Mind Map Gallery Game Theory
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Game Theory
This is the mind map about the game theory, which talks about the basic concepts, the participants, and other important concepts, check details now!
Edited at 2020-09-18 06:45:41
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Game Theory
Basic Concepts
Basic assumption
Man is rational
Refers to the ability to reason, the purpose of choosing specific strategies is to maximize their own interests
Important conditions and basic content
At least two independent game participants
The players in the game have the possibility of strategy choice (that is, there is a strategy space)
Participants will get a certain payment under different combinations of strategies (usually represented by payment matrix)
For game participants, there is a game result
The game involves equilibrium, Nash equilibrium (all games have at least one Nash equilibrium point)
Types
Cooperative game
Participants reach an agreement or form an alliance, and the result is beneficial to both parties (such as the formation of a company)
Non-cooperative game
Participants did not reach a binding agreement (such as the prisoner’s dilemma)
Static game
Both sides of the game act at the same time or in a sequence but do not know each other
Dynamic game
Participants have a sequence of actions, and the latter can observe the first action before making a decision
Complete information game
All participants are fully aware of each other’s strategic space and payment under each combination (such as Prisoner’s Dilemma)
Incomplete information game
Asymmetric information between participants
Several typical games
Prisoner game
As long as China does not change the current system of test-oriented education, no matter any advocacy for stress reduction and burden reduction, it is the best choice for candidates to increase their burdens.
Cockfighting game
Such as the Cuban Missile Crisis, the United States and the Soviet Union will not give in
Riding a tiger
The US-Soviet arms race, both sides continue to invest, similar to sunk costs
Zero-sum game
It is a non-cooperative game, which means that the gains of one party of the game must lead to the losses of the other party, and the sum of the gains and losses of both parties is zero. As follows
Coordination game
There are multiple equilibrium points, through a certain agreement or belief to coordinate the actions of the participants, so that neither party has the idea of changing the action and the encouragement mechanism, so that a certain equilibrium point can be realized
Coordinated attack problem
Due to the low timeliness and reliability of intelligence personnel, the parties to the cooperation cannot form public knowledge to attack the enemy at the same time
Public knowledge
Definition
1 and 2 know proposition a, 1 knows 2 knows proposition a, 2 knows 1 knows proposition a, 1 knows 2 knows 1 knows proposition a...that is, 1 and 2 have common knowledge about proposition a.
Basics
The proposition that people believe is true
People should be familiar with or understand this proposition
People have to believe what he knows
Participants are rational people
Note: Public knowledge is relative to a certain group. For example, public knowledge among scientists is not necessarily public knowledge of ordinary people.
Does Game Theory Fairness Exist?
Voting game
In fact, it is to "wear a hat" on candidates, that is, the process of giving individual social attributes to the society
Voting paradox
In the distribution of the results of democratic voting, A>B, B>C does not necessarily lead to A>C, so democratic voting may not necessarily reflect the overall social preferences of the group. Such as Trump was elected President of the United States.
Bankongfu Power Index
The power of each decision maker in decision-making is embodied in the number of times it can appear in the winning alliance as a "key joiner. The more the number, the greater the power. This number of occurrences is generally called the "power index."
Sharpe value
Label
Speech game
Claimed strategic decision
E.g. diplomatic language
Real strategic decision
Action
Arrow's Impossibility Theorem
That is, no social preference function can be found, which can reflect the social preferences of all groups
Three prerequisites need to be met: 1. Preference type suitable for everyone; 2. Non-authoritarian society; 3. Pareto principle, that is, if everyone prefers A>B, the social preference is also the same. 4 Individuals' preference for A>B remains unchanged. , Then the social preference of A>B remains unchanged
Injustice leads to revolution
When the polarization of social wealth is extremely serious and people's preferences are not expressed, most people demand the redistribution of social wealth, and revolutionary opportunities will occur. This is actually an extreme way of voting
On the Tragedy of Collective Action
Harding tragedy (tragedy of public resources)
For example, all herders in a pasture want to raise more cattle to make money, even if the unit income of cattle decreases because of the decline in the amount of grass. Eventually, the grass could not be loaded, and all the cattle starved to death.
Countermeasure
Country (rules)
Through centralization to form a coercive authority (such as the state) or formulate effective rules, the disadvantage is that the cost is too high, and it is difficult to centralize the development of backward areas
Moral
Through the combination of moral and decentralized rewards and punishments, the disadvantage is that it is not mandatory, and it fails when the benefits of unethical behavior are higher than the sense of accomplishment brought by ethics.
Future, Past
The future of collective action cannot be predicted in principle, because you don't know what you know in the future, and you don't know how much the things you know in the future will affect the future. At the same time, the past of collective action cannot be changed, because it is impossible for one thing to happen and not to happen, and it is impossible for a person to exist and not to exist. All, crossing does not exist in principle. The so-called prediction is only the possibility of developing in a certain direction in the future under certain conditions.
Important Methods
Deduction
One of the most common methods of logic
Induction
Game theory is commonly used, but has many disadvantages
Backward method (reverse induction method)
When the opponent participant makes a decision, he can accurately predict the opponent's behavior through the analysis of the final stage, thereby confirming his own behavior (similar to mathematical inversion)
Other Important Concepts and Real Games
Auman theorem
If two people have the same pre-existing knowledge, and their post-examination knowledge of an event is public knowledge, then these post-examination knowledge are equal. Speaking of people means rational people who have different views on a thing at the beginning. Their views will be convenient under different information states. If the changed views are public knowledge, then their views should be consistent. For example, when investors have fully communicated that the information of all parties is exactly the same, under the same public knowledge, different rational people should get the same point of view
Edge strategy
Creating risks for opponents, bringing them to the brink of disaster, and forcing them to yield (as the US military did in the Cuban missile crisis) can sometimes act on oneself, such as Xiang Yu.
Mixed strategy
Refers to randomly choosing different actions based on predetermined probabilities. If the king of Rutian Ji horse race chooses a horse at random to go out, his chances of winning can be increased
Limitations of Inductive Learning
Too rude, if you can't think that a person will always be a bad person because he has done bad things. 2 It is useful when the summarized content is true and it has not become the public knowledge of everyone, but it becomes useless after becoming Everyone can increase their own income when they find that a certain kind of fertilizer can increase the yield. When everyone knows it, it will be useless.
Bar problem
No one can predict the number of people going to the bar with any method, because it is a chaotic phenomenon and unpredictable
Minority game
That is, if the group becomes a minority, the benefit is greater. For example, investors are predicting the ideas of other investors, trying to become a minority of people who make money
Auction game
British auction (second-price auction, more common)
Multiple bidders start to increase the price of the item in turn at a certain minimum bid price, and each time at least one minimum increase amount is added, and the highest bidder gets the item. However, the final price must be paid at a price higher than the final price by a minimum mark-up amount. This is conducive to honest bidding
First price sealed auction
Bidders write their own prices on paper, seal them and give them to the auction house, and the highest bidder pays at the written price and gets the item. Engineering bidding is this variant
Equilibrium point of n-person game