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Game theory is a branch of mathematics that studies rational behavior in decision-making, where the outcome depends on every player’s choice.

Applied game theory attempts to either anticipate or influence the decisions of independent actors involved in any type of competitive context. There are many scenarios in everyday life where game theory applies, such as politics, economics, business, and technology, including in blockchain and cryptocurrencies.

The concepts underpinning game theory are visible in a game like chess, where the move of one player can be influenced by the moves of their opponent; or even by the belief that the opponent will make a certain move.

Game theory can also be seen during price negotiations between a buyer and a seller (like in real estate transactions). In these instances, a seller will pitch their starting offer at a level acceptable enough to attract buyers, who can either accept the offer or enter into a negotiation.

## History and fundamentals of game theory

Game theory emerged as a discipline in the 1920s; however, the earliest work focused only on two-person, winner-takes-all scenarios, also known as zero-sum games (explained below). The development of game theory into more sophisticated modeling took off in the 1950s, partly thanks to the efforts of John Nash. Nash notably won the 1994 Nobel Prize for Economics for his work on the Nash equilibrium.

The Nash equilibrium is the point in which the outcome of a game can no longer be decided by a player changing their strategy. Take, for example, a simple 2-person game in which the players can choose between winning \$1 or losing \$1, and neither player’s selection impacts the other’s outcome. In this case, both players will logically choose to win \$1. Knowing the other’s strategy won’t change their choice.

The Nash equilibrium, or simply equilibrium, is one of the terms commonly used in game theory. Other terms and elements in game theory are:

• Players – the decision-making actors in a game
• Actions – the choices available to the players
• Information – the knowledge available to players while making their decisions
• Strategy – the plan or rules created by a player to direct their decision-making process
• Outcomes – the results that unfold as decisions are made and the game progresses
• Payoffs – the incentives sought by players

### The prisoner’s dilemma

Devised in the 1950s, the prisoner’s dilemma is one of the most well-used examples to illustrate game theory.

In this scenario, two people imprisoned for the same crime are faced with a choice – stay quiet about what happened or betray their partner in crime. Importantly, neither offender can communicate with the other. The offenders are faced with three potential results:

1. Both offenders remain quiet: Both will receive a one-year sentence in the absence of any other evidence.
2. One offender betrays the other: Betrayer will walk free while their partner is sentenced to ten years.
3. Both offenders betray each other: Both will each receive a five-year sentence.

This dilemma illustrates how the prosecutors have set up the rules of the game to optimize a Nash equilibrium in their favor. Regardless of the other prisoner’s actions, the best option for each prisoner is to betray the other. If the other prisoner remains silent, the betrayer walks free. If the other prisoner also betrays, they both receive only five years instead of receiving ten years by remaining quiet.

## Types of games in game theory

### Cooperative and non-cooperative games

A non-cooperative game is a competition-based game between players. Cooperative games include elements of cooperation between players, for instance, by working in teams to achieve outcomes, as in football or basketball.

Game theory in non-cooperative games examines how opposing players will make decisions towards their own goals. Game theory in cooperative games could predict how alliances may form, which strategies a team may use, or how payoffs are allocated between players.

### Zero-sum and non-zero-sum games

Zero-sum games assume that for each winner, there is a corresponding loser. Football is a cooperative game, but a football tournament is a zero-sum game where only one team takes the prize.

Conversely, a non-zero-sum game does not assume a straightforward balance of wins and losses but multiple outcomes with different payoffs for players. The prisoner’s dilemma is one example of a non-zero-sum game, where multiple outcomes are possible with varying payoffs for both prisoners.

Game theory in zero-sum games is relatively simple, as there are only two outcomes – wins or losses. Game theory in non-zero-sum games can be substantially more complex, involving modeling of many different outcomes.

### Simultaneous move versus sequential games

Some games require players to make their moves simultaneously, whereas others involve moves that take place in a sequence.

Typically, negotiations take place sequentially, as each party puts forth its counteroffer based on the last move of their opponent. However, when two startups launch a comparable new product at the same time, they are engaged in a simultaneous move game.

Applying game theory to sequential games is done in stages as each player makes their move, creating a new outcome. In contrast, applying game theory to simultaneous games uses a matrix to model the available outcomes.

## How game theory is used in blockchain and cryptocurrencies

Many elements of game theory are used in the development of blockchain platforms, decentralized applications (dapps), and tokens as a way of incentivizing good behavior and in some cases, penalizing bad actors.

### Game theory in blockchain consensus

Blockchain platforms rely on decentralized, widely distributed networks of node operators to maintain pristine ledgers of transactions. Therefore, they’re designed to ensure that node operators don’t attempt to launch an attack to steal funds.

Consensus methods like proof of work (PoW) and proof of stake (PoS) incorporate game theory, requiring nodes to make a relatively large up-front investment in computing power and energy consumption for PoW systems or a minimum stake to participate in PoS ones. In return, they typically receive a portion of the block rewards based on their contribution. However, if they act maliciously, they risk losing a portion (or all) of their investment.

The rules of the protocol may vary, but they’re always constructed in such a way that the most rational actions by network participants are those that serve the network.

### Game theory in DeFi

Decentralized Finance (DeFi) protocols, such as lending protocols and decentralized exchanges, deploy game theory to attract users and liquidity.

With a lending platform like Aave or Compound, the players include:

• Liquidity providers – seek the payoff of rewards for staking their tokens in lending pools
• Borrowers – take out loans at the lowest possible interest rates
• Project team – Design the system that balances the payoffs for liquidity providers and borrowers alike.

### Game theory in tokenomics

It is common practice for token issuers to design their tokenomic models using the principles of game theory.

For instance, tokens allocated to founders or team members in the early stages of a project are often subject to a lockup period during which they can’t be sold. This prevents a mass selling of the tokens onto the market when the token initially launches on an exchange, during which time the value is typically high.

Similarly, many projects allocate tokens using initiatives such as airdrops as a way of incentivizing players to use their projects – in other words, creating a payoff for players.

## Game theory essentials

• Game theory is a branch of theoretical math that examines logical decision-making and attempts to predict or influence outcomes.
• Game theory is a relatively new discipline but has broad applications in business, economics, politics, and other sectors.
• Elements of game theory that enforce or incentivize good behavior by paying rewards or imposing penalties are visible in the design of blockchain platforms, applications, and tokenomics.