the video podcast we filmed to discuss these five big trends in detail. Models are getting better and hallucinating less, and they’re also being trained to do agentic tasks. Another feature that the model providers are researching is a way to use the LLM as a judge, and as models get cheaper (something we’ll cover below), companies can use three or more models to

OpenAI’s red teaming innovations define new essentials for security leaders in the AI era

Join our daily and weekly newsletters for the latest updates and exclusive content on industry-leading AI coverage. Learn More OpenAI has taken a more aggressive approach to red teaming than its AI competitors, demonstrating its security teams’ advanced capabilities in two areas: multi-step reinforcement and external red teaming. OpenAI recently released two papers that set a new competitive standard for improving the quality, reliability and safety of AI models in these two techniques and more. The first paper, “OpenAI’s Approach to External Red Teaming for AI Models and Systems,” reports that specialized teams outside the company have proven effective in uncovering vulnerabilities that might otherwise have made it into a released model because in-house testing techniques may have missed them. In the second paper, “Diverse and Effective Red Teaming with Auto-Generated Rewards and Multi-Step Reinforcement Learning,” OpenAI introduces an automated framework that relies on iterative reinforcement learning to generate a broad spectrum of novel, wide-ranging attacks. Going all-in on red teaming pays practical, competitive dividends It’s encouraging to see competitive intensity in red teaming growing among AI companies. When Anthropic released its AI red team guidelines in June of last year, it joined AI providers including Google, Microsoft, Nvidia, OpenAI, and even the U.S.’s National Institute of Standards and Technology (NIST), which all had released red teaming frameworks. Investing heavily in red teaming yields tangible benefits for security leaders in any organization. OpenAI’s paper on external red teaming provides a detailed analysis of how the company strives to create specialized external teams that include cybersecurity and subject matter experts. The goal is to see if knowledgeable external teams can defeat models’ security perimeters and find gaps in their security, biases and controls that prompt-based testing couldn’t find. What makes OpenAI’s recent papers noteworthy is how well they define using human-in-the-middle