{"id":91036,"date":"2025-11-14T15:00:00","date_gmt":"2025-11-14T12:00:00","guid":{"rendered":"https:\/\/forklog.com\/en\/?p=91036"},"modified":"2025-12-05T06:26:29","modified_gmt":"2025-12-05T03:26:29","slug":"what-is-game-theory-and-how-is-it-used-in-cryptocurrencies","status":"publish","type":"post","link":"https:\/\/forklog.com\/en\/what-is-game-theory-and-how-is-it-used-in-cryptocurrencies\/","title":{"rendered":"What Is Game Theory and How Is It Used in Cryptocurrencies?"},"content":{"rendered":"
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What is game theory?<\/h2>\n

Game theory is a branch of applied mathematics that studies decision-making models in situations where participants\u2019 interests diverge. Its aim is to identify equilibrium outcomes in which no player can improve his result by unilaterally changing strategy.<\/p>\n

The first mathematical treatment came from John von Neumann in the 1928 paper \u201cToward the theory of strategic games<\/a>\u201d. From this work comes the notion of a \u201czero-sum game\u201d, in which one player\u2019s victory always entails another\u2019s loss. Mutual gain or loss is ruled out: the winner takes all.<\/p>\n

By contrast, non-zero-sum games allow joint wins or losses. They reflect economic processes more faithfully, but are far harder to compute.<\/p>\n

A simple example is a business partnership. Two entrepreneurs consider collaborating. If each acts alone, they earn $10,000 apiece. If they combine efforts, income rises to $30,000\u2014$15,000 each. If one cheats (say, by pocketing profits), the opportunist can get $28,000 while the other is left with just $2,000.<\/p>\n

Thus the total payoff is variable and depends directly on behaviour. Everyone can earn more by cooperating than by going it alone.<\/p>\n<\/div>\n

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What is Nash equilibrium?<\/h2>\n

In 1950, Princeton graduate student John Forbes Nash published a short paper<\/a>. He proved that any game with a finite set of players and strategies has at least one equilibrium point<\/span> at which no one can improve his result by acting alone.<\/p>\n

A Nash equilibrium is a state in which all players have chosen strategies such that none has an incentive to deviate, given the others\u2019 choices. Consider several entrepreneurs deciding whether to cut prices. If one undercuts, others are forced to follow to avoid losing customers. The market settles into an equilibrium in which any unilateral change reduces profit.<\/p>\n

Honest play is a rational strategy that yields a Nash equilibrium. In blockchains this can be seen in miners\u2019 behaviour: attacking the network is unprofitable because the loss of trust devalues the reward.<\/p>\n

Nash later developed the idea in \u201cNon-cooperative games<\/a>\u201d (1951) and \u201cTwo-person cooperative games<\/a>\u201d (1953).<\/p>\n

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John Forbes Nash, 1951. Source: Wikimedia<\/a>.<\/figcaption><\/figure>\n

The Nobel laureate\u2019s idea became a mathematical description of a stable balance of interests and a cornerstone of modern decision theory.<\/p>\n<\/div>\n

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What is Bayesian equilibrium?<\/h2>\n

In 1967\u20131968 John Charles Harsanyi, in a series of papers<\/a>, introduced equilibrium under incomplete information. He drew on Thomas Bayes\u2019s formula<\/a>, formulated two centuries earlier.<\/p>\n

Bayesian equilibrium applies when information is incomplete\u2014players do not know one another\u2019s strategies. It has practical use in DeFi<\/a> protocols. In 2023 a group at Columbia University (New York) published \u201cA Myersonian Framework for Optimal Liquidity Provision in Automated Market Makers<\/a>\u201d.<\/p>\n

The authors present a model explaining how participants with different levels of market knowledge can rationally provide liquidity to DeFi pools<\/a> to balance risk, fees and rewards.<\/p>\n

It is built using Bayesian analysis: each liquidity provider chooses a strategy based on probabilistic beliefs about others\u2019 behaviour and the state of the market.<\/p>\n<\/div>\n

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What is an evolutionarily stable strategy?<\/h2>\n

In 1973 John Maynard Smith and George Price described a strategy that cannot be displaced by an alternative once adopted by a majority. Their paper \u201cThe logic of animal conflict<\/a>\u201d brought game theory into biology and the behavioural sciences.<\/p>\n

Smith\u2019s classic \u201cHawks and doves\u201d game shows that aggressors gain only up to a point. As the population of predators rises, conflicts make the strategy unprofitable.<\/p>\n

There are two types of players: hawks (aggressive) and doves (peaceful). They compete for a scarce resource (food or territory, for instance).<\/p>\n

Players follow two strategies:<\/p>\n