Game theory 1 [Bashi Game], Game Theory

Source: Internet
Author: User

Game theory 1 [Bashi Game], Game Theory

First, this is basically a series of articles about ACM game theory.

Today, let's talk about the simplest game-bashgame.

Its game rules are as follows:

There are a pile of n stones, two smart people to play, each person can go to 1 ~ M stones, the last stone wins.

For example, n = 7, m = 3

The procedure is as follows,

Take 3 first, then I first, and 4-I first, so that the first hand gets the last stone. (3 + I + 4-i = 7, so 4-i contains the last one ).

In fact, the idea is very simple.

When n % (m + 1) = 0, the first hand will lose, otherwise the first hand will win.


When n % (m + 1) = 0, the first hand gets I, the latter hand goes to m + 1-i (this is legal, because the first hand cannot finish, but take at least 1), so that a round can generate m + 1, and n % (m + 1) = 0, so n/(m + 1) round, the latter can get the last one.

When n % (m + 1) = k, k> 0, then go to k first, then the stone returns to n % (m + 1) = 0, in the previous case, the first hand and the latter hand exchange the order of acquisition (that is, in the case of n % (m + 1) = 0, the first hand gets the first hand), and the first hand wins.

The problem arises.


Http:// Pid = 1, 1846


HDU2188 (or bare question)

Http:// Pid = 1, 2188


HDU2897 (Bashi game deformation)

Http:// Pid = 1, 2897


POJ2368 (Bashi game deformation)

Http:// Id = 2368


A question about economics Game Theory

I remember this is a game problem in western economics. It is about monopoly market pricing. A and B both companies make decisions at the same time, which means that the two sides do not consider the decision of the other party. For example, if the market capacity of both companies is 100, the two companies consider their own market capacity as 100 when making decisions, the influence of the other party is not considered. Successive decision-making means that the oligarchy takes the lead in decision-making, and then the other party makes a decision on the basis of the first decision-making, and then the first party makes a decision on the basis of the second party's decision-making, in this way, after several cycles, the final result is that both parties share one. This tells us the truth: "in an economic and social context, we must take into account the response of the other party when making decisions, and assume that the other party is as smart and diligent as you are.

Terms of Game Theory

I have recently been watching game theory. You should understand the basic concepts of participants, utility functions and payments, actions, information, public knowledge, and strategies. Of course, there are many kinds of Nash equilibrium you mentioned, but they are all based on the principles of the Nash equilibrium, such as multiple Nash equilibrium, subgame refined Nash equilibrium and reverse induction, and refined Bayesian Nash equilibrium. Games are generally divided into several types: full information static/Dynamic Games, and incomplete information static/Dynamic Games. You can refer to some game theory books. In case of any errors, please kindly advise.

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