Manhattan Reborn 1978

new York.

night~

Manhattan, in front of the Blue Crystal Hotel.

Lilith, who had just returned from a banquet, glanced casually at both sides when she got out of the car and inadvertently discovered a familiar-looking car parked not far away.

She stopped and looked into the distance, and soon confirmed that she was not mistaken, and walked slowly towards it with curiosity in her heart.

But when she took a few steps out, the door of the car was opened by someone inside.

"Mike.. Polly?"

"Why are you in the car and not inside?"

Polly Sidrich closed the car door casually, shook her head with a tired look on her face, walked quickly to Lilith and explained with a smile.

"I just got back from work and wanted to sit in the car and wait for David to finish his work before going back with him."

"Isn't he... coming to see the instructor?"

"It's so late, Professor Bartlet should have gone to bed, right?" Lilith looked down at her watch and found that it was almost half past ten. She asked in surprise.

"I don't know either..." Polly held Lilith's arm and chuckled.

"Well... I just happen to want to visit Bartlett, so don't wait here, let's go together."

"Yeah." Polly nodded with a smile. The fatigue on her face seemed to be relieved by the smile.

Black Mike stood beside the car and saw the two women walk into the hotel side by side. He tilted his head and thought for a moment, then locked the car and followed them in.

. . .

On the top floor of the hotel, in Giles' room.

David asked with a surprised smile when he saw Lilith and Polly appearing outside the door together.

"I was just complaining to everyone, asking why God didn't send an angel to help me ~ I didn't expect you to show up right away!"

"Hehe~" Lilith walked up to David with a smile, gave him a quiet look, handed Polly beside her to him, turned and walked towards Professor Bartlet who was resting on the sofa, and greeted him with concern.

Pine, Giles, Bloomer, Carnes and Professor John Nash all know the complicated relationship between David, Polly and Lilith.

So they all tacitly continued to stare at the huge logical chain on the ground that David had constructed using various game theories.

Polly took David's arm and leaned against the wall with him, silently observing the people behaving differently in the living room, and asked in a low voice.

"Is Professor Nash here too?"

"You asked him to come here because you have some math problem that you want his help with?"

"Yes."

David took out a bottle of Coke from the ice bucket beside him, opened it, took a few gulps, and sighed while burping.

"This time my head is really empty, there's nothing left!"

"Empty?" Polly looked at everyone's feet curiously and found the ground was covered with papers with handwriting and mathematical formulas.

"Are we disturbing you?"

"No~ It's almost over." David tilted his head back and drank the Coke in his hand. After feeling a little refreshed, he pulled Polly to his mentor, Professor Bartlet, let her sit down steadily, turned his head and looked at the few people and said.

"It's getting late, let me help everyone summarize."

"OK~" Everyone nodded readily and gathered around Professor Bartlet.

David took the initiative to walk over and rearranged the papers on the ground according to his own ideas while speaking.

“Game theory is not only a new branch of modern mathematics, but also an important discipline in operations research or strategy.”

"In 1928, John von Neumann proved the basic principles of game theory, thus announcing the official birth of game theory."

"In 1944, von Neumann and Morgenstern co-authored the epoch-making masterpiece Theory of Games and Economic Behavior, which extended the two-person game to the n-person game structure and systematically applied game theory to the economic field, thus laying the foundation and theoretical system of this discipline."

"In 1950-1951, Professor John F. Nash used the fixed point theorem to prove the existence of game equilibrium points in his seminal papers, such as "Equilibrium of N-Person Games" and "Non-Cooperative Games", laying a solid foundation for the generalization of game theory and giving the concept of Nash equilibrium and the equilibrium existence theorem."

"In addition, Professor Reinhard Selten, based on his research in game theory and its applications and experimental economics, introduced the concept of Nash equilibrium into dynamic analysis and established the subgame perfect Nash equilibrium theory."

"This study is the first to improve the Nash equilibrium and select a more convincing equilibrium point."

"Then, Professor John C. Harsanyi added a random variable to the game based on the Bayesian game analysis method to complete the Harsanyi transformation, and then used the probability theory method to maximize the expected benefits of the game participants."

"His greatest contribution to game theory is his historic breakthrough in the study of incomplete information problems."

"Because this game situation of incomplete information will reduce the ever-changing incomplete information to the subjective judgment of the players on others."

“The traditional interpretation of the concept of mixed strategies is that the players apply a random method to determine the pure strategy to be chosen.”

"This explanation is unsatisfactory both theoretically and practically, and Harsanyi proposed a more precise explanation."

"He showed that every real gaming situation is subject to some tiny random fluctuations."

"In a standard game model, these effects appear as small independent continuous random variables, one for each strategy of each player."

“The specific values ​​of these random variables are known only to the relevant players, and this knowledge becomes private information.”

"The joint distribution is the shared information of the players. This is called a variable payoff game."

"The Harsanyi transformation successfully transforms incomplete information that is difficult to model into mathematically tractable incomplete information, that is, players can make subjective judgments about the size of the probability based on their experience and knowledge of the opponent's type, which is a mathematical prior distribution."

“This explanation is a conceptual innovation of great significance and is a cornerstone of Professor Harsanyi’s Bayesian approach to game theory.”

By this time, David had basically completed the rearrangement of the entire "logic map".

He walked to the window with his hands in his pockets, pointed at the ground and spoke as loudly as he could.

“The general view in academia before the 1960s was that cooperative theory was more important than non-cooperative theory.”

“Because cooperation is profitable, why would people give it up?”

"Professor Harsanyi was one of the game theory researchers who helped to bring about this change in thinking, recognizing the need to model cooperative opportunities in the form of non-cooperative games."

"From this point of view, cooperation theory can be regarded as a simplified form, and a non-cooperative model with more details needs to be established, which provides a methodological breakthrough in the construction of non-cooperative models."

"In 1973, British evolutionary biologists John Maynard Smith and Professor George Preuss published an article titled "The Logic of Animal Conflict" in the famous journal Nature."

"They were the first to introduce the analytical methods of game theory into the competitive behavior and selection problems in the process of biological evolution, abandoning the assumption of complete rationality and taking Darwin's theory of biological evolution and Lamarck's genetic theory as their ideological foundation."

“From the perspective of systems theory, the adjustment process of group behavior is viewed as a dynamic system.”

"This dynamic system is simultaneously relative, in which the behavior of each individual and its relationship with the group are individually characterized. The formation mechanism from individual behavior to group behavior and the various factors involved can be incorporated into the evolutionary game model to form a macro model with a micro foundation."

(Note: The relativity of simultaneity means that two events occurring in different locations appear to be simultaneous in one inertial system, but not simultaneous in another inertial system.)

"Therefore, it can more truly reflect the diversity and complexity of behavioral subjects and provide a theoretical basis for macro-control of group behavior."

David looked up at his mentor, Professor Bartlett, and spread out his left hand with a helpless smile, saying, "I asked someone to find Professor John Maynard Smith's contact information and left him a message to ask him some questions."

"But he didn't call me back. He just told me that he was busy organizing his research results and preparing to publish a new book called Evolution and the Theory of Games."

"So, I can only temporarily refer to all of his research as Evolutionary Game Theory."

"Yeah." Professor Bartlet frowned and looked at the ground, then nodded in response.

David let out a long sigh and continued.

"Based on my understanding of game theory and evolutionary game theory, the model of evolutionary game theory probably has several characteristics~"

“First, we take the participating groups as the research object, analyze the dynamic evolution process, and explain why and how the groups reach this state.”

“Second, population evolution involves both selection and mutation processes.”

“Third, the behaviors selected by the group have a certain inertia.”

"From this we can see that the application of evolutionary game theory in the field of economics is different from the use of evolutionary game theory to explain biological evolution phenomena, and it is almost impossible to apply it in the field of economics."

"The concept of dynamic evolution is far more complex than the static concept!"

"But I agree more with the theory of evolutionary game that the Nash equilibrium can only be achieved after multiple games!"

"It requires a dynamic adjustment process, which is also a kind of path dependence."

“When there are multiple Nash equilibria, if a Nash equilibrium is bound to be adopted, there must be some mechanism that can lead to the emergence of an equilibrium that each player expects.”

"However, the concept of Nash equilibrium in game theory itself does not have such a mechanism."

“Therefore, when there are multiple Nash equilibria in a game, even if we assume that all players are completely rational, it is impossible to predict the outcome of the game. If the players are only of limited rationality, it is even more difficult to predict the outcome of the game.”

"In evolutionary game theory, the refinement of equilibrium is achieved through forward induction, that is, the participants choose their future behavioral strategies based on the history of the game, which is a dynamic selection and adjustment process."

"So, if we unify the static concepts and dynamic processes in evolutionary game theory, the trajectories starting from any small neighborhood of a certain equilibrium point of the dynamic system will eventually evolve toward the equilibrium point, and the equilibrium point is said to be locally asymptotically stable."

"Such a dynamic stable equilibrium point is the evolutionary equilibrium."

"If we combine Nash equilibrium, eye-stable strategy and evolutionary equilibrium and study the relationship between them, we can find ~"

“Every Nash equilibrium is actually the equilibrium point of a dynamic system.”

"Evolutionary equilibrium must be Nash equilibrium!"

“An evolutionarily stable strategy is not necessarily an evolutionarily balanced one.”

“So the most useful and widely used equilibrium concept in evolutionary game theory is not evolutionary stable strategies, but evolutionary equilibrium.”

"Because the assumption that the behavior of game players changes over time in a certain dynamic way is more realistic and reasonable."

After David finished speaking, he gently rubbed his sore temples with his hands and took a deep breath.

“Game theory is also known as game theory, game theory, etc.”

“We can use it as a mathematical theory and method for studying phenomena that are of a fighting or competitive nature.”

"We can also apply it to reality, predict the behavior of a group of people, and formulate more optimized mixed game strategies based on their historical behavior or effective information, and accurately find the Nash equilibrium that maximizes our own interests."

"But the development trend of many things is not something we can predict or fully control in advance."

"So in order to protect our own interests in the investment game, we must plan out the options at each decision point before the dynamic game begins!"

“Even though this decision point may not come, we must prepare for it in advance!”

"For example, members of the Federal Reserve's Open Market Committee may now have major differences on whether to continue to implement the interest rate hike policy."

"If we classify them according to their past behavior and performance, they can be roughly divided into five groups~"

“Hard-line hawks who advocate continued rate hikes → Hawks who are relatively aggressive in supporting rate hikes → Centrists who have no clear position → Relatively conservative doves → Doves who believe that the market has full self-regulatory capabilities.”

"From the monetary policies released by the Fed in the past six months, the hawks who advocate continued interest rate hikes to curb domestic inflation have clearly gained the upper hand."

"But this is only temporary!"

"When inflation slowly declines due to the interest rate hike policy, a new economic cycle will restart."

"Okay, that's all for today..."

"Teacher, shall I take you back to rest first?"

"No need." Professor Bartlet stood up from the sofa, glanced at the people around him, and waved his hand.

"You guys should get some rest early, I can go back by myself."

"Ok!"

David, Giles and Bloomer followed Professor Bartlet and took him into the elevator.

Pine crossed his arms over his chest and stared at the ground with a frown, lost in thought.

Polly and Lilith came later, and they both felt that they didn't quite understand what David was talking about.

Only Professor John Nash, who has done in-depth research on game theory, discovered the most valuable points in David's summary.

Evolutionary equilibrium must be Nash equilibrium!

Every Nash equilibrium is actually the equilibrium point of a dynamic system.

Therefore, the most useful thing in evolutionary game theory is evolutionary equilibrium!

It can not only be used in the study of game theory, but also in the analysis of mutual games between people and groups!

"Huh~" Professor Nash turned his head to look at the door of the room, sighed with a smile, and smiled at Polly.

"David is a genius who is much smarter than me!"

"Oh, really?" Polly asked with a smile, covering her mouth with her hands in surprise.

"Yes!"

Professor Nash glanced at Lilith and Pine who were looking at him, raised his eyebrows and said teasingly.

"At least he is qualified enough to be my mentor in handling private social relationships."

"Hahaha~" Polly blinked quickly a few times and couldn't help covering her mouth and laughing.

Pine and Lilith also laughed out loud due to Polly's laughter.

And right next to them, where the four of them were not paying attention, Kanes was staring at the door of the room, muttering a few words silently.

David's performance tonight made him truly realize what a genius is! !