# Game Theory

### What is Game Theory?

> Game theory is the study of [mathematical models](https://en.wikipedia.org/wiki/Mathematical_model) of strategic interactions among [rational agents](https://en.wikipedia.org/wiki/Rational_agent). It has applications in many fields of [social science](https://en.wikipedia.org/wiki/Social_science), used extensively in economics as well as in [logic](https://en.wikipedia.org/wiki/Logic), [systems science](https://en.wikipedia.org/wiki/Systems_science) and [computer science](https://en.wikipedia.org/wiki/Computer_science). Traditional game theory addressed two-person [zero-sum games](https://en.wikipedia.org/wiki/Zero-sum_game), in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 21st century, game theory applies to a wider range of [behavioral relations](https://en.wikipedia.org/wiki/Human_behavior), and it is now an [umbrella term](https://en.wikipedia.org/wiki/Umbrella_term) for the [science](https://en.wikipedia.org/wiki/Science) of rational [decision making](https://en.wikipedia.org/wiki/Decision-making) in humans, animals, as well as computers.

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Game theory in depth
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### How to solve the problem?

Consensus:

* Mechanism to ensure that all parties agree that a certain state of the system is correct
* The Truth (verifiable)
* Consensus mechanisms are based on game theory

> A Byzantine fault (also Byzantine generals problem, interactive consistency, source congruency, error avalanche, Byzantine agreement problem, and Byzantine failure) is a condition of a computer system, particularly [distributed computing](https://en.wikipedia.org/wiki/Distributed_computing) systems, where components may fail and there is imperfect information on whether a component has failed. The term takes its name from an [allegory](https://en.wikipedia.org/wiki/Allegory), the "Byzantine generals problem", developed to describe a situation in which, to avoid catastrophic failure of the system, the system's actors must agree on a concerted strategy, but some of these actors are unreliable.

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Byzantine General Problem Described
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### Properties of Proof of Work (PoW)

Proof of Work is the consensus algorithm intended to provide incentives for responsible behavior for blockchain transactions.

* Concept by Cynthia Dwork and Moni Naor in 1992 in the paper "Pricing Via Processing, Or, Combatting Junk Mail, Advances in Cryptology"
* Named by Markus Jakobsson and Ari Juels in 1999 in the paper: "Proofs of Work and Bread Pudding Protocols"

#### Mining

* PoW ensures that participants in the network agree on the state of the ledger (i.e. the order and validity of the transactions) through a process that involves solving complex cryptographic puzzles
* "Miners" do mathematical calculations on their computers to verify that the transactions are valid.
* Mining comes from trial and error of finding a Nonce (random number) that satisfies the degree of difficulty of the network
* Difficulty ensures that the process of adding new blocks to the blockchain requires a significant amount of computational work. This makes it economically infeasible for malicious actors to manipulate the blockchain

#### Asymmetry

* Requires a significant amount of computational effort to solve a puzzle or perform a certain task
* Verifying that the work has been done in a relatively simple and quick manner.

### Properties of Proof of Stake (PoS)

Proof of Stake provides an alternative to PoW in the application of consensus algorithms and the security of the blockchain.

* Known as proof of participation
* To participate in the validation, the amount of coins that the validator has is used, instead of the computational power
* The validator must place his deposited coins in a kind of safe to "prove" his participation, without moving the coins
* The more coins you have, the greater the chance of validating transactions and earning from them
* In terms of energy, it is more economical than PoW
* It should bring more security and decentralization, but it makes larger coin holders more likely to get more coins.

### Properties of Proof of Authority (PoA)

Proof of Authority provides another alternative to PoW/PoS systems. It is a consensus algorithm suitable for private and permissioned blockchain which relies on a number of pre-chosen authoritative nodes called the validators. (Singh et al., 2020a)

* Used in permissioned Blockchains
* Group of AUTHORITIES. These Authorities are the Validators check whether new transactions align with the network’s rules and ensure that the sender has adequate funds to complete the transaction
* Specific Nodes are defined and authorized to create new blocks in a chain. It needs approval from most of the nodes for the block to be created
* Used in private Ethereum networks and others